There seems to be a lot of misunderstanding around the issue of the gravito-thermal effect as it appears in the work of scientists such as Hans Jelbring, and Nikolov & Zeller. Without trying to recapitulate their theories in detail, I thought it might be worth going through a few basics in order to dispel some of the fog some people seem to be surrounded by. I’ve thought about a few different ways of doing this, and settled on the style of a Platonic dialogue to give it some continuity, rather than a set of disconnected facts, like you might get in a Q&A, or FAQ. Some people might think I’ve got some stuff oversimplified or just plain wrong. Feel free to offer alternatives in comments below. H/T kdk33 for improved phrasing in the Glickstein section.
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So these guys think most or all of the extra warmth there is at the surface of planets with atmospheres compared to those without is due to gravity? Are they serious?
Deadly serious. This is a real scientific theory.
But how can gravity cause heating of anything? It just pulls stuff together – right?
Right, but it’s what happens to the stuff that gets pulled due to other physical laws which come into play that causes the heating, not gravity itself.
But that means work has to be done by gravity to get anything else to happen doesn’t it? Otherwise it’s a perpetual motion machine.
In classical mechanics terms, gravity is not a type of energy, but a force. It is constantly applied by masses on other masses. It is an intrinsic property of mass, not an energy state which can ‘get used up’. In terms of relativity theory, it is a property that mass has which causes the warping of space-time around the mass, which causes other masses to fall towards its ‘gravity well’.
Ok, but how does ‘force’ make things like heating happen? Heating needs energy doesn’t it?
At the microscopic level, heat arises because all matter which is at a temperature above absolute zero vibrates and moves around, knocking into other bits of matter. The energy of collisions makes the atoms and molecules vibrate and the rate they vibrate at determines their temperature. The gravitational force can cause matter to fall, gather momentum and bash into something else. As the mass falls towards another mass it is gravitationally attracted to, the gravitational potential energy it has by virtue of its altitude from the other mass diminishes, and the momentum, which is a product of its mass and velocity increases. When it hits another mass on the way down, some of that energy of momentum gets turned into heat because the collision makes the molecules vibrate more.
But you said gravity isn’t energy. Now you are saying the mass turns gravitational potential energy into heat. What’s going on?
Although gravity itself isn’t an energy, by virtue of its action as a force, it causes mass which is not at rest at the centre of gravity to have the potential to accelerate towards that centre of mass. That’s why we talk about mass having ‘gravitational potential energy’. The higher above the centre of gravity a mass is, the more of its total energy is locked up as gravitational potential energy. This means less of the total energy is available to be thermalised as heat in collisions.
So is that why its cold at high altitude and warm near the surface? Ira Glickstein said it only works once, when the air is first pulled down and compresses, then the heat dissipates back to being the same temperature everywhere again.
That’s one way of looking at it, from the point of view of the classical mechanics of the microscopic scale. Ira is right in one sense, but wrong in another. Although initial heating caused by sudden compression dissipates, the ongoing action of gravity as a force keeps the air compressed more near the surface. This means air is denser at low altitudes, and that means more molecules are having collisions more often, thermalising energy.
But energy must be conserved to satisfy the first law of thermodynamics mustn’t it? Where does the extra energy come from?
There is no extra energy, it is equally spread through the troposphere. If the whole of the troposphere was the same temperature as the surface it wouldn’t make it warmer. But gravity causes there to be a temperature gradient from cold high up, because more of the total energy is locked away as gravitational potential energy compared to warm at the bottom where the near surface air is hotter than the average because less of the total energy is locked away. Again, total energy remains equally distributed throughout the troposphere, as the second law of thermodynamics demands, but because of the difference in gravitational potential energy between molecules at the bottom and top, there is a thermal gradient.
But that’s just the classical mechanics way of looking at it. What’s really happening physically? There’s convection to consider too.
Yes, the throughput of solar energy coming in, being absorbed and turned into other kinds of energy and causing processes like convection complicates the picture. All of our ways of looking at things are just our conceptions of reality, not reality itself. Whether our conceptions are right or not is tested by making predictions and seeing if reality does what we expect it to according to theory. A good start is to see if the ideas all fit together logically and without internal contradictions or paradoxes. If that test is passed, it’s experiment time.
OK, but how do we perform an experiment on the whole troposphere? It’s a messy place with all sorts of different energies and processes like convection going on in it.
Good point, that’s why the science isn’t settled. But we can perform gedanken experiments to see if they can shed any light on how stuff really works. That’s a kind of thought experiment where we simplify things and test our ideas in a framework which limits the complexity of the real world. A relevant example here is the ‘model planet’ used in the theory written by Hans Jelbring. That one is properly defined and conceived in such a way as the result can be accurately computed. Rather than looking at the microscopic level that theory deals with bigger ensembles of molecules of a billion or so. That way, it can consider other processes like convection which happen in the real troposphere.
But that theory doesn’t have any Sun and it doesn’t permit radiation to space. How can that be any use for understanding reality? And why do they talk about pressure?
It doesn’t need those in order to reach a conclusion regarding the way gravity affects the surface temperature of any planet, whether or not it’s close to a sun. The pressure in the troposphere varies being lower at the top and higher at the bottom because of all the extra weight of the rest of the atmosphere being piled on top of it, being pulled down by gravity. That means the air is denser at the bottom too, so there are more collisions happening and more energy is thermalised as heat. Stick around, and if we’re lucky, Hans himself will take up the challenge of explaining his theory and how it relates to the real world in terms anyone can understand.
Tallbloke's Talkshop 
Please replace “atmosphere” with “troposphere”. It is a very important distinction to make.
As for gravito-thermal effects, once again Jupiter is the best example.
http://www.universetoday.com/15097/temperature-of-jupiter/
I do not know how many experiments can be done with our atmosphere, but I know even less how many more planetary atmospheres behaving the same way are needed before people accept the fact that gravity means a temperature gradient in every troposphere.
Ok, willdo. Thanks Maurizio. Does it seem ok to you otherwise?
Nice!
Am I right in thinking that what N & Z and Hans Jelbring describe is a different, additional way of looking at atmospheric processes involved in warming, rather than an either-or, excluding all other, previous ways?
Thanks CM. So far as I can see, they both think that whatever GHG’s might do to surface temperature, gravity is doing a lot more.
In fact, the adiabat (lapse) rate on Earth and Venus is not very much different, even if the atmospheres couldn’t be more dissimilar.
Some still-relevant thoughts on this: http://omniclimate.wordpress.com/2008/03/02/venus-warming-revisited/
Where does the extra energy come from?
Not everyone agrees with Miles Mathis
But his approach resolves a lot of the BS that is peddled as settled science.
In view of observations, I am inclined to believe that the surface temperature is indeed determined essentially by surface atmospheric pressure and top-of-atmosphere insolation. However, I don’t believe that this result would prevail in the complete and total absence of greenhouse gases, as I understand Hans Jelbring to be contending.
I hasten to add that to me tallbloke seems to believe that Jelbring actually assumes some minimum amount of greenhouse gas, that according to Jelbring the irrelevance of greenhouse-gas concentration prevails only beyond some level the earth passed a long time ago.
If my understanding of Hans’s theory is correct, though, it is based on the assumption, stated in his proof section, Section 2.2, that “The temperature lapse rate in our model atmosphere also has to be –g/cp, since its atmosphere is organized adiabatically.” Now, this “organized adiabatically” state is supposed to prevail in a hypothetical situation, set forth in his Section 1.1, in which no energy flows into or out of the atmosphere at any location: the atmosphere’s molecules can exchange energy only with each other. So that assumption appears to this layman to impose one of two alternative requirements. One alternative is that convection continues forever and thereby maintains the lapse rate despite the absence of any external energy source. The other alternative is that the atmosphere ultimately assumes a state in which there is no gross motion such as convection but that the maximum-entropy state of the atmosphere is one characterize by a temperature lapse rate of -g/cp.
The former alternative does not commend itself to my laymen’s intuition about the way things wind down. The latter alternative seems at odds with the conclusion stated in the Velasco et al. paper discussed in the Loschmidt thread. That paper admits that an isolated ideal-gas system in a gravitational field will indeed adopt a significant pressure lapse rate, but it concludes that the atmosphere’s temperature lapse rate, given by that paper’s Equation 8, will be although non-zero, negligible if my calculations (set forth in detail in the Loschmidt thread) are correct.
I am therefore of the opinion that either Jelbring is wrong on the theory–although possibly not on the result that prevails beyond a minimum greenhouse-gas content–or Velasco et al. are.
By the way, I have to say that I’ve taken the long way around the barn, but I did so because the penultimate sentence of Hans’s Section imposes the further assumption that the earth does not radiate. I take it that Willis Eschenbach’s failure to observe this constraint is part of the reason why he and tallbloke are arguing past each other. I leave to others to decide whether that constraint robs the hypothetical of any real-world relevance.
This is my latest effort over at WUWT:
1) Willis knows that his non GHG atmosphere will produce a dry adiabatic lapse rate with the warmest temperature at the surface.I am assuming some movement via convection to achieve it.
2) The warmth at the surface is NOT due to gravitational compression ( although a tiny fraction of it would be) but gravity IS responsible for placing the maximum density of non GHG molecules at the base of the atmospheric column.
3) That maximium density causes the greatest number of molecular collisions to occur just above, or in contact with, the surface.
4) Such collisions transfer energy between molecules by conduction and not radiation. The surface converts incoming solar shortwave radiative energy into kinetic energy and the non GHG gases in contact with or in close proximity to the surface retain that kinetic energy by exchanging the energy via conduction between themselves and between themselves and the surface until it can be released upward by the surface as outgoing longwave IR.
5) It is that delay that allows the surface temperature to rise as energy accumulates within the system and most particularly at or just above the surface.
6) The greater the density of the non GHG atmosphere, the more molecular collisions occur, the longer the delay and the higher the equilibrium temperature must become. The increased density does NOT slow down the rate of conduction. Instead it increases the proportion of radiation that is retained for longer within the system in the form of slower moving conduction leading to an average net reduction in energy flow through the system at any given level of input.
7) At equilibrium we now have solar shortwave hitting the surface at 240W/m2 and IR longwave leaving the surface at 240W/m2 but additionally we now have a backed up pool of kinetic energy bouncing between air molecules at the surface and between those molecules and the surface giving the necessary temperature boost at the surface.
Any flaws ?
Thanks for this post. The existence of FUNDAMENTAL uncertainty on such everyday matters as why the surface temperature is higher than temperatures at altitude is startling.
I’ve come to believe in what I call the Principle of Opposites: whatever you think is going on may be the opposite of what is really going on. Here, the application is that the premise – gravity has nothing to do with surface temperatures – should be also viewed as gravity has EVERYTHING to do with surface temperatures. Only when the opposite is shown to be impossible, not implausible, should the premise be accepted as “certain”.
This post-subject demonstrates that certainty is very difficult to achieve. A “working hypothesis” is what we really should call almost every theory-as-fact. But how could you raise money or political power with a “working hypothesis” in the CAGW game?
From human affairs to nuclear physics, it is all the same. Nothing settled, nothing certain.
I’m certain of that (or completely unconvinced: both hypotheses seem to account for my dilemma).
Well, if Stephen is correct then I way oversimplified my approach here. but these things take time, and I don’t mind this being a work in progress subject to group revision. So lets hear some more opinions and keep reformulating until we’re all happy. Could take a while. 😉
This is how I tell it, but then I am not qualified in anything anyway. 🙂
Take a volume of air at sea level and compare it to an identical VOLUME at say 7,000 metres. You will see that the lower volume has almost exactly twice the number of molecules as the upper. Now it is quite possible for ALL the molecules in both volumes to have the same kinetic energy level. Stick a thermometer in each and the lower will read a higher temperature. Why? Because the molecules in the lower sample are closer together and the molecular collision rate is higher.
Q.E.D.
Is Condition 7 in Stephen Wilde’s non-greenhouse-gas world one in which the area average of the product of emissivity, the Stefan-Boltzmann constant, and the fourth power of temperature exceeds the emitted 240 W/m^2? If not, does his theory rely on the non-greenhouse gases’ changing the emissivity from what it would be in their absence?
Actually, I trust that, despite his talk about collisions and such, Stephen Wilde does not intend to imply that, as Richard111 sees it, a denser gas packet will register a higher temperature than a less-dense gas packet if the two packets’ molecules have the same mean translational kinetic energy?
Joe, temperature is only part of the story. There’s heat capacity to consider I think.
Doug Proctor says: January 16, 2012 at 5:06 pm
The existence of FUNDAMENTAL uncertainty on such everyday matters as why the surface temperature is higher than temperatures at altitude is startling.
So many of these everyday matters seem to be glossed over with some very tacky explanations.
Here is one of my favourites 🙂
CONVECTION
The key point about convection is that it replies upon density differences:
Less dense [hotter] gas/liquid rises.
More dense [colder] gas/liquid falls.
The MASS of the gas/liquid does not change with temperature…
But its VOLUME does… it expands and contracts with temperature…
Hence the change in DENSITY.
Now the problem is: Why does the hot gas/liquid rise?
Or to put it another way:
How does the hot gas/liquid overcome the downward force of GRAVITY?
The MASS of the gas/liquid has not changed….
We are told GRAVITY doesn’t care about DENSITY…
[remember the feather and hammer experiment]
So what exactly is causing the hot air to rise?
That is why I find Miles Mathis very interesting: http://milesmathis.com/hot.html
When reading through some settled science topics you will find that CONVECTION is an important part of the settled science, for example:
a) Plate Tectonics relies upon convection in the Earth’s Mantle
b) Geomagnetism relies upon convection in the Earth to drive the Dynamo Theory
Now the important thing about convection is that it is driven by density… so always check that CONVECTION is really possible when it is cited.
So take another look at CONVECTION in the context of Plate Tectonics and the Dynamo Theory.
The interior of the Earth gets hotter as we move down from the crust… but CONVECTION is driven by DENSITY… As we move down from the crust the pressure increases… the Mantle becomes increasing compressed with depth and its density increases.
Therefore we do not have the right density conditions to support CONVECTION in the Mantle… the deeper, denser Mantle is already below the less dense upper Mantle… so NO CONVECTION… no driving force for Plate Tectonics… no driving force for the Dynamo Theory…
So beware… the invocation of CONVECTION in a theory is frequently bogus!
The same applies to the THE CORIOLIS EFFECT…it is not a force… but that is another story.
tallbloke:
“Joe, temperature is only part of the story. There’s heat capacity to consider I think.” Could you flesh that out a little? I’m not sure exactly what you’re responding to or how it’s relevant.
I understand that air has heat capacity and that a given volume of air contains more energy at a given temperature if its pressure is greater. But I can’t see how to use that fact in such a way as to answer either of the last two questions I posed or to decouple Hans Jelbring’s theory from the assumption that an isolated vertical gas column will tend toward a significant temperature lapse rate.
Any help you can provide will be welcome.
“Is Condition 7 in Stephen Wilde’s non-greenhouse-gas world one in which the area average of the product of emissivity, the Stefan-Boltzmann constant, and the fourth power of temperature exceeds the emitted 240 W/m^2? If not, does his theory rely on the non-greenhouse gases’ changing the emissivity from what it would be in their absence?”
Well it isn’t a theory. It is an attempt at a description of observations that tries to avoid offending the Laws of Physics. It is a work in progress and subject to amendment if I’ve got something wrong.
I see the non GHG world as demonstrating that one doesn’t need GHGs to obtain a warmer surface from more atmospheric mass. Non GHGs will do just fine in setting up a basic dry adiabatic lapse rate such as that which we see.
In that situation I think the surface does become warmer than one would expect from the basic S – B equation.
In order to maintain equilibrium the surface needs to become warm enough to provide enough outgoing IR from the surface to satisfy S – B as regards the radiative energy exchange AND to provide enough upward conduction to balance the downward conduction from the warmed base of the atmosphere.
It seems that that is necessary with no GHGs at all which is why I consider the gravity/pressure/density based ‘Greenhouse Effect’ to be far more significant than any similar such effect from GHGs.
Joe: Hans says in his paper that:
In an ideal gas atmosphere, the adiabatic temperature lapse rate has to be –g/cp
where cp is the heat capacity of the gas (ref 2 p. 49). Theoretical calculations are well
confirmed by observational evidence in the atmosphere of Earth. The adiabatic
temperature lapse rate on Earth is thus –9.81/1004 = –0.0098 K/m. As James R.
Holton concluded after deriving this result: “Hence, the dry adiabatic lapse rate is
approximately constant throughout the lower atmosphere.”
Follows as a logical consequence from his model.
I can’t fault it. Can you? If you can’t then you might agree with me that it is not an assumption that g/Cp will describe necessarily existing dry adiabatic lapse rate but a logical consequence following from an investigation of the model planet he posits.
Stephen Wilder:
“In [a situation in which conduction from the surface is causing conduction to a purely non-radiating atmosphere and thereby producing a temperature lapse rate] I think the surface does become warmer than one would expect from the basic S – B equation.” Here I replaced “that situation” in your response with what I understand you to mean by it. Note in particular that I’m assuming that by “non-GHG” atmosphere, you meant that the atmosphere need not radiate at all, even as a result of aerosols, etc.
An ambiguity may reside in what you mean when you say “warmer than one would expect from the S-B equation.” But I’ll assume you mean what I said above, which is that the area average of the product of emissivity, the Stefan-Boltzmann constant, and the fourth power of temperature exceeds the power the earth’s surface radiates away. I assume you don’t simply mean that the average temperature is greater than it would be in the absence of an atmosphere, a condition that does not require a departure from the Stefan-Boltzmann relationship.
There’s one more assumption I’m making about your description, namely, that the earth’s surface is radiating out (on average) as much as the sun is radiating in. I believe you stated that previously.
So here’s the power balance. Radiation totally balances: the amount the sun radiates in is the amount the earth’s surface radiates out, and no other radiators are involved. The surface is also conducting heat to the atmosphere, causing the lapse-rate-maintaining convection. And, since what comes up must come down, the air that comes down conducts heat to the surface, thereby canceling the conduction out. Radiation out equals radiation in, conduction out equals conduction in, energy is conserved, God’s in His heaven, etc.
Do I have it right so far?
If so, then the only physical-law violation I see is that the earth radiates less than the Stefan-Boltzmann relationship says it should. And I’m a retired lawyer, not a physicist, so I can’t tell you why Stefan-Boltzmann law has to be right and applicable in this case.
What I understand you to say, though, is that the departure from Stefan-Boltzmann is a consequence of the earth-surface temperature’s resulting to some extent from cooling by conduction, i.e., not exclusively from radiational warming. So let me ask you this: Since a light-bulb filament gets its heat by conduction rather than radiation, should its radiation, too, be less than the Stefan-Boltzmann relationship would otherwise require?
Is this one of the premiss?
Mass retains no more than it’s potential gravitational energy and it is it’s density in a gravitational field that regulates it’s thermometric properties of convection and conduction.
“Since a light-bulb filament gets its heat by conduction rather than radiation, should its radiation, too, be less than the Stefan-Boltzmann relationship would otherwise require?”
No, because a light bulb behaves more like a GHG in being fully capable of radiating energy away.The model I proposed is not capable of radiation from a non GHG atmosphere such as Nitrogen.
My sole purpose was to show that one does not necessarily need GHGS to produce warming at the surface of a planet as a result of atmospheric density rather than atmospheric composition.
tallbloke:
Yes, I can fault Hans Jelbring’s conclusion that a temperature lapse rate is a logical conclusion of his model, which is an ideal-gas atmosphere disposed in a uniform gravitational field, with no energy entering or leaving the atmosphere, and left that way for an infinite amount of time.
I fault it because, with no energy entering or leaving the atmosphere, there’s nothing to drive convection, which is part of the conventional explanation of the lapse rate. Absent convection, the laws of probability gradually drive the atmosphere to the state of maximum entropy, which, if Velasco et al. (Equation 8) are correct, is one in which the temperature lapse rate would be negligible in an atmosphere of the pressure we’re talking about.
Hans has told me that the maximum-entropy state is instead the one in which the temperature lapse rate is the dry adiabatic lapse rate. But, except for starting with a continuous phase space rather than a quantized one, Roman et al., on which Velasco et al. is based, begins about as close to first principles as you can get. So, if Hans would have us accept his version of what the maximum-entropy state is, he should explain with specificity where Velasco et al. or Roman et al. is wrong–or, more likely, show where I understood them incorrectly.
So far he has not done so.
Tallbloke,
In order to understand what is occurring, you first have to understand the cause of the atmospheric lapse rate. This has been explained often and well, including on wiki: http://en.wikipedia.org/wiki/Lapse_rate Please read that before proceeding. Hans Jelbring, and Nikolov & Zeller make a basic mistake of confusing the adiabatic lapse rate as having an absolute temperature level. It does not, it is a GRADIENT. An atmosphere with out greenhouse gases (I am neglecting aerosols here) will have a surface temperature controlled by absorbed surface radiation and outgoing radiation from the surface. An atmosphere of any single atom molecule gas such as Argon or Helium will not absorb or radiate in the temperature range on a planet, and thus not change the average surface temperature by radiation.
Two atom gases such as O2 and N2 will only absorb and radiate at very short wavelengths such as UV. However, at reasonable planet temperatures, UV is not significant, so even though they absorb a small amount of incoming sunlight, they will not radiate out, so would not have any significant effect on surface temperature. However, three and more atom gases will absorb and radiate at wavelengths in the range of planet temperatures found on Earth and most other planets with atmospheres, and even small concentrations can have a significant average warming effect.
Solar energy is the source of energy input to the Earth surface and atmosphere (with a very small added effect from underground radiation heating of the Earth, but this is ignored here). When sunlight is absorbed on the Earth, this short wave radiation heats the Earth (oceans, ground and atmosphere). The warmed Earth radiates nearly as a black body at longer wavelengths. If the temperature average is long term constant, the average outgoing (to space) long wave thermal radiation energy has to match the absorbed solar incoming energy. If the temperature is (on long term average) increasing or decreasing, there has to be storage or release from water, ground, and atmosphere, but the levels of this long term unbalance (if any) is presently and generally significantly smaller than the atmospheric greenhouse effects for the cases examined here, so will be ignored in the present write-up.
Most of the energy from the warmed Earth is not transported directly from the ground and oceans to space by radiation. This is where the atmospheric greenhouse effect comes in. Since the Earth’s atmosphere does contain absorbing (and radiating) gases at the thermal optical wavelengths, there is considerable absorption and re-radiation throughout the atmosphere. In addition, atmospheric convective heat transfer from ground level and convective transport of evaporated water carry most of this energy from the ground up to the higher atmosphere, and condensing water vapor also releases the latent heat of the water vapor also at higher altitudes. The presence of the absorbing gases (and aerosols and water droplets) reduces the net direct surface radiation heat transfer rate out over the no greenhouse case. The absorption by and radiation from these gases and particles, combined with atmospheric convection, carry the absorbed solar energy (from the surface and directly absorbed by the atmosphere) to a range of altitudes where radiation to space finely occurs. The net average outgoing radiation to space has to match the net absorbed solar radiation if average surface temperature is not changing much.
If the average of the locations of outgoing radiation to space is used as a reference single location for black body radiation to space (from the IR emitting molecules plus aerosols and clouds), the S-B relation can determine an effective temperature for this average effective altitude, and this effective temperature has to be the same as the average surface temperature (neglecting the local latitude and day/night variation in a simplified analysis) for the case of no greenhouse gas, but with the surface albedo the same. We thus raised the altitude of the location of the S-B evaluated temperature with greenhouse gases present. We now go back to the adiabatic lapse rate, which is a GRADIENT, not a level of temperature. By forcing the value of temperature on a single level of the atmosphere, and using the adiabatic lapse rate to calculate the ground temperature, we have found the cause of increased ground temperature above the no greenhouse case. The increase is the adiabatic lapse rate times the increased elevation of outgoing radiation. That is all there is to the process.
Stephen Wilde says:
January 16, 2012 at 4:57 pm
Stephen,
No major faults that I can see. Your description works well with the results I obtained through empirical experiment. I used identical clear containers with a black interior target surface, one with a higher internal air pressure. When both containers were exposed to full sunlight the internal air temperature of the higher pressure container was consistently higher than the lower pressure container. This was measurable even with the low pressure differential achievable with a fish tank air pump.
In a situation where non-radiating gases such as nitrogen and oxygen can convect away from the surface, it is possible for the gases to have a higher Tav than the surface that heated them. If it were not for atmospheric circulation and a diurnal cycle, the Tav of the gases in our atmosphere could rise to match the Tmax of the hottest point on the surface.
When a physical (non radiative) greenhouse effect such as this exists the role traditional GHGs should be re-considered. Up to a certain percentage of the atmosphere CO2 may provide a slight radiative greenhouse effect. (very slight over the oceans). However at higher percentages it may act as a net coolant, radiating far more energy obtained through conduction with the surface and atmosphere to space than it has received as LWIR from the surface.
“Stephen Wilde says:
January 16, 2012 at 9:08 pm
My sole purpose was to show that one does not necessarily need GHGS to produce warming at the surface of a planet as a result of atmospheric density rather than atmospheric composition.”
Lets talk changes. Changing the atmospheric composition will change the emission rate of excess potential gravitational energy because of changes to the atmospheric density, and is measurable.
Changing the atmospheric composition will only increase potential gravitational energy of its particles, not it’s mass.
Stephen Wilde:
Thanks for your response.
I assume it included an implicit yes to my question, “Do I have it right so far?” If so, I believe I largely understand your description, which includes your having found a previously undiscovered limitation on the Stefan-Botzmann law’s range of applicability.
I must admit to a good deal of skepticism on that point, although my understanding of Stefan-Boltzmann is not deep enough to entitle me to an opinion.
Leonard: many thanks for your detailed comment. I’m puzzled though by this statement:
Hans Jelbring, and Nikolov & Zeller make a basic mistake of confusing the adiabatic lapse rate as having an absolute temperature level. It does not, it is a GRADIENT.
I thought Jelbring was well aware of that when he said in his 2003 paper
“In an ideal gas atmosphere, the adiabatic temperature lapse rate has to be –g/cp
where cp is the heat capacity of the gas (ref 2 p. 49). Theoretical calculations are well
confirmed by observational evidence in the atmosphere of Earth. The adiabatic
temperature lapse rate on Earth is thus –9.81/1004 = –0.0098 K/m. As James R.
Holton concluded after deriving this result: “Hence, the dry adiabatic lapse rate is
approximately constant throughout the lower atmosphere.”
The temperature lapse rate in our model atmosphere also has to be –g/cp, since its
atmosphere is organized adiabatically. Hence, it is possible to calculate the
temperature difference (GE) between the surfaces with areas A and S in our three
thought experiments. The solution is identical in all three experiments and its value is
simply Dg/cp.”
Leonard Weinstein:
Thank you for your detailed explanation.
Just in case you are still interested in the isolated-gas-column-in-a-gravitational-field problem in which you were a primary disputant about a year and a half ago at SOD, I commend to your attention the Roman et al. and Velasco et al. papers tallbloke got for us on his Loschmidt thread. They are the most convincing treatments I’ve seen, although there are a few calculus hurdles in them I have yet to get over.
Joe Born: thanks for your reply at 9.15
OK, let’s look again.
Hans says:
“The temperature lapse rate in our model atmosphere also has to be –g/cp, since its
atmosphere is organized adiabatically”
So, what is the evidence that it is?
Hans says:
“The energy content in the model atmosphere is fixed and constant since no energy
can enter or leave the closed space. Nature will redistribute the contained atmospheric
energy (using both convective and radiative processes) until each molecule, in an
average sense, will have the same total energy. In this situation the atmosphere has
reached energetic equilibrium. The crucial question is what temperature difference
(GE) will exist between A and S?
The physical situation above is well known in meteorology from treating adiabatic
processes. For such a process the sum of kinetic, internal and potential energy is
constant by definition (ref. 2 p. 229).”
So it seems then, that Hans places his trust not in first principles statistical mechanics, but in established theoretical meteorology. The question is, is this a justifiable thing to do given the admixture of atmospheric gases (including GHG’s) in the atmosphere those theories built from?
I note here that his citation (ref2 page 229) appears to contain a typo, because ref 2 is his own thesis ‘Wind Driven Climate’ which runs to 111 pages. I know, because I have a copy. I suspect it should be ref 3, which is Holton, J. R. 1979. An Introduction to Dynamic Meteorology. Academic Press, London and New York. 391pp.
Hans says:
“The generally claimed importance of “greenhouse” gases rests on an unproven
hypothesis (ref 1). The hypothesis is based on radiative models of energy fluxes in our
atmosphere. These are inadequate, since radiative processes within the atmosphere are
poorly described, convective energy fluxes are often inadequately described or
omitted, and latent heat fluxes are poorly treated. The whole GE in these models is
wrongly claimed being caused by “greenhouse gases”. The considerations in this
paper indicate that effects of the greenhouse gases, other radiative effects, and
convection effects all might modulate GE to a minor unknown extent.
Hence, the atmospheric mass exposed to a gravity field is the cause of the
substantial part of GW(sic). The more atmospheric mass per unit planetary area, the greater
GE has to develop.”
So it comes down to whether you agree with Hans that the radiative models are inadequate. Given that they don’t include those processes he notes, I’m tempted to go with Hans on this. Also supporting his thesis is the evidence that Nikolov and Zeller have from other solar sytem bodies which have a wide variety of compositions, but which conform to a fitted curve similar in shape to the Clausius curve.
I’m liking it. 🙂
How about you guys?
malagaview says:
January 16, 2012 at 3:45 pm Something about a field charge.
What is the magnitude of the field charge? There is a thermal/non thermalradiation cross over in the range of 64Wm-2, but there should be a noticeable change in its magnitude if it were a direct force on surface climate. I would think it is more likely a thermochemical boundary. For example, the Arctic stratosphere is having some cooling to -90C or so in the range of 65Wm-2. The Arctic ozone concentration is lowering.
I would think that the field charge is not causing warming by adding energy, but limiting the rate of cooling when the energy does not meet the requirements of thermochemical reactions. The Antarctic ozone hole didn’t read the Kyoto documents it seems. Now the Arctic ozone is being a bit rebellious. Don’t you think the troposphere stability is more of an issue that surface temperature, since the tropopause is the heat sink for the surface?
Its more like Custer’s Last Stand… or do I mean The Battle of the Alamo…
Either way: King Canute knew he could not hold back the real world.
Sometimes I have to laugh… otherwise I would cry… sad to see it unfold..
Leonard Weinstein says:
January 16, 2012 at 9:21 pm
How would you slot conductive energy exchange between surface and atmosphere into that scenario ?
The Oxygen and Nitrogen have to acquire their ambient temperatures somehow and apparently it is not from radiation.
“your having found a previously undiscovered limitation on the Stefan-Botzmann law’s range of applicability. ”
Unlikely.
More likely it was taken as read 50 years ago that a planetary surface could be warmed by the density of the atmosphere. That is certainly how I recall it.
S -B was just used in connection with planets without atmospheres in those days.
Leonard Weinstein,
thankyou for your very elegant description of the GH effect and role of lapse rate. I don’t think people give enough consideration to the fact that all the GH effect is doing is raising the altitude at which Earth effectively radiates away energy.
Joe Born,
Thankyou for drawing attention to the Velasco et al. paper. I originally highlighted this work on the Loschmidt thread but hadn’t the time to expand on the implications of this work. I intend to do so in a note that Roger has graciously said he will post for me.
Over at the WE thread at WUWT I was trying to impress on WE that his model atmosphere was effectively an isothermal one. He refused to accept that the atmosphere he described would reach a constant temperature throughout the profile and seemingly understood the lapse rate to be a result of the Loschmidt effect. I tried several times to bring the Coombes and Laue, and Velasco et al work to his attention.
Interestingly there is a very nice explanation of the temperature distribution of an isothermal atmosphere in a gravity field over at Victor Toth’s web site. If you understand the concept of phase space then the proof, which is essentially that of Coombes and Laue, is very easy to follow.
I hadn’t realised there had been a discussion at SoD.
Paul: Looks like it’s going to be the meteorologists vs the physicists then. 😉
I’m intrigued by the statistical mechanics in the hard for me to comprehend Coombes and Laue paper and need baby stepping through the intricacies, so I look forward to your ‘101’ treatment with interest.
Stephen Wilde,
I haven’t followed closely enough your theory for the ‘GHE’ in gravitational fields and need to do so over the next few days. I’m using ‘GHE’ in inverted commas just to indicate a warming above the S-B temperature by any process. However, one thing I thought I noticed over at the WUWT thread was that you seemed to suggest that thermal conductivity would depend on gas density. i.e. at higher gas densities (pressures) the rate of thermal conductivity increases and changes the partitioning of energy flux between conduction and radiation?
However the thermal conductivity of a gas is independent of the molecular density or pressure.
Paul Dennis:
My take on Velasco et al.’s paper is that they disagreed with Coombes and Laue in theory, although the practical effect is negligible for an atmosphere of the size we’re interested in. That is, whereas Coombes and Laue came up with a zero temperature lapse rate, Velasco et al. came up with one that’s non-zero but, if my calculations are correct, very small. I invited others to check my work, but I received no convincing objection to it. The purpose of this response, of course, is to invite more-thorough vetting.
Joe Born:
that’s an interesting observation. I’ll need to go back and look at the Velasco et al paper. My reading was that they agreed with the Coombes and Laue work and had looked at two different situations of a finite and infinite system finding both to have a zero gradient in temperature but for two different reasons. However, I skim read it because it apparently confirmed Coombe and Laue’s treatment. I can see I’ll need to do a fair bit of reading over the next few days to bring myself up to speed.
Is this paper useful?
The virial theorem and planetary atmospheres
Viktor T. Toth⋆
⋆Ottawa, Ontario K1N 9H5, Canada
March 9, 2010
http://arxiv.org/abs/1002.2980
Joe Born:
I’ve just re-skimmed Velasco et al. There are two situations as I thought: the finite and infinite. In the in finite system the approach used by Coombes and Laue is correct and the gradient is zero. For the finite bounded system the microcanonical approach of Velasco et al show that the velocity distribution is no longer described by the Maxwell-Boltzmann function. That’s an interesting observation. What it means for the temperature gradient I don’t know. You said you have calculated it and found it to be very small and nearly isothermal. Is this correct?
tchannon:
almost certainly. I’ll look tomorrow after a good nights sleep!
tallbloke:
I think you’ve zeroed in on the issue: Hans relies on a meteorology result whose derivation he has not shown is based on the situation to which he applies it. (Simply saying “adiabatic” doesn’t do it for me.) Velasco et al. show their work. I hope others will look on Velaso et al. critically so that I can be more comfortable that my interpretation is valid.
However, i’m inclined to agree with you that the observational evidence strongly suggests that, at least beyond some level, optical density has little effect. I’m just not impressed with either Nikolov & Zeller’s or Jelbring’s theory in support of that result.
Paul Dennis:
Here’s an R routine showing my calculation of Velasco et al.’s Equation 8.
z = seq(0,1e6,1e5); # altitudes
f = 3 ; # degrees of freedom
E = 2e9; # guesstimate of total ebergy in a meter-square gas column arbitrarily high
k = 1.38e-23; # Boltzmann’s constant
VRW_Eqn8 = function(z, f, E){
N_0 = 6.023e23; # Avogadro’s number
w_m = 29; # “molecular weight”
m = w_m / N_0 /1000; # molecular mass
g = 9.8; # acceleration of gravity
P_0 = 1.01e5; # atmospheric pressure at sea level
M = P_0 / g; # atmospheric mass per unit earth-surface area
N_m = 1000 * M / w_m; # moles of atmosphere per unit earth-surface area
N = N_m * N_0; # number of molecules per unit earth-surface area
f * E / (f * N + 2 * N – 2) * (1 – m * g * z / E);
}
(2 / 3) * VRW_Eqn8(z, f, E) / k
I’d love it if others could give me their reactions.
tallbloke, not bad at all. I’ll have some suggestions but it is taking a wihile to compile. And that is partially from the time it is taking to just read and considering the vast amount of text being generated on the blogs. This subject of gravity sure stuck a chord, didn’t it, then there must be something there. My only hint right now is stay close to the high density at the surface, that seems where the addditional heat to raise the temperature is created by two different paths and the absorption of sw directly by the atmosphere itself seems one of the keys.
One of those suggestions, it seems to hinge on the amount of incoming solar radiation *directly* into the atmosphere. Here you find absorption lines in argon, o2, n2, h2o and co2. Look at the bodies, venus absorbs nearly all before it can get to the surface, mars neearly zero but not zero, the moon and mercury zero, and earth sets right between with, what?, about 76 wm-2 or ~1/3 of incoming radiation, and, it is all absorbed according to density. I think that is one major, major factor. Now look at N&Z’s chart, you will find that horizontally they all jibe.
Well really, both horizontally and vertically.
Wayne: Yes, the empirical results should be given strong weight here, because no-one has yet disabused me of the notion that classical and statistical mechanics are based on Maxwell’s 150 year old thought experiments. (That’s provocative and I hope it jogs someone to point me to the modern body of work which shows me the empirical curves for air at various pressures.)
Joe: Hans has valid concerns about the radiative models. Who knows what the opacity at which the necessary processes saturate is? His reliance on meteorological theory which goes along with Loschmidt is interesting don’t you think? and takes us straight back to mid C19th arguments over the distribution of energy vs temperature, as I outlined in the headline post.
What I need to read up on, is how statistical mechanics gets from total energy minus gravitational potential energy type classical mechanics thinking (still in use by meteorologists) to Velasco et al. The trouble is, I have another heavy weeks work ahead of me from tomorrow morning onwards. Oh well, library lunch hours…
Could I venture a question here?
As I read the discussion at WUWT, I wondered about the possible inconsistency and confusion arising due to two things –
One part of the discussion seems to be concerned with surface behaviour – and this tends to focus on S-B as an estimator of surface temperature. An example is WE’s thought experiment which asks whether surface can rise above a temperature governed by S-B.
Another part of the discussion relates to the behaviour of gas. This tends to revolve around the gas laws, the kinetic model, and the radiative properties of gas (e.g. emissions at discrete wavelegths).
I acknowledge that surface and atmosphere are connected by (at least) conduction – however we do not need to consider conduction to be very effective, and this would rasise the possibility that near-surface gas temperature may be different to the solid surface temperature.
If we compare a solid and a gaseous planets with otherwise very similar circumstances, including a source of heating which requires radiation for thermal balance at the surfaces . Could I put this question to the phsicists.
Is it reasonable to expect the solid surface to approach a grey body temperature which is somwhat higher than the ideal S-B blackbody temperature at balance? (Slightly higher because “grey” spectrum is a less efficient radiator than the ideal black body.)
However, the gaseous surface is constrained to emit at only discrete frequencies. Does this mean that it will tend to deviate even further from the black body spectrum? If that makes it an even less efficient radiator, should we generally expect a gaseous surface to have a higher temperature than a solid surface at radiative balance (where all other things are comparable)?
Thanks for replies – I might wish to discuss more, depending on answers
Roger, you say “point me to the modern body of work which shows me the empirical curves for air at various pressures”… well this is not probably what you were looking for but ponder on this one for me for a while.
N&Z’s equation really needs to be tied to real physical properties of the bodies of the soar system of course. And, it needs to be in a form that can be physically measured (well, most have already been measured) and put that equation into a proper form for right now it is but a best fit. But, such fits can coerce out the physics relationships.
Take their equation:
Nte(Ps) = Ts/Tgb = exp( 0.233*Ps^0.6512 + 0.0015393 Ps^0.385232 )
or equally:
ln(Ts/Tgb) = 0.233*Ps^0.6512 + 0.0015393 Ps^0.385232
which gives an alternate that also fits the curve:
ln(Ts/Tgb) = 0.253164*Ps^0.043478 + 0.0042735 Ps^(1/3)
The last one has at least one term that I had expected to see and that is the third root you now see in the equation. The 0.0042735 curiously when inverted is very close to 1/234 or more curiously 1/(740-288). It’s almost as if you could take that form and say it as 1/(740 K – 288 K) and that is the scalar. Anyone recognize these? But, mathematically I am not sure if this makes physics sense except if that ratio between Venus and Earth sets that parameter that *also* creates the curve that all other bodies fall on. That was very curious for sure, but probably just a coincidence.
Of the left term it seems, possibly, that this should take a form on density instead of pressure, still working on that one. This is going to take some help from others better than myself in mathematics and proper physics.
Have no idea if this is even approaching it correct but that is, as I said, curious. But, the curve does fit so, somewhere, there is a equivalent proper equation that has parameters that make physical sense and fit the data too. I think N&Z are so very close but not quite there yet.
Correction TB: that 1/(740-288) got covered up in excel, it was close to 1/((740-288+16)/2). As I said, probably a coincidence. Just looking for the real parameters.
“surface can rise above a temperature governed by S-B”?
Keep in mind it is solar flux, a slightly odd thing for humans. A flux is equivalent to a constant current as an electrical analogue. A constraint is the source limit. This means that an object can dependent on environment assume a temperature between cold space and ~5500K with distance independent.
For earth add to this the fact the earth is revolving.
There is exactly one point with sun directly overhead, in most cases is water. Further complication appears off overhead, ultimately to reflection (brewster angle etc), circles of different conditions and the poorly understood polorisation effects, perhaps even including reflection hitting the underside of atmospheric structures. None of this is consistent across the whole spectrum.
Mention is around of peculiar thermal effects with the sun below the horizon, presumed to be about IR reflecting or ducting or whatever.
Little mention is made of the asymmetric dayside/nightside where atmospheric conditions do change very fast so assuming the same conditions both sides is wrong. This alone alters SB, with addition or omission of albedo a common mistake/trick. (in my book albedo has no effect in the simple case on body temperature, cancels to unity but might not be the case)
All far from simple so some kind of approximation is about the best we can do.
I wish I had more time to read all the comments and make a considered reply.
I some extent I am with Miles Mathis about energy fields and gravity but I do not agree about photons. It has been shown that energy waves can be absorbed, reflected, transformed, and amplified through focusing.
I have been thinking about the similarity of electricity conduction and heat conduction. By definition conduction takes place in a solid or between solids in physical contact. Some consider that electricity flow is by the movement of electrons but experiments have shown that to be wrong. The energy flow occurs in waves. During the flow of electricity some energy is transformed to heat energy. The transfer of electrical energy only goes in one direction from a high voltage point to a lower voltage point. Now think about arc welding or lightning. For the latter ice particle in motion in clouds rub against each other building up static electicity ie momentum is transformer to electric energy. When the voltage is sufficiently high discharge can occur in the form of lightning which gives off light rays so that it is visible. I have seen trees hit by lightning strikes. It is rare for any signs of burning but branches appear to be torn apart. It is likely that the lightning contains concentrated microwaves which heat the water in the sap causing boiling and blowing apart by the sudden expansion of water vapour (ie phase change) similar to experiences in a microwave oven.
Another, aspect of welding and ligtning is the chemical changes of the atmosphere around the electrical discharge ie the formation of ozone.
Please Stephen Wilde think again about conduction, convection, energy fields, physical and chemical potentials. You are a thinker and maybe we all can learn something. My best wishes.
I am an engineer and always like to bring in reality. My experience indicts that the radiation absorption of CO2 in the atmosphere (which is insignificant) has no measurable impact on anything. The proponents of AGW clearly have no understanding of the complexities of heat and mass transfer, energy fields, nor energy conversions (or energy transformations)
Tallbloke,
Must say I’m enjoying all the intrigue and personality clashes on this topic. This might make a good movie some day.
As a layman, I’ve enjoyed reading all the various positions and think I’m maybe even learning some things, which is always good. Some of the discourse at WUWT is a little acrimonious, but for the most part people are just being passionate about what they see as obvious (to them) that others cannot seem to see with the same clarity. It says more about humanity in general than about any particular individuals.
I left one post on Willis’s recent thread that I thought got to the heart of what’s being discussed/debated:
“Willis,
Your whole argument is pointless. Nikolov & Zeller argued two points:
1) the currently accepted understanding of how to apply physics to a planetary body’s surface temperature is wrong. (i.e. the laws of thermodynamics, Stefan-Boltzman, etc. are correct, they are just being misapplied)
2) based on the (in their view) correct application of physics, they claim to be able to explain what governs a planetary body’s surface temperature.
To clarify, you have to accept (1) in order to understand (2), if they are correct.
What you, Joel Shore, and others keep saying is “based on the currently accepted understanding of how to apply physics to a planetary body’s surface temperature, N&Z’s (2) is clearly wrong” (paraphrasing). Well, yes, I think even they would agree to that. So what?
The only important argument (so far) is whether “the currently accepted understanding of how to apply physics to a planetary body’s surface temperature” is correct or not. So far, all they have come up with is an unsubstantiated and unsupported assertion that it is not. Unless and until they can make their case, the status quo “wins” by default. You don’t have to do anything at all. But it’s clearly a waste of time to argue something that even they would agree with.”
Willis’s argument is clearly right based on the “settled” science (sorry). Arguing with him on those terms is going to get you nowhere. Nikolov and Zeller argue that the correct way of applying physics to the problem will make an airless body ~100 Kelvin colder than what is commonly accepted. They claim to be able to prove that based on actual temperature measurements of the Earth’s moon.
IF they can make this case, then they will have established that the settled science isn’t so settled after all. AFTER making this case (if they do), they proceed to explain what is really causing the earth to be warmer than it would be without an atmosphere. Presumably, their methodology for measuring outgoing vs. incoming radiation will back them up.
I really look forward to their upcoming clarification.
So the point of all of this would be that the temperature at the bottom of the troposphere depends on the temperature at the top. As temperature will rise according to the adiabatic lapse rate, it is the temperature at the tropopause that sets what the temperature will be at the surface. If you increase the amount of heat in the system (turn the sun “up” a notch) the rise in temperature of the troposphere will cause the tropopause to rise in altitude (the point at which it finds the stratospheric temperature inversion rises) but then again, maybe it doesn’t because if you have additional UV, maybe the stratosphere heats up pushing the point of that temperature inversion downward. Or maybe they both heat up equally and the troposphere stays where it is. But in any case, the temperature of the surface generally will depend on the temperature at the tropopause.
Roger,
Having thought about this a bit, I have come to the conclusion that a certain person whose name I will not, as a matter of delicacy, mention is correct in asserting that gravity does not affect the temperature of the surface of a planet with a transparent atmosphere.
Here’s how I reach this conclusion.
Consider an airless, sunless planet without an internal heat source that passes through a cloud of gas, thereby acquiring an atmosphere.
Initially the planet surface temperature will approximate to the microwave background temperature of 2.75 K. However, as gas accumulates around the planet, the gas is compressed gravitationally, with resultant heating in accordance with the gas laws. The warmth of the atmosphere will heat the planet surface, which will then radiate more energy than it receives from outer space.
Eventually, the thermal energy released in the gravitational compression of the atmosphere will be entirely dissipated, by which time the temperature of the planet surface will have returned to its original value of 2.75 K, though the atmospheric pressure gradient from the surface to outer space remains.
So the gravitational effect on the surface temperature is transient only.
According to this account, the internal temperature of large gas planets must be due either to residual heat acquired during the process of formation, or produced by nuclear reactions, such as as account, in part, for the Earth’s internal heat.
Is this not correct?
These problems understanding convection , it has been around a long time and surely is a simple process. Any object even a molecule that is less dense than the medium it is in at a point were it can overcome gravity will rise until it reaches equivalence. Otherwise a boat would not float and a hot air balloon would not rise, and neither would the smoke in your chimney.
Conduction is the main culprit that causes convection in an atmosphere, tell me I have it wrong and it is caused by some imaginary force.
One does not have to agree with Prof Claes Johnson but he makes one think. His latest posts are http://claesjohnsonmathscience.wordpress.com/2012/01/16/questinoning-relativity-2-unphysical-lorentz-transformation/ and http://claesjohnsonmathscience.wordpress.com/2012/01/16/questioning-relativity-1-herbert-dingle/ In the latter the following could be applied to climate science
“Dingle recorded his experience of questioning relativity theory in Science at the Crossroads including harsh truths about physicists:
They are, briefly, that the great majority of physical scientists, including practically all those who conduct experiments in physics and are best known to the world as leaders in science, when pressed to answer allegedly fatal criticism of the theory, confess either that they regard the theory as nonsensical but accept it because the few mathematical specialists in the subject say they should do so, or that they do not pretend to understand the subject at all, but, again, accept the theory as fully established by others and therefore a safe basis for their experiments.
The response of the comparatively few specialists to the criticism is either complete silence or a variety of evasions couched in mystical language which succeeds in convincing the experimenters that they are quite right in believing that the theory is too abstruse for their comprehension and that they may safely trust men endowed with the metaphysical and mathematical talents that enable them to write confidently in such profound terms.
What no one does is to answer the criticism.”
The sentence, “they do not pretend to understand the subject at all, but, again, accept the theory as fully established by others and therefore a safe basis for their experiments. “, certainly applies to all believers of AGW and the vast numbers who may call themselves as “lukewarmers” which appears to be the case with some of the regulars who post at WUWT. The lack of understanding of the applicability and limits of the Stefan-Boltzman equation is part of the wider lack of understanding of energy transfer.
CanSpeccy,
For an isolated body without a sun, yes.
For a rotating planet with sun, no. (for at least the reason the atmosphere is never in steady state)
This is off topic but related, and probably involves some stupid basic conceptual mistake, so feel free to hand my head back to me after decapitation. Concerning conservation of energy and gravity, I’ve never been able to pinpoint why this wouldn’t work (and I don’t believe in free lunches, I just can’t figure out where the flaw is)- can anyone explain this?
I can break water into hydrogen and oxygen, a certain mass of water by performing a certain amount of work via electrolysis. I can put hydrogen and oxygen back together into water by performing a certain amount of work, via a spark. If I separate water into 2H2 and O2 at the bottom of a gravity well in some gas medium that is heavier than O2, the O2 should eventually rise to the top of the medium. Same with the H2. If I put it back together at the top and the medium is lighter than H2O, the water should eventually fall to the bottom. The wierd thing is, it looks to me as if gravity is doing all the work for free here. What’s my stupid mistake?
A note from Ned Nikolov & Karl Zeller at wuwt:
I have been tied up with personal business for the past week or so and am now trying to catch up with all the Tallbloke threads. You guys have been busy. I also looked at the Willis thread at WUWT – what a mess!
There are a lot of good ideas floating around but I would like to bring us back to the basics and try to tie some of these ideas together. These basics are also germane to understanding the Jelbring paper. There is a lot of talk about “conservation of energy” so let’s go to the foundation of that premise – the first law of thermodynamics.
For a “dry” atmosphere in an electromagnetic and gravitational field, the first law can be written:
dU = CpdT + gdz (1)
This equation is also known in meteorology as “dry static energy” and is closely related to “potential temperature”. For a quick derivation and identification of terms see my earlier post (and link to my 2010 E&E paper) at
For a system (atmosphere) in steady state equilibrium, the internal energy (U) of the system is constant (conservation of energy) and dU = 0. This means that at any point in the system (atmosphere):
CpdT + gdz = 0 (2) and
CpT + gz = constant (3)
This is the focal point of the Jelbring paper. As you ascend vertically in the atmosphere the thermal energy (and therefore temperature) decreases and the gravitational potential energy increases. Energy is conserved. Thus there is a vertical thermal gradient in an atmosphere that is under the influence of both an electromagnetic and gravitational field. The gradient can be represented by rearranging equation (2) to give:
dT/dz = -g/Cp (4)
Thus the vertical temperature profile in an ideal steady state atmosphere is solely a function of the gravitational acceleration and the specific heat capacity (at constant pressure) of the atmospheric gas. It does not matter if the gases are GHG’s or not, it does not matter what the down welling radiation is, it does not matter what the pressure is (as long as it is above 0.2 atm.), it does not matter what the density is, it does not matter what the absolute temperature is at any given point. The dry adiabatic temperature gradient is a constant, is a function of gravity and heat capacity only, and is a direct result of the first law and the conservation of energy.
The temperature at any given point is a function of the total heat content of the atmosphere. The heat content is a function of the incoming solar radiation and the outgoing long wave radiation. The total heat content can change (due to a change in the effective emission height for instance), and therefore the absolute temperature at any point can change, but once steady state is reached, the temperature gradient remains a constant. In all cases, the temperature at the surface will be warmer than the temperature at any altitude.
The “green house effect” is simply the difference between the surface temperature and the effective temperature at the effective emission altitude (z) (Jelbring’s outer sphere). It is controlled by the adiabatic lapse rate, not by “back radiation”. “Back radiation” is a function of the surface temperature, not the other way around.
This is the Jelbring hypothesis and it is very straight forward. If you add water vapor to the mix, things get a little more complicated but the results are still based on the first law and the conservation of energy. See my E&E paper for one example of how latent heat is treated in this manner.
———————————————————————————————————-
There also seems to be a lot of discussion concerning gravity and its relation to energy. This is an important concept and is key to understanding how energy is conserved in the troposphere by transforming thermal energy (CpT) to gravitational potential energy (gz) and vice versa. As pointed out by Tallbloke, gravity is a force, not energy. But when this force acts on mass, energy is created. If this force causes the mass to be displaced, work energy is the result. If this force acts on mass but displacement does not occur, then we call this potential energy.
In the troposphere, if gravity causes displacement of a gas (compression), we refer to this as PV work energy. Thermodynamically, this is PV work that is done to the gas by the surroundings. But a gas can also expand. This is mass displacement against the force of gravity and is considered PV work done by the gas to the surroundings. This can be shown by rewriting the first law as expressed in equation (1) as:
dU = CvdT + gdz – PdV (5)
where Cv is the specific heat capacity at constant volume. (See my earlier post above and the link to my paper for an explanation of the derivation). If heat is transferred to a gas parcel (e.g., conduction from the surface), dT > 0 and the parcel will expand and perform PV work on the surroundings against the force of gravity. In doing this, thermal energy (CvT) is converted to PV work energy and the parcel cools, but energy is conserved. The parcel now has a higher pressure than its surroundings and will rise to a lower pressure area. (Note: buoyancy is caused by a pressure differential, not a density differential. Where heat transfer is driven by ∆T, mass transfer is driven by ∆P. Density is a result, not a cause). The parcel rises, expands and cools further until it reaches an isobaric location. During its rise the parcel is doing PV work on its surroundings while displacing other parcels. Once the pressure with the surroundings is equalized, the parcel becomes stationary and contains an additional gravitational potential energy equivalent to the PV work energy that was expended. Thus thermal energy has been converted to gravitational potential energy via PV work energy. Energy is conserved isentropically throughout the process. This is convection.
Convection is a reversible process and mass transfer can also occur in a downward direction. This is called subsidence. In this case the parcel can cool and PV work (compression) will be performed on the parcel by the gravitational force from the surroundings and the parcel will descend. This PV work energy will be transformed to thermal energy during compression. Energy is once again conserved.
In summary, I cannot understand why respected people like Willis and Anthony have this mental block against the recognition of the very significant role that gravity plays in the thermodynamics of the atmosphere. Work energy is the crux of the heat and mass transfer distribution throughout the troposphere. And work energy is performed either with or against the gravitational force created by the gravitational field. It is the “dynamics” of atmospheric thermodynamics. Why do they think the tropopause is higher at the equator than at the higher latitudes? Why does the tropopause fluctuate in height at the equator? Hint: PV work against gravity.
———————————————————————————————————-
I have not yet had the time to study the Velasco and Coombes papers, but I have skimmed them. I am not sure why they come up with an isothermal temperature gradient. But I have played around with the kinetic theory of gases and the equipartition theorem a little bit and I know they have trouble dealing with diatomic gases at ambient or lower temperatures. They both have trouble predicting the specific heat capacity of diatomic gases. And this is just with the Cv. I am not sure how well they handle Cp which encompasses PV work. And since the first law formula for the dry adiabatic lapse rate is dT/dz = -g/Cp, I think they may be using the wrong tool, i.e., statistical mechanics, to do this work. But this is not my area of expertise. I’m just a dumb engineer.
————————————————————————————————————
I have not yet gotten through all of the Unified Theory and Loschmidt threads. Some of what I have discussed may be covered there. I look forward to reading them. I welcome any critique that any of you may have to my above analyses. I am still learning. I will post this at both the Jelbring and Gravity threads just in case.
Bill
The nature of “temperature” is crucial to figuring out such things.
Applying the thermo-kinetic theory, molecules with the same kinetic energy will have the same “temperature”; but what happens if the frequency of molecular collisions is greater due to higher density? There will be more frequent kinetic energy exchange.
Is that warming/warmer? How can we measure it?
Logicallly, an object will change its temperatre more rapidly when exposed to a higher-density fluid than a low-density one, even though the kinetic energy of each gaseous molecule is still the same. If that object is a thermometer, then it’s measuring the density/frequency of collisions.
CanSpeccy says:
January 17, 2012 at 3:01
Initially the planet surface temperature will approximate to the microwave background temperature of 2.75 K. However, as gas accumulates around the planet, the gas is compressed gravitationally, with resultant heating in accordance with the gas laws. The warmth of the atmosphere will heat the planet surface, which will then radiate more energy than it receives from outer space.”
Could a atmosphere of gas when compressed (pressurized) form denser mass which increases the potential gravitational energy (PGE) of the sunless planet without an internal heat source. Could the increased PGE attract energy relative to it’s density, therefor, warming the planet by the additional work (collisions) of its molecules, transparent to IR or not. The temperature retained because of the force of gravity on its molecules and its mass.
Is the potential gravitational energy of this planet increased by the addition of a atmosphere. Is the increased PGE a mechanism required to keep that atmosphere within the gravitational field?
I can’t imagine a sunless planet, certainly not a planet without a PGE.
Thanks Bill, I’m a gazillon times clearer now.
Tallbloke, Roger,
This is the most interesting and engaging thread that I have read for a long time.
At present there are many disjointed eddies and contradictory currents in the comments.
(Your original post was quite clear however).
I do urge you to synthasise what survive critical analysis, when work load permits and when the dust has settled. (In the fullness of time etc etc).
If Nikolov & Zeller are flat wrong, then I want to know why their equations lock together so well to forecast real temperatures of various planets and moons and why the ratio of observed temperature to N&Z’s grey body temperature (Nte) for Earth, Mars and Mercury are quite similar but why Venus is so different; while CO2 content for Earth & Mercury are similar, but so different to both Mars and Venus.
If you forget about Greenhouse, then this all seems to fall into place.
markus says:
January 17, 2012 at 5:52 am
X2
“If you forget about Greenhouse, then this all seems to fall into place.”
That’s exactly what I have found and N&Z and Jelbring seem correct that out temperatures have very little to do with specfic GHGs as long as there are adequate GHGs present. And you know, that has bounced around comments for years, that about 95% of co2 sets idle in its ground state at any given moment, so I’ve have have a real problem reconciling that fact, that absorbing gas has already absorbed most of those frequencies anyway, that is the bite you see from 20km measuring downward. What is adding 30% or even 100% going to do but make some 97% idle. Made zero sense. Looks like we can soon toss that co2 monster into it’s bottomless pit.
I read an interesting chapter in a book by Petty yesterday on radiation and one statement really caught my eye, it stated that 95% of radiation in the co2 wavenumbers are absorbed in the first one+ meters of the atmosphere. THAT is why co2 does nothing and solar radiation controls it all. From that point on it just bounces about keeping us warm down here at the surface just like the 60+ water moleclues for every one of co2, they all eventually make their way to space.
Also, thanks to ‘anna v’, a particle physicist, over at wuwt, I finally received a gut level description why all gases do in fact radiate after all, all of them if not a lone molecules and in a black body manner, though only at about two or so percentage compared to stronger vibrational lines, that is emissivity would have to be taken into account. You can see this looking at a spectrum taken from the ground upward, notice the small gap underneath the “window” frequencies. It is all finally falling together. Go read, they are near the 850th comment downward in the “A Matter of Some Gravity” thread, seach ‘anna v’.
Well explained William Gilbert and thanks to the link to your paper. I had read it previously but did not save it. I have now recorded it with the the web link and my computer file site into my disorganised reference list so I can digest it more.
The success of this blog is probably due to engineers such as you and Tallbloke providing sensible posts and comments.
Having read what Paul Dennis said on Jan 16 10.37pm:
“However the thermal conductivity of a gas is independent of the molecular density or pressure”
I thought it was a bit counter intuitive so checked:
The thermal conductivity of a gas IS dependent on its’ density.
Thermal conductivity K = n** λ * CV /3 NA.
Where
n= particles per unit volume
= average speed of the gas
λ = mean free path of the gas particles
CV = Molar heat capacity of the gas
NA= Avogadros’ number
Consider one molecule of O2 coming into contact with the ground. It will take x joules of heat away from the surface. Now consider two molecules of O2 coming into contact with the surface: they will take 2x joules of heat away; four molecules will take away 4x joules etc.
Air is a poor conductor of heat anyway but convection and winds speed up heat loss.
Paul in UK:
Your formula for thermal conductivity is incorrect as written (I’m sure it is a typo). It should be:
k = n*lambda*Cv/3NA
However, the key point is the thermal conductivity is proportional to n*lambda, where n and lambda are as you’ve defined above. Now here is the crux of the issue, lambda, the mean free path is given by:
lambda = 1/(n*sigma)
where sigma is the collision cross section and is a constant for any particular gas.
Thus we can write for the thermal conductivity:
k = (1/sigma)*Cv/3NA
We observe that k is indeed independent of pressure and density (n).
I know that this is counter intuitive and take some getting your head around. I became interested in thermal transport in gases when I wanted to understand cryogenics and in particular the performance of vacuum vessels. The thermal conductivity between the walls of a vacuum vessel only reduces once the pressure is reduced to a point where the mean free path is greater than the distance between the walls of the vessel. For most dewar flasks etc. this is a surprisingly high vacuum. It also shows that it is better to have as small a gap as is possible between the walls of the vessel. Again a counter intuitive notion that goes against all our best instincts.
Some great overnight (for me) contributions and I have too little time to answer them all, so thanks an apologies. Thanks especially to Bill Gilbert for his clear exposition which takes what I set out with in the headline post and raises it to the higher level of integrated understanding concerning atmospheric processes. I also note his same comment was favourably received by Hans Jelbring on his thread.
A tiny nit I have is with this statement:
“But when this force acts on mass, energy is created. If this force causes the mass to be displaced, work energy is the result. If this force acts on mass but displacement does not occur, then we call this potential energy.”
Bill, never never say that energy is created in discussion with physicists, it makes their knees jerk. 🙂
The key point here is that it’s not a question of “when this force acts on mass”; it always has and always will, so the energy is always there, it’s just that it is sometimes evident as the energy of motion (in freefall for example), and sometimes ‘locked away’ as ‘gravitational potential energy’
I suppose you could argue Bill is strictly correct in that gpe is potential energy, not actual energy, and therefore energy is created from gravitational potential energy when the gravitational force is acting on a mass (making it accelerate). Just don’t argue that way with people whose eyes instantly glaze when you talk about “creating energy”. 🙂
Wayne, like your thinking in trying to play around with the numbers to see if interesting quantities drop out which relate to measured physical reality. I do that too in looking at other planetary orbital parameters etc. This solar system of ours truly is a system, complete with feedback loops from planets to Sun. One day, we’ll fully understand how it works. Meantime, we need to accept that the way cybernetic control systems with lags work, is to oscillate about means. Thankfully, during the last 10,000 years, the oscillations have been pretty small and benign. long may it continue.
Bernd, yes. It seems to me analogous to a nearly exhausted car battery. It still measures nearly 12V when you put a meter on it, but as soon as you demand any real current flow, the voltage plummets. Similarly, you can have two objects at the same temperature, but the one with low thermal mass will cool real quick when you bring it into contact with a large cold mass.
Cementafriend: Bill Gilbert and Dean Brooks have a thread here too, with links to their papers and sites. Unfortunaately it has been leapfrogged by the brooaha between the Talkshop and WUWT – my apologies to Bill and Dean.
MarkB electrolysis uses lots of energy! No free lunch for you my lad. 🙂
Back to Bill’s comment:
“I have not yet had the time to study the Velasco and Coombes papers, but I have skimmed them. I am not sure why they come up with an isothermal temperature gradient. But I have played around with the kinetic theory of gases and the equipartition theorem a little bit and I know they have trouble dealing with diatomic gases at ambient or lower temperatures. They both have trouble predicting the specific heat capacity of diatomic gases. And this is just with the Cv. I am not sure how well they handle Cp which encompasses PV work. And since the first law formula for the dry adiabatic lapse rate is dT/dz = -g/Cp, I think they may be using the wrong tool, i.e., statistical mechanics, to do this work. But this is not my area of expertise. I’m just a dumb engineer.”
+1. I’m just a dumber HNC engineer with a history/philosophy of science degree, but I have the same intuition about the stats mechanics here. Hopefully this will be resolved when physicist Paul Dennis guest authors here soon. I hope he will address our concerns.
Meantime it’s back to the library for me to continue reading Heimann’s 1970 Leeds thesis on Maxwell’s sources and influences. Something happened between Maxwell’s earlier considerations of the colliding gravel in Saturns Rings, his initial thought experiments on gases, and his later adoption and development of Clausius’ statistical mechanics.
It might just be, that in common with much of the rest of climate science, the averaging of averages has been taken a step too far, and ended up smearing the gradient into isothermal conformity…
William Gilbert:
Thank you for your explanation of lapse rate. Unfortunately, it did not allay a suspicion I’ve been harboring, which is that those who are relying on the adiabatic lapse rate to arrive at the behavior of a thermally isolated gas in a gravitational field are unwittingly assuming that convection continues to occur.
Your derivation begins with an adiabatically rising parcel. To me that sounds as though the parcel has been heated somehow to impose the temperature (and thus density) difference that drives convection. (Yes, yes, I know you say it’s a pressure gradient that drives convection, and that’s true, but the pressure gradient results from a density difference in a gravitational field.) So your derivation assumes some non-equilibrium situation.
So now that the parcel has been raised and a temperature lapse rate has thereby been imposed, what happens when there’s no more convection? Air’s thermal conductivity is small, but it is non-zero, and what we’re talking about is equilibrium. We have a temperature gradient, heat tends to flow down a temperature gradient, and we have to investigate the degree to which gravity interferes with that tendency. To me it is not self-evident that talking about a non-equilibrium process, namely, convection, sheds much light on that subject.
This is why I am inclined to credit the Levasco et al. result; it is not based on a non-equilibrium assumption, and it begins with the basic reason why heat flows: probability.
That being said, I am indeed inclined to believe that the planetary observations people like Nikolov & Zeller made say something about the irrelevance of optical density beyond a certain point. It’s just that the theory they’ve advanced in support is not compelling.
On Jelbring, Dr. Brown has reviewed his paper and perhaps Hans may want to reply. Robert’s view on N&Z was kind of… wait and see:
Seems Dr. Brown has the same view I was holding a weeks ago that over time, even in a gravitational gradient, a tall column of air will be isothermal and the average molecular speed will be the same from top to bottom irregardless of pressure or density without added external energy. That to not break thermodynamic laws, specifically the zero td law. I’m still a bit confused but I do see his viewpoint… was there before taking that last left turn ;-).
The problem here is “solutionizing”.
People tackle the problem of why bumblebees fly, some ideas are thrown around, those ideas are incomplete, so people come to the conclusion that since there is no solution to the problem, bumblebees don’t fly.
In the meanwhile, bumblebees fly. Back to square one.
In management circles, this is all pointed out as a fundamental error…the fact that you don’t have a solution doesn’t mean the problem is impossible to solve. It simply means you should concentrate on analysing the problem and in collecting more data, rather than immediately try to identify a solution.
For those harder in understanding, the observation is that independently from the composition of the atmosphere and the presence of a solid surface underneath it, every planetary atmosphere in the solar system has a “troposphere”, defined as the part where downward lapse rates are positive, i.e. temperatures increase as the distance from the top of the troposphere increase.
The same thing applies to any self-standing gas cloud anywhere in the universe. There is always surface “below” which temperatures increase with pressure. Otherwise stars won’t ever ignite.
Now if this is because of whatever Hans has said, or N&Z, or it’s Tooth Fairies, that is not a question that will ever be answered in blogs (and especially, in their comment sections). But anybody stating that what the whole cosmos is alight by is “impossible”, they do have a problem telling truth from fantasy.
This is getting a bit technical for me. I just want some clear rules that I can then apply to the climate system.
The more discussion there is the further away from the climate implications we seem to be getting.
Even in that column wouldn’t gravity place more molecules at the bottom with more collisional activity and more heat generated at the bottom ?
I haven’t had time to read the whole thread so apologies if someone already covered that.
“one thing I thought I noticed over at the WUWT thread was that you seemed to suggest that thermal conductivity would depend on gas density. i.e. at higher gas densities (pressures) the rate of thermal conductivity increases and changes the partitioning of energy flux between conduction and radiation?
However the thermal conductivity of a gas is independent of the molecular density or pressure”
That is what Willis though I was saying but not quite so.
I was suggesting that solar radiation reacts with matter and is converted to kinetic energy and then longwave.
So if there is denser matter more of the radiation will be in the form of kinetic energy for longer before it leaves the system as longwave.
As kinetic energy moves from molecule to molecule by conduction which is slower than radiation then with more energy in kinetic form for longer one gets a backing up of energy flow within the system leading to a higher equilibrium temperature.
Stephen Wilde:
If you haven’t received many comments in response to statements such as “more molecules at the bottom with more collisional activity and more heat generated at the bottom,” it may be that some readers, like me, aren’t sure what you’re getting at.
True, more molecules in the same space means more collisions. It’s not clear to me that the collisions *generate* heat, but, everything else being equal, there would be more heat per unit volume. Still, I don’t see how it follows that the temperature in a higher density is necessarily higher than somewhere with lower density, fewer collisions, and and less heat.
Was that comment at all germane to your point?
Stephen Wilde:
You say that “with more collisional activity and more heat generated at the bottom”. The collisional activity between molecules doesn’t generate heat.
We can treat the molecules as rigid spheres that interact elastically during collisions and thus no energy (heat) is created or destroyed, or disspated by this process. The temperature of a gas is determined by the Maxwell distribution of molecular speed.
[…] actual problem as I see it is called […]
Paul Dennis,
Thank you , that helps.
Should I therefore say ‘ with more collisional activity and more heat present at the bottom’ ?
wayne said:
“the average molecular speed will be the same from top to bottom irregardless of pressure or density without added external energy”
Which seems to gell with what N & Z said (I think) namely that the differential warming between top and bottom only comes into play when the external energy source is added.
So is the idea that there may be higher density at the bottom from gravitational causes but no thermal consequences of that unless one provides the external energy source and then a temperature gradient becomes apparent ?
Which brings us back to what Rog said at the outset:
“Right, but it’s what happens to the stuff that gets pulled due to other physical laws which come into play that causes the heating, not gravity itself.”
So, given all that, what is the value of the proposed experiment involving an isolated vertical column when we all know that there will be more molecules at the bottom due to gravity and we all seem to know that that in itself has no special thermal consequences.
In a sense more heat can then be ‘generated’ at the bottom but only if an external energy source is provided because more of the incoming is converted to kinetic energy if the density is higher.
Am I getting any closer ?
Somehow this stuff has to be translated into words that the average but reasonably well educated non scientist can have faith in.
First, a repost of my riposte at Willis wry paste at WUWT:
Willis, dang, you could do the proverbial selling fridges to Eskimos.
I think I can falsify your “elevator speech”. I think others have already done so, that I read and took on but it seems you did not. Namely, that non-gh gases can still catch heat by conduction and radiate that, to keep the laws of physics. Only difference with gh gases is that gh gases can absorb energy in TWO ways: conduction and absorption of radiation.
However, I could be wrong. And I still suspect that ghg effects are there in the mix. Witness the strange “W” shape of our atmospheric temperature profile with increasing height. That middle range, to me, is likely to be where ghg effects overcome lapse rate effects.
Trouble is, there are now about ten recent posts all about this, Jellbring, Nikolov & Zeller, Monckton, Glickstein, Brown, Coray, here and at Tallbloke’s, your last one here being nearly a thousand comments long and still rising. I’ve tried to go through them methodically but fell asleep even worse than usual at the keyboard. I shall continue to try. And Anthony says he’s had about enough of “this” (?subject ?for the moment ?heated conversations).
All this underscores more and more what I see as a sore need to develop a form of climate skeptics’ wiki that can handle the actual science, development thereof, alternative theories, and all in language that a reasonably intelligent but not necessarily science-educated layman can understand. And of course, firing intelligent interest but basically keeping courtesy… and keeping room for the latecomers & newcomers, who may be slowest to articulate their love and truth, like Cordelia in Shakespeare’s King Lear, but may still be the most honest, the deepest, the best scientists.
What to do with trolls and folk like Joel Shore is a serious issue. I really don’t think there is a simple answer. Therefore it will need a lot of open exploring as to the ethics of what to do.
I’m working on an article for Tallbloke to take this further.
but dang, you keep interrupting, Willis! fast shot cowboy, certainly! Unfamiliar to us Brits who need time to think. Yes, that goes for me too. That’s why I said nothing on the Night of the Scissors.
Joe Born said:
“everything else being equal, there would be more heat per unit volume. Still, I don’t see how it follows that the temperature in a higher density is necessarily higher than somewhere with lower density, fewer collisions, and and less heat”
Thanks Joe, could you clarify why more heat per unit volume would not necessarily translate into a higher temperature if the greater heat per unit volume is due to higher density ?
Physics and its fundamental relationship with nature is the most exciting academic sphere known to man. Unknowns, yet to be known.
Probably, when fully understood, it will allow us to interact with nature in unimaginable ways.
Undoubtedly, climatic science is the hottest topic around, justifiably, as it concerns the atmosphere that, was not only essential to the creation of life, but is essential to its sustainability.
Our perception of the physical universe defines our psychology and, it seems, we either fear or embrace our knowledge of it.
Yet, fear has it consequences. Relative theory borne of bias always remains in the philosophical, and constantly questioned. It is this illogical branch of reasoning that spawns thought into the unknowns, furthering knowledge of the universe and our relationship with it.
Climatic reasoning is flawed, the scientific hypothesis is an appeal to authority, it relies on a censuses biased by our psychology. The strength of its theory relies on disproof.
Reasoning cannot disprove the truth, or otherwise, of our perceptions which are only of the theories known to us
.
For example, as a Theory of Relativity the following;
It is the arrangement of electrons in atoms and molecules that radiates in equilibrium to its range of covalent bond. The chemical composition of molecules obtains isothermal properties from conduction with the electrons working the covalent bond. It is this conduction and then convection that dominates our climate and regulates its oscillation. This theory disproves Co2 forcing on temperature other than the radiative performance of the pairing of its electrons. No energy is added atmospherically by radiation. It is conduction from the work of the covalent bond and the convention of molecules within a gravitation field that denotes the heat of a planetary body (that is surrounded by vacuum).
The Potential Gravitational Energy of a planetary body indicates its temperature due to stratified isothermal laws. It is the velocity of rotation to mass that indicates the Potential Gravitational Energy.
This theory of relativity complies with all known laws of physics.
See, I invite you to disprove me. The more general in its application the longer it will take you. It has taken decades to know that the paradigm of climatic reasoning, as the consensus stands, deserves skepticism.
Is that like swimming with the pack, Rog?
“… tried to go through them [the 1000’s of comments] methodically but fell asleep even worse than usual”
Lucy, that’s classic :-)! Me too! Overload.
Reading non-stop about gravity just sinks me into my chair. lol.
[ Yep, practical demonstration of gravity and heat input lapse rate. anon]
In the intro above, Rog said this:
This means air is denser at low altitudes, and that means more molecules are having collisions more often, thermalising energy.
That seems to contradict:
“We can treat the molecules as rigid spheres that interact elastically during collisions and thus no energy (heat) is created or destroyed, or disspated by this process.”
I’d guess that thermalisation is an energy conversion process rather than creation or destruction or dissipation of energy. If so then my earlier comment would be correct in that heat is indeed ‘generated’ via thermalisation.
Could someone clarify please.
Leonard Weinstein says: January 16, 2012 at 9:21 pm
Tallbloke,
In order to understand what is occurring, you first have to understand the cause of the atmospheric lapse rate. This has been explained often and well, including on wiki: http://en.wikipedia.org/wiki/Lapse_rate Please read that before proceeding.
Well I did, and there is nothing about the CAUSE of the atmospheric lapse rate, contrary to what you stated, there are only definitions and descriptions. Tallbloke OTOH explains his perception of “cause” pretty well IMHO. Here are the relevant contents of the wiki article to illustrate my point:
1 Definition
2 Mathematical definition
3 Types of lapse rates
3.1 Environmental lapse rate
3.2 Dry adiabatic lapse rate
3.3 Saturated adiabatic lapse rate
4 Significance in meteorology
Stephen Wilde:
“Joe, could you clarify why more heat per unit volume would not necessarily translate into a higher temperature if the greater heat per unit volume is due to higher density ?”
Glad to. Packets A and B of the same monatomic ideal gas have equal volumes V and equal temperatures T but different densities N_A / V and N_B / V. Packet A’s heat is (3/2) * N_A * k * T, and Packet B’s is (3/2) * N_A * k * T, where k is Boltzmann’s constant. Same temperature, different heat amounts.
By the way, I’m not a physicist; I’m just parroting what the smart guys tell me.
“I’d guess that thermalisation is an energy conversion process rather than creation or destruction or dissipation of energy. If so then my earlier comment would be correct in that heat is indeed ‘generated’ via thermalisation.
Could someone clarify please.”
Possibly only add to the mist, anyway;
Conduction of molecules from the unstable arrangement of electrons around them is the energy conversion and convection is the thermalislation of that heat into a atmosphere. Building it until destabilization.
I do find your theory that basically, The temp of a planet is relative to its density, plausible.
I’m terribly bad on the theory – I find that you need to understand EVERYTHING before you play with theory, otherwise you can misinterpret things subtly…
But I do have a feel for good science. And one of its features is that it can make specific predictions which can then be looked for, or it can propose experiments which will either prove or disprove a theory. One of the major reasons I am an AGW sceptic is that I see no such experiments, and when predictions are made like the tropospheric hot spot, they are not treated as conclusive if they fail.
In this case, I would love to see some specific predictions, or proposals for an experiment along the above lines. That would give me a lot more confidence that we are talking about a real issue here…
“Same temperature, different heat amounts.”
Ok got that. Density holds heat but the extent to which the heat is reflected in temperature is down to the Boltzmann’s constant. Is that right ?
But that is a radiation only calcualtion.
What happens to temperature if non radiative processes such as conduction are operating in parallel ?
Wouldn’t you then find that the temperatures might be the same because the non radiative energy supplements or offsets the radiative energy at the sensing point ?
Just a thought:
Could the unequilibrium nature of electrons +/-, within in a chemical molecule, be reason enough to suggest that, the entropy produced, is the mechanism converting the potential energy of IR in mass to heat, then recoverting as it radiates unlimited but for by mass.
” I find that you need to understand EVERYTHING before you play with theory, otherwise you can misinterpret things subtly”
Not possible. We would still be in caves on that basis.
The trouble, too, is that experts in specialisms develop a need for very specific terms that then restrict their ability to keep the big picture in mind.
I had an exchange with Robert Brown where that happened.
I used the term ‘force’ as meaning anything that affects movement. He limited it to the four accepted forces of nature such as gravity etc. Well obviously he is right but you need the wider definition to interpret many features of the world.
So, because he wouldn’t use the broader term I couldn’t engage his mind on the point I was trying to get across.
Willis then used that as an excuse for insults and mockery in public not once but twice.
But, hey, when I see what the experts say to one another I’ve nothing to grumble about.
Lucy Skywalker:
I believe you’ll find that the basis for the lapse-rate derivation in meteorological circles is that packets of air at the surface are heated to higher temperatures than their neighbors’, making them rise like balloons until the work they do by expansion cools them to the temperatures that prevail at their new elevations. In other words, something has imposed a non-uniform temperature field at the atmosphere’s base, and this is what maintains the lapse rate.
Folks like Hans Jelbring believe that the base-of-the-atmosphere temperature is largely independent of greenhouse-gas concentration, and the evidence leads me to believe they’re probably right. However, to advance an explanation of this result, Jelbring proposed a thought experiment in which the atmosphere is, unlike the earth’s, at equilibrium, and he says the adiabatic lapse rate should prevail there, too.
A lapse rate at equilibrium seems to be a matter of controversy among physicists (a group to which I do not belong); some, like those who wrote the Velasco et al. paper discussed here https://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/#comment-13708, believe that at equilibrium the lapse rate would be negligible (if my–layman’s–calculations are correct). If Velasco et al. are correct, then, to the extent that Jelbring’s explanation of the observed phenomenon depends on his thought experiment, it is faulty.
In my response above to William Gilbert, I have indicated why, to this layman, Velasco et al.’s argument is more compelling.
Note that the issue is Jelbring’s and Nikolov and Zeller’s explanation of a phenomenon (insensitivity to greenhouse-gas concentration), not the existence of the phenomenon itself.
Perhaps if we really understood what is going on the discussion would become less heated (see WUWT thread)… 🙂
The Stefan-Boltzmann equation specifies the maximum amount of radiation that is emitted at a given temperature for a black body in thermodynamic equilibrium. It also insists that the black body must be a solid uniform body which is made from a perfect absorber of all wavelengths in the EM spectrum, and exists in a vacuum.
However in the real world, the planet never is in equilibrium, and emissivity varies each nanosecond due to planetary rotation, varying geography, tides, cloud cover…e.t.c. It is obvious that Earth is not a perfect emitter and, with an air pressure of ~1bar at the surface, it is far from existing in a vacuum.
This is the danger of using averaged behaviour of a complex dynamic system and expecting it to make any sense. This limits the usefulness of simplified experiments (thought or real) in understanding what’s happening and only a top-down holistic approach which encompasses all climate sun-systems has any chance of success.
Stephen Wilde: “But that is a radiation only calcualtion.”
I assume you inferred that from the fact that I uttered “Boltzmann.” But Boltzmann’s constant actually comes from the ideal-gas law, PV = NkT, no radiation required. You assume that law, imagine a bunch of gas molecules banging around in a box to exert pressure on its walls, and thereby determine the relationship between k and an individual molecule’s mean translational kinetic energy. Again, no radiation required.
“Wouldn’t you then find that the temperatures might be the same because the non radiative energy supplements or offsets the radiative energy at the sensing point ?” I apologize, but I couldn’t understand this question well enough to attempt a response.
Geez the internet is a good place, you can end up thinking a lot of things, like:
Black holes are vacuums whose lack density, therefore lack of gravity is a grater force than the gravitational fields upon it.
Tenuc, well put! The Stefan-Boltzman equation does not apply to gases. There is a big doubt about the nature of radiation from the Sun. No one knows its diameter. There is evidence that there maybe a solid core but no one knows the size. There is plenty of evidence that the corona of the sun and the core are higher temperature than calculated from the S-B equation. There is evidence that Jupiter is hotter than that calculated by S-B equation.
With respect to the Earth people are forgetting that clouds radiate to space. The emissivity of water and ice at cloud temperatures is high.
The atmosphere and the various energy transforms, and chemical reactions (production of ozone and its energy absorption-emission) are very complex.
William Gilbert and Tallbloke, thank you both of you.
I found TB’s use of the Platonic dialogue superb, delightful, a pleasure to read. And I found Gilbert’s post really helpful in understanding this interesting under-our-noses-how-dare-we-admit-we-don’t-understand business.
However, I’d really like to see some graphic illustrations of the kind of evidence that supports this way of thinking – temp/altitude charts to show lapse rates and temps at 1 bar for Jupiter, Venus, Earth, Mars; a graphic pic of the heat in Jericho and deep mines BUT the cool in the deep oceans; the “W” strange temp/altitude profile here on Earth.
I gave up on radiative physics a while back and essentially took Monckton’s line, use IPCC maths against itself, whether or not it’s even essentially correct, in order to disprove the catastrophist abuse of science.
But I do care about Science being advanced, and for that, this thread clearly handles a key issue. Hugely as I respect Anthony Watts, he does have problems handling issues that are nonessential to CAGW debunking, but have strong opinions around them. But if he spent the time mulling and researching fringe material that I do, he’d never be able to cope with his blog.Too many Joel Shores on my forum forced me, in effect, to give it up.
William Gilbert says: January 17, 2012 at 5:15 am
Thank you…
Especially for the explanation of convection in terms of buoyancy and subsidence caused by a pressure differential.
I think most people have an understanding of buoyancy…
Stones fall through the air… wood falls through the air…
Stones sink in water… but wood floats on water.
An object sinks to the bottom if it is denser than the surrounding fluid.
An object floats to the surface if it is less dense than the surrounding fluid.
Buoyancy and subsidence need differences in density…
Convection needs differences in density….
However, the convection of a parcel of gas [or liquid] within a larger body of gas [or liquid] is harder to understand.
Looking at the above picture of steam is it easy to see the individual parcels of “water vapour” rising in the air… I had
always assumed that these parcels of “water vapour” where tiny “droplets of water”… but I can’t see how “droplets of water”
could be buoyant in air… but if I adjust my thinking to “bubbles of water” then I can understand that they could be
buoyant.
So my thinking so far:
We have a “parcel” of warm water vapour… the water vapour cools and condenses at the boundary layer of this “parcel”…
thus a film of water encapsulates a bubble of warm water vapour to form an “bubble”… and overall this “bubble” is less
dense than the surrounding air.
Then you write:
The parcel now has a higher pressure than its surroundings and will rise to a lower pressure area.
Now this high pressure parcel is quite special:
In my example of a “bubble” of water vapour this “bubble” would pop if the internal pressure was too high… or collapse if
the internal pressure was too low… this “bubble” also remains remarkably stable while it cools as it slowly rises up
through the surrounding air. It also seems rather confusing because this warm “high pressure parcel” moves up towards a
colder “lower pressure area” until the densities are equal [or the “bubble” pops/collapses].
Gravitationally, this “bubble” of water vapour is also quite special… it overpowers the force of gravity and rises through
the air… and how does it do this… by the pressure of the surrounding air?… so the air pressure below the “bubble” is
greater than the air pressure above the “bubble”.
Given the very small size of the this “bubble” the difference in air pressure above and below must be very very very small…
especially given our understanding that gases are difuse and that air pressure is caused by gravity…. yet the mass of the
“bubble” visibly rises through the air!
Now this example relies upon a phase change in H2O to form a low density “bubble” of water vapour surrounded by water.
If we look at a warm particle of CO2 it becomes even very harder to understand convection.
CO2 is a heavy particle in the atmosphere and has a tendancy to sink towards the ground… yet this heavy particel of CO2
seems to be able to rise through the air when it is warmed… it doesn’t change its mass when it is warmed… but when it
warms it magically overcomes the force of gravity… the force of gravity above and below this particle has not changed…
the air pressure above and below this particle hasn’t changed.
The only way I can see that buoyancy (or convection) can work is if DENSITY determines the gravitional force exerted upon a
particle or parcel in a fluid… the evidence of buoyancy and convection supports this conclusion.
The only problem is that settled science tries to contradict this view using the feather and hammer experiment
by showing that gravity accelerates the feather and hammer at the same rate.
However, try reversing this experiment by throwing two objects at the ceiling… say a light tennis ball in one hand and a
heavier cricket ball in the other hand… now throw the balls together so that they hit the ceiling at the same time… and
it is apparent that the heavier [more MASS] object requires more force to overcome gravity in a identical manner.
So we have a paradox…
MASS determines the gravitational force on solids…
DENSITY determines the gravitational force on fluids.
Joe Born says:
January 17, 2012 at 1:23 pm
Sorry Joe, the mention of Boltzmann automatically sent my mind to the S – B equation and not the Ideal Gas Law.
” It also insists that the black body must be a solid uniform body which is made from a perfect absorber of all wavelengths in the EM spectrum, and exists in a vacuum.”
So as soon as one adds an atmosphere the body is no longer in a vacuum and the S – B equations cease to apply.
An atmosphere will always interfere with the radiative process due to the presence of non radiative means of energy transfer.
The big issue then is whether it is atmospheric MASS that does the interfering or atmospheric COMPOSITION via GHGs that does the interfering.
Since an atmosphere of ANY mass will be capable of conduction and convection it follows that the degree of interference with the radiative process must be dependent on mass.
AGW relies on mass having little or no effect and GHGs having a substantial effect.
All that N & Z and Hans are pointing out is that which was widely known 50 years ago when I was taught this stuff, namely that the S – B equations cease to apply when a planet acquires any sort of atmosphere that has mass.
At some date in last few decades someone decided that only an atmosphere with GHGs could interfere with the radiative processes.
It all went wrong from that point.
The apparent increase of the compressed gas temperature is not caused by the compression. As the density (the number of molecules per volume) is increased the amount of energy in the space is densified. The energy level per molecule is not appreciably changed, only the amount of energy in the space is changed. As gravity pulls the molecules down they compress, take up less space, The amount of energy per molecule is not increased. The temperature average of the area is increased as more molecules occupy that space.
There are way too many moving parts in this disscusion to keep the important parts in a straight line. 😦 pg
“As gravity pulls the molecules down they compress, take up less space, The amount of energy per molecule is not increased. The temperature average of the area is increased as more molecules occupy that space.”
Yes that’s what I would have thought but then Joe said:
“Packets A and B of the same monatomic ideal gas have equal volumes V and equal temperatures T but different densities N_A / V and N_B / V. Packet A’s heat is (3/2) * N_A * k * T, and Packet B’s is (3/2) * N_A * k * T, where k is Boltzmann’s constant. Same temperature, different heat amounts.”
What do you make of that ?
“The Stefan-Boltzmann equation specifies the maximum amount of radiation that is emitted at a given temperature for a black body in thermodynamic equilibrium. It also insists that the black body must be a solid uniform body which is made from a perfect absorber of all wavelengths in the EM spectrum, and exists in a vacuum.”
Tenuc, could you firm up on the vacuum point please, it has been questioned elsewhere but seems obvious to me.
Can you link to a suitable source ?
I agree with the idea that a gravitational field can lead to this temperature gradient, provided that the gravitational force also has a gradient.
When we look at the troposphere, we have a distance of about 10 km. Compared to the Earth’s radius, this is a ratio of 10/7000 or 1/700. Since the Force is inversely proportional to the square of the distance, I would say that the difference between the gravitational force on a molecule at the top of the troposphere differs from that at the surface by only one part in 490,000.
How can such a tiny variation in the gravitational force have the affect being claimed by N and Z?
@Stephen: Same gas, same volumes, equal temperatures, different density = different energy content in each volume, yes
And I dislike physics algebraic short hand as it is a priest language to confuse laymen and prove to them that they are too stupid to understand science.
When I was young I was considered too stupid to learn to read and write, but science was easy.
Learning to read and write was a lot harder. Any scientist that has to use the priest language to converse with laymen is not smart enough to translate to real language.
Just the opinion of an old dirt farmer/refrigeration engineer/electrical engineer/etc. 😉 pg
It really boggles my mind how people can fail to see the elegant simplicity of this argument. It’s visible EVERYWHERE and it is EASILY testable.
Step One: Does gravity create air pressure? Of course, if we remove the earth from the atmosphere then the atmosphere would race in all directions unhindered and the pressure within would drop to zero.
So, easy enough and self evidently true… gravity causes pressure.
Step Two: Does pressure cause heat? Of course. Take a test tube of air, and normal room temperature and pressure. Now begin to raise apply a piston to the top of the tube, increasing the pressure in the tube without increasing the mass of the air in the tube. What happens to the temperature? It rises.
Increased pressure causes heat. It’s a fundamental law of physics.
So far so good.
Ah HAH! the opposition says.. but warm air has LESS pressure than cold air. Well, yes, because the atmosphere can be considered as being bound by an elastic container (gravity) which allows for the expansion on the atmosphere when heated, to an extent. It’s obviously not fully open to free expansion or there would be no atmosphere to speak of!
That counter pressure on free expansion of the energized gas manifests itself in HEAT because insofar as the gas is not allowed to shoot off into space, the energy can only turn to heat.
Likewise, there is another known variable that is so often missed in the “equilibrium” of the atmosphere: Atmospheric Escape. In this known process, super energized molecules of gas achieve escape velocity and leave the atmosphere all together. This is LONG been describes by science a “boiling” of the atmosphere, and I would bet the effect on the atmosphere is very similar to boiling water. With water, the act of boiling stalls the heating of the water at 100 degrees C as the energy is lost to steam.. in the gravitational theory of planetary warming we lose energy in the atmosphere to this boiling of the atmosphere to space.
This to is self evident as these energized particles, of leaving the atmosphere, take their energy with them.
So what have in the gravitational model is a system so pure and elegant that it not only applies directly to the Earth’s atmosphere, but is also equally applicable and observable on other planetary bodies and other systems both micro AND macro in nature.
Again, when we boil water at higher elevations the TEMPERATURE of the water is lower because the PRESSURE is less and the water more readily EMITS STEAM. This same function is in play with the atmosphere itself. The lower in the atmosphere you go, the higher the pressure and the more heat is required to reach equilibrium with expansion pressure.
Therefore, by very simple observation and deduction, gravity adds heat.
I do apologize for all of the typos in my last post. This proves the old adage that if you don’t care enough to proof read it then you shouldn’t care enough to submit it. 🙂
Ah, so it is wrong to conflate energy content with temperature and introducing the concept of ‘heat’ causes confusion because it could be applied to either.
So the denser air at the base of the atmosphere can have a higher energy content without a rise in temperature ?
That seems to provide a reason why one needs an external energy source to provide the temperature gradient.
Without excitation of the molecules from an external energy source the density doesn’t matter. The temperature will become even throughout the column.
With excitation the greater number of molecules in the denser region will absorb more of that energy and convert it to kinetic form to raise the temperature more than the temperature rises in the less dense areas. There will be a temperature gradient from bottom to top, dense to less dense.
If the external energy supply stops then the temperature gradient will fade away again.
In a non GHG atmosphere the problem is that one cannot get a radiative external energy source to produce an effect throughout the verical column so one is reliant on conduction from the irradiated surface.
We need to look at the example of a non GHG atmosphere in order to seperate out the gravitational GHE from the radiative GHE.
Conduction leads to convection even in a non GHG atmosphere so after a while one should still get the temperature gradient from bottom to top even in a non GHG atmosphere.
The denser molecules lower down must still absorb a disproportionate share of the energy supplied (this time from the surface) even at equilibrium and, just as before, will produce more kinetic energy and a higher temperature at the lower levels.
Any problems there ?
Joe ryan said:
“Increased pressure causes heat. It’s a fundamental law of physics”
IncreasING pressure certainly does but a problem arises when the pressure is no longer increasing.
There is still a gravitational effect but too small to achieve the outcomes observed. To deal with that one has to find an amplifying mechanism such as a differential response of air at different densities to an external energy source.
That seems to be implicit in the N & Z scenario and I’ve been trying to pin it down for some time.
See my post just after yours.
Hi Tallbloke,
As I’ve posted — with detailed calculus-y explanations — over on WUWT, thermal equilibrium is isothermal. It is literally a textbook exercise to prove this — it is one of the assigned problems in Caballero’s online book, for example. It is isothermal because one has to have detailed balance across any given surface in equilibrium — the same number of molecules moving in and out with exactly the same distribution of velocities and hence the same temperature.
What you’ve done (not really “you”, but you as a proxy for e.g. Jelbring) is asserted that gravity functions like a Maxwell’s Demon, letting faster moving molecules fall across a surface and slower moving molecules rise across a surface at the surface. This does not happen. If it did, one could rig up a Carnot Cycle engine from the bottom of a room in static thermal equilibrium to the top of the room and turn it on to move a fan that blows all of the air around and do work “forever” as gravity “resorted” all of those faster moving molecules to the bottom to drive the Carnot cycle once gain. The total energy of the room does not change (perpetual motion machine of the second kind.
So I’m sorry to say that Jelbring’s paper in particular is in clear violation of the laws of thermodynamics and more or less asserts as a “paper” the incorrect solution to textbook problems in thermodynamics, quite independent of any climate science. The definition of thermal equilibrium of any system is that it is isothermal. This is the zeroth law of thermodynamics, and the first paragraph in this reply is a nutshell/elevator speech proof of it in the context of gas confined to an adiabatic container. Only if the MB distribution of speeds of molecules moving in both directions across any interface in the fluid is the same (implying equal temperatures) and the number of molecules moving in both directions is the same (implying non-varying densities and pressures) is the fluid in equilibrium, whether or not the surface is vertical or horizontal or anything in between.
rgb
“IncreasING pressure certainly does but a problem arises when the pressure is no longer increasing.”
Ah, but applying heat to that compressed air causes it to heat faster that the air outside the tube under lower pressure, does it not? What pressure does is make the gas generate heat rather than expand. We can see this with water as sea level versus water at 7000ft in altitude. The PRESSURE forces the water to hold more heat as it impedes the formation of steam to a greater extent at sea level than at higher altitude.
The same is true for the atmosphere. Why can people readily accept that atmospheric pressure governs the boiling point of water yet completely miss the very same mechanism in the atmosphere itself?
In BOTH cases the true governing factors is gravity as atmospheric pressure doesn’t exist without it.
The moon is absent an atmosphere because it’s gravity is so low that an atmosphere can never be of sufficient mass to overcome the atmosphere’s ability to expand and the sun, therefore, accelerates all would-be atmospheric particles to escape velocity.
A thought experiment
If we construct an imaginary gaseous atmosphere with the pressure gradient requried by gravity (I think it can be of arbitrary thickness and arbitrary gravitational constant), and we then impose the constraint that there be no Gibbs free energy gradient. Does this require a temperature gradient, and will this be the adiabatic lapse rate?
So the denser air at the base of the atmosphere can have a higher energy content without a rise in temperature ?
How can it not? The energy per molecule is the same, and the air is denser and has more molecules!
Temperature is related to your choice of 1/2 kT per degree of freedom (equipartition) or (in a gas) the Maxwell-Boltzmann distribution of speeds. These things are directly connected to the definition of thermal equilibrium. The molecules at the base have, on average, the same MB distribution of speeds, but there are more of them and hence they exert a greater net pressure on the walls of the container (or surrounding fluid) confining them. The pressure and density adjust until buoyancy is neutral (producing a pressure/density profile that depends on the details of the intermolecular forces via the bulk compressibility of the material) but in thermal equilibrium the velocity distribution per molecule is the same everywhere or else transport occurs until it is. Gravity is a reversible force that generates no heat (the total gravitational potential of the system remains constant in equilibrium) and is irrelevant to detailed balance.
rgb
Robert Brown says:
January 17, 2012 at 5:48 pm “the total gravitational potential of the system remains constant in equilibrium)”
What equilibrium?
The earth’s atmosphere is in a state of constant change, when does it meet the equilibrium that you speak of?
“distribution per molecule is the same everywhere or else transport occurs until it is” is just not possible, if it was you would never have Tornadoes & Storms, they show massive heat differentials.
They way you speak is of theoretical “Ideal” gas conditions, when the atmosphere is anything but that because of all the water.
“Ah, but applying heat to that compressed air causes it to heat faster that the air outside the tube under lower pressure, does it not? ”
Yes I believe so and that is the amplification process that I mentioned.
So it isn’t the gravity in itself. Gravity just reorders the mass in the atmosphere so that when energy is added there is much more retained at the lower levels.
Thought experiment posed another way: what is dT/dP at constant G?
“letting faster moving molecules fall across a surface and slower moving molecules rise across a surface at the surface. ”
Isn’t it that the sun adds energy to the surface which then via conduction excites the molecules in contact with the surface giving them more kinetic energy and a higher temperature so that they then rise via convection and are replaced with cooler molecules that then receive the same treatment until all the molecules in the atmosphere become warmer but with a temperature gradient from surface to space ?
And the densest air being at the surface (due to gravity) that air insulates the surface for longest thus raising the surface temperature. Effectively delaying the loss of energy to space so that energy builds up in the atmosphere until a new higher temperature equilibrium is attained ?
A conductive greenhouse effect rather than a gravitational greenhouse effect then ?
So we have a radiative greenhouse effect and a conductive greenhouse effect but the latter depends on mass and not composition and so vastly outweighs the former ?
Robert Brown:
Your description of the reason for a uniform temperature distribution is quite compelling, and, believe me, I do understand that the mass fluxes across a horizontal plane have to be equal.
But, but . . . . There seems to be an “and then a miracle occurs” step between that fact and the conclusion of equal temperatures. Moreover, the equal-flux requirement does not seem inconsistent with the Postma animation over at WUWT. (Which shows a temperature lapse rate at the eventually reached equilibrium.)
No doubt there’s something extra in your explanation that blindingly obvious to you physicists, but, take it from me, some of us laymen find it a little elusive. I know it’s presumptuous after the effort you’ve obviously already put into making this stuff accessible, but could I impose upon you to take one more run at that part of the explanation?
So we have a paradox…
MASS determines the gravitational force on solids…
DENSITY determines the gravitational force on fluids.
The paper by Nikolov and Zeller also implies that DENSITY determines the gravitational force exerted on a fluid:
That is why the atmosphere and oceans stratify into layers.
That is why the Earth’s crust is lighter than the Mantle…
and the Earth’s Mantle is lighter than the Earth’s Core….
That is why a Professor of Nuclear Chemistry writes:
Proposed elevator speech for Willis’s parameters with a zero gas atmosphere, verses a non GHG atmosphere. (Any comments on this are appreciated in advance to correct my understanding.)
At its most basic only two things can effect the heat content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system. (David’s Law) ++NOTE
The addition of a non GHG increases the residence time of the specific heat at the surface, thereby increasing the specific heat above the S-B equation.
ThERE DONE!! (-; A few further basics for a longer elevator ride.
++ note, adding an atmosphere changes the system to a different system, with increased volume requiring more energy to have an equal T, which naturally happens to establish a radiative balance.
A zero atmosphere surface cools strictly through radiation. The specific heat of the BB surface reaches a certain level determined by the SB law, at which point the radiating temperature, radiates the heat away to match the input.
The existence of an atmosphere adds a second method of cooling the surface. That method is conduction.
Now the surface has two methods of cooling. These methods are not additive, (they do not accelerate the cooling) They are subtractive. (Now less of the specific heat is radiating from the surface, as some of the specific heat is now conducting.) ??????
The dry adiabatic lapse rate is g / Cp, where g is gravity and Cp is the specific heat of the atmosphere The lapse rate may be constant, but it is a constant VARIATION, which appears to be predicated on g and Cp. (IE, the greater the gravity in an otherwise equal atmospheric content of non GHG, the higher the specific heat of the atmosphere once it reaches a radiative balance) What does “specific heat emanate from? If specific heat, which is the heat capacity per unit mass of a material, then the more mass per volume, the greater specific heat per volume. Therefore an atmosphere of denser mass, (caused by either more atmosphere, same gravity, or more gravity, same atmosphere) will have a higher specific heat content then a thinner atmosphere. The lapse rate will be the same in all atmospheres, just the starting point or temperature will be different.????????
Conduction, just like radiation from a GHG, flows both ways. Some of this conducted heat flows back to the surface, similar to what a GHG does except via conduction instead of through radiation, and or also slows the flow of heat from the surface, raising the temperature of the surface above the S-B law.??????????
Stephen Wilde says:
January 17, 2012 at 6:34 pm
Stephen, we appear to be saying the same thing in slightly different ways.
Stephen Wilde says:
January 17, 2012 at 6:22 pm
“Ah, but applying heat to that compressed air causes it to heat faster that the air outside the tube under lower pressure, does it not? ”
Yes I believe so and that is the amplification process that I mentioned.
So it isn’t the gravity in itself. Gravity just reorders the mass in the atmosphere so that when energy is added there is much more retained at the lower levels.
Yes, but arguing an “amplification” isn’t particularly helpful in the real world where there is the Sun which provides the energy. While you can argue that without the sun the earth temperature drops to that of the surrounding space (or very nearly), so therefor the gravity doesn’t apply direct heat you can also argue the sister point to that without gravity there is no added heat either as the gas freely expands.
As such, the presence of pressure, due completely to gravity, can only result in added heat to the system. Given the “amplification” effect of gravitational pressure, it can be said that gravity adds heat to the system.
As I said over on the WUWT site, Willis’ argument isn’t compelling because he attempts to show “perpetual motion” in the gravitational theory by introducing a perfect, non-conductive atmosphere to prove that heat won’t remain in the system… but that is like using an imaginary perfect insulator to prove that refrigeration isn’t impossible because a refrigerator with a prefect insulator breaks the laws of thermodynamics. It’s the imaginary substance, not the theory, that breaks the law.
So it isn’t the gravity in itself. Gravity just reorders the mass in the atmosphere so that when energy is added there is much more retained at the lower levels.
I think this is a semantic argument at this point since you agree that with a given energy source and a given atmosphere the introduction of gravity raises the temperature of the atmosphere. We can argue what happens when the Sun goes out, or gravity disappears since that won’t be happening — the former for billions of years the latter never barring a planetary collision… in either case we aren’t worrying too much.
The N&Z Theory as presented gives us a very useful tool for establishing current and future climate because it measures the increased heat in the atmosphere that is introduced by the existence of gravity and air pressure, a “forcer” or “amplifier” that current models don’t account for and theirfor erroneously attribute to other forcers, mainly CO2.
Their theory is no different that the AGW theory that argues X amount of CO2 adds X amount of heat to the atmosphere…. obviously the CO2 isn’t generating the heat, right?
FINALLY, what we also get from the gravitational theory is another piece of the explanation for why solar variance is so amplified in the Earth’s climate while also giving us a coherent argument for the potential of AGW as a function of atmospheric mass and pressure. The combustion of solid fossil fuels into gas increases the mass of the atmosphere and a resulting change in overall pressure. Granted, that change is infinitesimal… but then we shouldn’t be disappointed by such a conclusion.
Hi David, yes I noticed that. I can’t understand why it isn’t so simple to everyone.
An atmosphere, any atmosphere interferes with the radiative energy balance by interposing non radiative energy transfer processes to make the surface temperature diverge from S – B.
I set it out at WUWT thus:
For a planet of Earth’s mass with a non GHG atmosphere:
i) Incoming to surface 240 W/m2 from sun plus conduction from atmosphere to surface 150 W/m2 = 390 W/m2
ii) Outgoing to space from surface 240W/m2 plus conduction from surface to atmosphere 150 W/m2 = 390 W/m2
Which explains why the outgoing radiation to space is less than the surface temperature would lead one to expect via S -B.
One just needs to attribute values to the dynamic (not static) thermal equilibrium between surface and atmosphere. Once one does that the numbers balance and it becomes obvious that GHGs are not necessary.
It is exactly the same process (delaying energy exit to space) as is suggested for GHGs so you can’t accept one without the other.
Either both are breaches of the Laws of Thermodynmics or neither are.
Both involve energy accumulation by delaying the exit of energy to space.
There is both a radiative greenhouse effect and a conductive greenhouse effect and the latter is vastly more powerful than the former because it involves the mass of the entire atmosphere.
Indeed it is likely that the radiative effect is neutralised by the ability of GHGs to radiate out to space.
It is all about mass, pressure and density. Gravity induced by mass creates the pressure and provides greatest density at the surface but it is solar input and conduction (and then convection) between surface and atmosphere that then plays the dominant role. The energy that accumulates at the surface in kinetic form is only indirectly a consequence of gravity.
“Willis’ argument isn’t compelling because he attempts to show “perpetual motion” in the gravitational theory by introducing a perfect, non-conductive atmosphere to prove that heat won’t remain in the system… but that is like using an imaginary perfect insulator to prove that refrigeration isn’t impossible because a refrigerator with a prefect insulator breaks the laws of thermodynamics. It’s the imaginary substance, not the theory, that breaks the law.”
I agree entirely.
At WUWT I pointed out that the only way Willis’s proposition could work was by insisting on a static equilibrium between surface and atmosphere with a zero interchange of conductive energy.
That allows him to ignore conduction altogether and it is that which introduces the energy imbalance in his scenario which he then uses to insist that GHGs are needed to resolve the ‘problem’ that his unreal scenario has caused.
Once the atmosphere heats up to surface temperature via conduction there is a lot of kinetic energy in air and on surface. It is inconceivable that the reality is a static equilibrium. The surface and atmosphere will be exchanging energy up and down via conduction all the time.
So all one needs to do is add a value to that energy interchange such that whatever goes one way also goes the other.
Do that and the whole energy budget balances with no GHGs required.
Needless to say that was the point at which he refused to accept my elevator speech despite having agreed the initial three stages.
His bias was palpable.
malagaview,
Looks like you double posted but my email server says your email server has a bad MX record, used to work. Email me please then I’ll delete this comment.
Tim
[Reply] Tim, my fault. I rescued the earlier post from spam without checking to see if MV had reposted it. – It’s happened before with MV and I don’t know why. – It’s a wordpress thang. I’ve removed the earlier post now. – Rog
Tallbloke,
“Bill, never never say that energy is created in discussion with physicists, it makes their knees jerk.”
Yes, I understand that. When I wrote that sentence my knees didn’t jerk, but my lip twitched and my toes curled. But I couldn’t think of another way of saying it, and It was getting late, so I plowed ahead anyway.
Thanks for the feedback.
Bill
rgb
Duke is a well funded University, why not carry out a larger scale version of the Loschmidt experiment at the Duke.
Robert Bown: Welcome, and thanks for calling by. It seems that meteorologists and engineers still use the classical mechanics outlined in the headline post, and come to the equal energy but thermal gradient conclusion, whereas physicists use statistical mechanics and arrive at the isothermal conclusion.
I’m curious as to why the two systems achieve opposite results. The whole issue seems to hang on this.
Roderich Graeff, who performed empirical experiments is sure there is a thermal gradient. He is a more than usually careful amateur experimentalist. Details of his methodology and results are to be found on the Loschmidt thread here
I second J Martin’s call for a well funded lab to replicate Graeff’s experiments. It might not decide the issue for everybody, but given that we still seem to be working with 150 year old thought experiments backing the classical and statistical mechanics theory, and given that real gases don’t behave much like ideal gases, it has to be worth a shot.
Wouldn’t you agree that such experiments might add to knowledge in fundamentally important ways?
Bill, never never say that energy is created in discussion with physicists, it makes their knees jerk. 🙂
Good point. I think some people (me included) are speaking of Earth’s climate in the parlance of climatology where X amount of a GHG adds X amount of heat to the system. Since, in the N&Z theory Gravity increases the atmospheric POTENTIAL to store energy we are too quick to adopt the same parlance and say that gravity adds heat. Both are wrong to a physicist even though the terminology has practical meaning given the assumed constant of energy input in the system we are setting out to describe.
It is not the climatic nature of matter that defines its energy, it is the electromagnetism of its molecules. Radiation causes conduction between electrons in the sub atomic particles of molecules.
To explain temperature, it is first necessary to understand the mechanism that creates it. That is, the effect on matter of the a Sun’s energy wave radiations.
The function of energy within matter emits radiation waves, in equilibrium with that received. Both infinitesimally small and those that we can see, matter conserves that which is needed to build molecules.
Energy cannot be stored beyond the equilibrium state of electromagnetism. Energy is emitted in pulses due to the lapse rate of dissipation of excessive introduced energy. Excessive energy is emitted by electrons not chemicals, they are emitted in waves.
Energy converted to conduction is prerequisite to convection and it is the thermodynamics of chemicals that reconverts Energy to radiation at the collapse of its atomic particles, rendering a end to the phenomenon in our atmosphere.
There are two facts of heat
1. It is energy relative to mass.
2. It has unlimited radiation in space.
But, gravitational energy controls mass and its convection (energy). Convection is not a cause of heat, but the thermodynamics of its distribution.
Therefore, the thermodynamics of GHG’s do not create energy, and the energy conservation cannot exceed the gravitational force of its matter.
Elevators! Gotta be a down button as well ya know Willis. IMHO, the paper that started all this is more robust then before these discussions.
But, gravitational energy controls mass and its conduction (energy). Convection is not a cause of heat, but the thermodynamics of its distribution.
…..sorry I meant to say conduction there.
@malagaview – comment January 17, 2012 at 2:34 pm…
Great idea which is not just a conjecture about why hot air rises, but has some ‘experimental’ support. Why when you blow a bubble does it rise at first then after a short time start to sink before it hits the ground? The more energetic warm air is trapped by the surface tension of the bubble and ‘floats’ up through the higher density air. It rises as a spherical parcel then, after a short time cools and slowly sinks back to the ground. Big question is why it cools so quickly!
Couple of links showing bubbles in action… 🙂
@Stephen Wilde – comment January 17, 2012 at 4:05 pm
Just something I know from my university physics course. I vaguely remember it had something to do with the second law and local von Neumann entropy. Local entanglement between the solid surface and gas molecules gives rise to an increase of the local entropy of the gas. Interesting and unpredictable thing always seem to happen at boundaries!
A search for “Clausius law | surface | entanglement” may yield a reputable source to quote?
Thanks to all the gerfuffle, I realized I really had to do my homework, and I’ve finally read Nikolov & Zeller properly.
It’s a cracker! a paradigm-shifter! easy to read (apart from the maths but the logic shines through)! a true nobel-prize winner! Halleluja. Amen brothers. Well, laughter aside, I’m all there.
Lots of important details the paper brought to my notice. Like the anomalously high downwelling radiation. And the really spatially-sensitive calculations that show the temperature increase over the “black-body” Earth without atmosphere is ~ 133°C, not 33°C. And the “fit” with moon temperatures (I also checked that at WP). And the “fit” with all the planets. And more. Far, far too much to simplistically dismiss.
Now it would help “sell” the paper IMHO if Nikolov & Zeller could convert their Fig 5 and Fig 6 into logarithmic scaled graphs, to produce straight lines. It would then be far easier to see how well Europa, Triton and Mars fit, and of course, Venus would be on the same page, no extension should be needed if scaled well. AND… the Earth graph of temperature/pressure should be scalable to make a direct overlay. This way we combine general knowledge from mountain climbing etc with reasonably easy checkable astronomical knowledge, in one compelling straight line graph…
It would also help “sell” if an FAQ could be prepared, to address key comments including from the likes of Willis and Joel, no matter how elementary, irrelevant or inane… 🙂 but I think you may already be working on this.
It’s also firing my imagination w.r.t. running a pilot wiki project targeted specifically on all this back-to-gravity stuff, N&Z, Jellbring, Bill Gilbert, etc
@tallbloke says:
January 17, 2012 at 9:01 pm :I’m curious as to why the two systems achieve opposite results. The whole issue seems to hang on this.
Meteorologists and engineers live and work in the real world and have to reach real solutions.
Physicists work and live in Ivy Towers and create beautiful mathematical constructs and pat each other on the back about their genius. Only they can understand the deep thought involved. It is not important if the world does not quite match their formula. If they yell loud enough and point to their “Letters” they win the argument. At some point those of us that have to get real work done have to quite the field and go back to work. Argument is their field of work.
“Physics is the science of things that don’t work.”
“Applied science is about of things that work”
If you want to create an understanding of the functions of the real world, demote the physicists to the level of noisy rabble as that is what they generally are. Meteorologists and engineers are more likely to understand the real world and will work together, as they have to reach real conclusions and solutions. pg
Tenuc says: January 17, 2012 at 9:49 pm
The more energetic warm air is trapped by the surface tension of the bubble and ‘floats’ up through the higher density air
Don’t know if you have watched the Water, Energy, and Life: Fresh Views From the Water’s Edge lecture by Dr. Gerald Pollack… wonderful research especially regarding surface tension… or the crystaline structuring of water in the boundary layer which has a negative charge [while the interior is positively charged]… which connects into many threads in science… amazing stuff!!!
Stephen, wouldn’t a non greehouse atmosphere be much like the subsurface soil of the moon? ie it only gains heat or loses heat by conduction. From memory, the temperature of the moon about a metre or more down does not fluctuate much over a lunar light cycle and the temperature approximates what a planet would be with no atmosphere at this distance from the sun.
Stephen Wilde says:
January 17, 2012 at 8:33 pm
“…Once the atmosphere heats up to surface temperature via conduction there is a lot of kinetic energy in air and on surface. It is inconceivable that the reality is a static equilibrium. The surface and atmosphere will be exchanging energy up and down via conduction all the time…”
Just had another off the wall thought while trying to get a handle on how much energy is transferred by conduction. This will depend on how many molecules are contacting the surface at any moment in time and the surface area available. That’s when I realised that because the surface of the earth is fractal in nature we need to calculate the size at the scale of the nitrogen molecule thus the effective surface area for collision will be far bigger than that of a smooth Earth size sphere.
Anyone know surface area of the Earth at the scale of a nitrogen molecule?
Answers on a (crumpled) postcard please… 🙂
dlb,
There is some discussion that there may be some radiative emission in non IR wavelengths but conduction seems to be the main pathway for energy to both enter and leave a non GHG atmosphere.
Air being much less dense than the ground a non GHG atmosphere also involves convection and associated overturning because you must get that with a rotating sphere and an uneven surface because the solar irradiation will be uneven.
Therefore I don’t think those who suggest a uniform temperature throughout the non GHG atmosphere can be correct. That deals with the potential problem of a non GHG atmosphere getting so hot that it gets blown off into space.Cooler ground will absorb more energy from the air by conduction when on the night side or in shadow and warmer surface will release energy to the air by conduction during the daytime so as to produce a circulation.
As to the distribution of that circulation globally I haven’t given that much thought as yet.
Mind you it could be very vigorous because here we are considering an atmosphere free of GHGs which includes water vapour and we all know how fast a surface beneath dry air radiates energy to space at night.
There could be huge and fast flows of air between night side and day side and if there is a tilt as with Earth also large flows of air between the poles due to their differing seasons.
I think I’m the first person to raise that interesting issue of a potentially very vigorous atmospheric circulation in a non GHG world.
Anyway I don’t think a comparison with the Moon’s subsoil would be appropriate.
@Stephen Wilde says:
January 17, 2012 at 11:37 pm “I think I’m the first person to raise that interesting issue of a potentially very vigorous atmospheric circulation in a non GHG world.”
How about Mars, IIRC It has little GHG (almost no water) and very high winds caused by heating differences of dark to day. pg
Good example PGS but GHGs on Mars are high in relation to total atmosphere.
Everyone discussing a non GHG atmosphere so far has been suggesting that the atmosphere would be very even and stable or with a dry adiabatic lapse rate similar to Earth’s.
I think they have been distracted by Willis’s highly artificial model with a flat surface and multiple suns.
Stephen,
Agree there could well be a very vigorous circulation but I still am certain when you average the atmosphere from night to day, surface to altitude the average temp of such will be the black body figure for this non GHG planet.
Steven Wilde; you said, refering to GHG and non GHG,…
“Both involve energy accumulation by delaying the exit of energy to space.”
plus many other things we apparently agree on.
Steven, then my “law” must appeal to you. Can you think of any exceptions to it?
Also is my simple elevator speech acceptable?
At its most basic only two things can effect the heat content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system. (David’s Law) ++NOTE
The addition of a non GHG increases the residence time of the specific heat at the surface, thereby increasing the specific heat above the S-B equation.
An earth size planet, nitrogen and oxygen only atmosphere, No water, no carbon oxides, no nitrogen oxides. no ammonia? Damn Stephen, I don’t think I can create one of those. It would violate too many laws of reality. Maybe Willis can create one, he is the genius that can create something like that. 😎 pg
BTW, I do not see how we possibly know how the Earth’s mean W/m2 radiation of the actual surface of the oceans and land. It would have to be measured directly, with no atmosphere, at 0 elevation. At every level of the atmosphere we are dealing with surface radiation, latent heat, convected heat within non GHG, etc. All we got is TOA incoming, maybe, and TOA outgoing, maybe.
?????
Actually even that won’t work, as oxygen and nitrogen are the true greenhouse as they are more transparent to incoming radiation then outgoing radiation.
Mind games are for confusion and not for illumination. pg
Some way above here, I raised the case of an airless, sunless planet without an internal heat source that passes through a cloud of gas, thereby acquiring an atmosphere, and argued that
“… eventually, the thermal energy released in the gravitational compression of the atmosphere will be entirely dissipated, by which time the temperature of the planet surface will have returned to its original value of 2.75 K (i.e., the microwave background temperature), though the atmospheric pressure gradient from the surface to outer space remains.
So the gravitational effect on the surface temperature is transient only.”
In response, tchannon stated:
“For an isolated body without a sun, yes.
For a rotating planet with sun, no. (for at least the reason the atmosphere is never in steady state)”
Well, I’m happy to spin the planet and add a sun for it to orbit, but I don’t see how this changes the mean surface temperature, provided that the atmosphere is transparent.
At equilibrium, planet-wide outgoing radiation at the top of the atmosphere matches planet-wide incoming radiation at the top of the atmosphere. But as the atmosphere is transparent, outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at surface of the planet, which means that the mean surface temperature must be the same with an atmosphere as without.
Admittedly, scattering may make a difference, but not one that will be affected by gravity. And the atmosphere will act as a thermal buffer, making the cooler and the nights warmer.
Is this not correct?
TB, I honestly don’t have anything to add to this conversation. It isn’t the focus of my involvement in the climate debate. I just thought I’d pop by and say hey.
In a nutshell, this is my take….. Gravity is a Force. A force causes work to be done.(It needs mass to do so.) Work cannot happen without energy.
I’ll let the rest of the able people work out the rest.
P.S. I was going to leave a note for Willis Eschenbach at WUWT in response to his claim that there is somehow a matter of principle involved in whether or not you allowed all and sundry to comment here. However, WUWT seems to be having a protest about something, which denies access to the relevant post, so I will make my point here: namely, that as I understand it, Tallbloke’s Talkshop is a personal blog, not a public institution and, therefore, the proprietor must be free to allow or disallow comments as he pleases. In fact, I did once read the rules of the place and recall that there was something sounding almost like a rule requiring participants to be polite. That, I should think, provides grounds to exclude most obnoxious people, and with fair warning.
@ CanSpeccy…… Yeh, there are a couple of bills in the U.S. congress that would change the internet, if passed. Basically, it would allow the entertainment industry to monitor the internet for infringement of their material.
The fact that they already do this, I guess, is beyond many. The implications are horrible and would, in essence, transform the internet into a corporate media extension. The clever people at Wiki and Reditt have determined the best way to show them they can’t infringe on our freedoms is to not exercise our freedoms! Like gravity/force/energy , I’m still working that one out. Seems G/F/E is more reasonable.
As to WUWT, Willis was in error on several levels. Anthony chose to shut it down by playing with the protestors. You see, we hate censorship, but if you state what we don’t like, well, then we’ll just shut it down. Surely you can see how morally superior that is as opposed to letting a person run his own blog?
Please note, I’m a faithful WUWT reader and commenter. And will probably remain as such. Willis to me is like fingernails on a chalkboard. And I despise hypocritical moral condemnation. Moral condemnation, I’m good with. It’s the hypocrisy I can’t stomach.
dld said:
“I still am certain when you average the atmosphere from night to day, surface to altitude the average temp of such will be the black body figure for this non GHG planet.”
That is the issue isn’t it ?
Earth’s atmosphere is warmer than the S -B black body equation says it should be so we need to know whether that is primarily due to composition (GHGS) or total mass (including Oxygen and Nitrogen).
There is bound to be an energy exchange via conduction and convection between atmosphere and surface isn’t there ?
That exchange is seperate from the in/out radiative exchange.
So given that the surface/atmosphere energy exchange is there disrupting the simple in/out energy flow of a simple black body how could you balance the energy budget without a rise in surface temperature ?
The surface has to become warm enough to support BOTH the surface/atmosphere conductive energy exchange PLUS the radiative system in/out exchange in parallel. The surface temperature must rise to achieve that and we see it on Earth where the surface pressure requires a surface/atmosphere energy exchange of 150W/m2 to balance the energy budget with 240W/m2 in and 240W/m2 out at equilibrium.That is why we see about 390W/m2 going out from the surface but only 240W/m2 leaving to space. The atmosphere (the total mass and not composition) requires that 150W/m2 to carry out the conductive energy exchange at the surface and the surface has to be warm enough to match it. Otherwise no equilibrium.
Over to you.
CanSpeccy said:
“outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at surface of the planet, which means that the mean surface temperature must be the same with an atmosphere as without.”
Not so, because the atmosphere decouples the surface from space.Outgoing has to match Incoming at top of atmosphere but NOT at surface.
The surface and atmosphere have their own independent energy exchange going on via conduction and convection and the system has to provide the energy for BOTH. Any leakage from radiative to conductive results in disequilibrium.
GHGs introduce an additional radiative component in the air but ther ability to radiate out probably negates their effect.
“BTW, I do not see how we possibly know how the Earth’s mean W/m2 radiation of the actual surface of the oceans and land. ”
It is done by measuring the outgoing at top of atmosphere by satellite and then applying the S _ B equation backwards to arrive at the temperature that the surface should be.
There is no empirical proof that the surface is therefore any particular amount warmer than it should be but there are estimates that suggest around 33C.
N & Z think it is actually more than that but I await their fuller details on that aspect.
Either way the difference is what the surface/atmosphere conductive energy exchange requires over and above that required by the top of atmosphere radiative energy exchange.
The surface / atmosphere exchange involves conduction and convection so ALL atmospheric mass is involved. It is not a radiative GHG issue.
Re Leonard Weinstein (January 16, 2012 at 9:21 pm).
So far so good, Leonard. Thank you for the clear exposition. But questions remain. For instance, in an atmosphere containing radiative gases what role do the non-radiative gases play in fixing the mean height of mean out-going radiation and thus the average surface T? None at all? If the amount of N2 (+/- O2) in the earth’s atmosphere was, say, doubled, or halved, or removed altogether (while keeping the content of radiative gases fixed) what effect (if any) would that have on surface temperatures? I find it hard to believe that there would be no effect. A comparison with Mars springs to mind. I presume there is material in the literature that would answer this question, but I haven’t come across it yet.
“Stephen, then my “law” must appeal to you. Can you think of any exceptions to it?
Also is my simple elevator speech acceptable?”
I have no problem with either. Getting others to accept it is the problem. N & Z are helping a lot.
I proposed my own ‘Law’ a while ago. Must try and find it 🙂
Tallbloke, always the gentleman -very kind to Robert Brown. P G Sharrow your words I have thought but did not want to say.
Could I suggest that Robert Brown reads the first 8 chapters of Perry’s Chemical Engineering. Maybe the empirical formulae and other maths is a bit much to grasp but he may just get some ideas which could open is mind. Could I just mention some words in these chapters – chap 2 ThermoDYNAMIC properties, transport properties, prediction & correlation of physical properties, chap3 Maths, Numerical analysis, statistics, chap 4 ThermoDYNAMICS, Chap5 Heat & Mass Transfer (including conduction, convection, phase change, radiation, emissivities of combustion products, flames & particle clouds, combustion chamber heat transfer, mass transfer) Chap 6 Fluid DYNAMICS (including compressible flow, multiphase flow, fluid mixing, computional fluid DYNAMICS -a speciality of Prof Claes Johnson). Chap 6 Reaction Kinetics Chap 8 Process Control (including Process DYNAMICS)
Stephen Wilde says:
January 18, 2012 at 8:37 am
“BTW, I do not see how we possibly know how the Earth’s mean W/m2 radiation of the actual surface of the oceans and land. ”
It is done by measuring the outgoing at top of atmosphere by satellite and then applying the S _ B equation backwards to arrive at the temperature that the surface should be.
There is no empirical proof that the surface is therefore any particular amount warmer than it should be but there are estimates that suggest around 33C…..
————————————————————————————————-
I am curious because as I mentioned it appears logical that as I stated , “Now the surface has two methods of coolinng. These methods are not additive, (they do not accelerate the cooling) They are subtractive. (Now less of the specific heat is radiating from the surface, as some of the specific heat is now conducting.) …then further talk about the exchange and conduction being slower then radiation, etc.
My understanding would increase with a better grasp of what ultimately happens as conducted specfic heat propagates to the TOA, and finally exits the earth’s atmosphere, It sounds to me like conducted specific heat in a non radiating GHG can only keep moving the energy back and forth through the atmosphere conductively, until that energy conducts to a material which radiates in the LWIR, this could be the surface, this could be GHG, primarily water vapor, this could be any number of particles within the atmosphere.
Regarding my Law, (-; really just once I understood that concept it has helped me think about energy and thermal dynamics with a lot less confusion, Indeed, incorporate the oceans with a 12 hour on energy and a 12 hour off energy plus the vast GHLiquid. with “residenced time” of days, years, decades, centuries, and no wonder we are far warmer then S-B. A warming ocean is each day recieving X energy, the next day some of X energy is still there as it recieves another dose of x energy, the next day some of the past two days x energy is still there as it recieves another dose, etc etc.
Steven Wilde, as I have seen very little response to what we have proposed, others have mentioned conduction as well, what is the best criticism you have seen so far, and what has Willis said, as I cannot find direct responses to any of several posts I have made.
@Stephen Wilde
““outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at surface of the planet, which means that the mean surface temperature must be the same with an atmosphere as without.”
Not so, because the atmosphere decouples the surface from space.Outgoing has to match Incoming at top of atmosphere but NOT at surface.”
I understand that the atmosphere decouples the surface from space. But we are talking about mean planetwide radiation.
All radiation from the surface of the planet must emerge from the top of the atmosphere, because the atmosphere is transparent, and, at equilibrium, outgoing radiation at the top of the atmosphere must match incoming radiation at the top of the atmosphere (if scattering is ignored), so my contention stands: the mean surface temperature must be the same with an atmosphere as without
suyts
Re: hypocrisy
Yes, it seems odd for anyone at WUWT to demand unrestricted free speech on someone else’s private blog while WUWT holds anything that I say there for “moderation.”
And unrestricted free speech is not exactly the basis upon which science has thus far advanced.
Any idea may be proposed, but publication and general circulation of the idea depends on whether the author can convince certain people that what they say is true.
And the fascinating thing about this process — and this is a point that few people understand — is that that the monitors, the editors, the peer reviewers, the owners of blogs etc., may be no less fallible than the cranks coming up with the new ideas!
Which means that scientific beliefs depend much than most people realize on opinion rather than on irrefutable demonstration of fact.
“because the atmosphere is transparent, ”
A non GHG atmosphere is not transparent to conduction. The conductive energy exchange betwen surface and atmosphere must be accounted for and it is that which accounts for the apparent imbalance.
David,
There has been no attempt to counter the conduction points. They have been ignored.
Anyway the Willis model is impossible for reasons I pointed out over at WUWT so I suggest we get away from it and focus on the Earth.
The N & Z proposals seem very satisfactory to me so far and very much mirror my 2008 article as here:
http://climaterealists.com/index.php?id=1562&linkbox=true&position=7
” Greenhouse Confusion Resolved”
In fact I’m hard put to find a significant difference 🙂
and since you mention the oceans see here:
http://climaterealists.com/index.php?id=1487&linkbox=true&position=5
” The Hot Water Bottle Effect”.
I’ve been busy the past four years.
Lucy Skywalker says:
“All this underscores more and more what I see as a sore need to develop a form of climate skeptics’ wiki that can handle the actual science, development thereof, alternative theories, and all in language that a reasonably intelligent but not necessarily science-educated layman can understand.”
I think your idea of a wiki able to hold data, relationships, equations and explanations in a ‘plain English’ format is very much needed. Absolutely! Such insight!
Blogs are absolutely terrible at doing so. As comments dig out and refine thoughts, they just get lost in the flow of posts. Such a waste! Huge waste!
These should be summarized and moved to some permanent archive so anyone can search on them and point to at any later time without carrying paragraphs around. Even though each entry may not be as beautiful as Wikipedia due to our limited time, that’s ok, at least they would easily make sense to everyone at all levels of education.
Great idea. That would be a winner. This may need a later top post but now, how does someone start one and who has a server? I wish WordPress would host it, it would significantly shrink their storage requirements overall.
OK, answers to a couple of questions. First, about Joe’s simulation on WUWT — good idea, poor implementation. An assumption that has to be satisfied in any discussion of temperature is “local thermal equilibrium”. That is, any parcel of gas to which you wish to assign a temperature has to be “in equilibrium”, which specifically means that it has to be thermalized, to have a distribution of e.g. velocities or energies consistent with the Maxwell-Boltzmann distribution. One particle does not have a temperature, even if it has an energy. Ten particles do not. ten thousand particles might, depending on context and time. In order to be able to describe temperature variation with height, the mean free path of molecules in the air/atmosphere in question has to be small compared to the variations in e.g. velocity imposed by gravity, or, as Joe states, air molecules will slow as they rise because they don’t hit anything and aren’t supporting any higher molecules via buoyancy. Buoyancy, incidentally, requires similar conditions — in order to describe the buoyant force on a coarse-grained chunk of fluid, there have to be many molecules that are incident on the “boundaries” of the fluid per unit time.
It’s a good idea, but Joe’s fluid in his simulation simply doesn’t have enough particles — the fluid isn’t in thermal equilibrium because the mean free path is almost as large as the container. To put it another way, if he plotted the velocity distribution as a function of height at no height would it look like a MB distribution at temperature T.
Second, my comment about egregious violation of the laws of thermodynamics were specific to Jelbring, who (IIRC, I’m not looking at his article again as I type this) explicitly asserted a column of fluid with no energy inputs, and then claimed that in equilibrium it would exhibit a thermal gradient. No, it wouldn’t. This violates the zeroth and second laws of thermodynamics. Thermal equilibrium means “has the same temperature”, and the spontaneous separation of the fluid into a hot to cold gradient gives the fluid the capacity to run a heat engine (completely contained in the adiabatic system) between the two reservoirs forever, because as fast as the heat engine equalizes the temperature, gravity resorts the molecules top to bottom and re-establishes the thermal gradient. This is a perpetual motion machine of the second kind. If you can ever build one of these given the results of some assertion, you know that you are in trouble because — no you can’t.
As for the zeroth law and thermal equilibrium, it’s difficult to do much better than I did with a moderately rigorous description of the calculus of detailed balance, but I’ll try.
Suppose you have a thermometer. A thermometer, recall, measures temperature. It does so on the basis of the zeroth law. You put the thermometer into thermal contact with (say) a fluid at some temperature and heat flows in or out of that fluid (presumed to have a lot more heat content than the variation so the thermometer itself isn’t changing the temperature much) until the two are in thermal equilibrium If it is a mercury thermometer, the mercury expands or contracts thermally out of a reservoir and you can read the temperature off of a little scale on the side that basically transforms the volume of the mercury into a temperature. Understand? Suppose your thermometer reads 20C.
Now you move the thermometer somewhere else. You put it into a glass of water, or take it with you on a road trip and drive a few hours. You wait for it to come to equilibrium with its environment and check it and again you see it real 20C. What does this mean?
Specifically, it means that the two systems (with well-defined local equilibrium temperatures) have the same temperature. If you put the thermometer into system A and it reads T_A, and put it into system B and it reads T_B, if T_A = T_B they have the same temperature. But what, exactly, does “have the same temperature” mean?
It means “if A and B are placed in thermal contact, they will be in mutual thermal equilibrium, specifically no net heat will flow from A to B or B to A.”
That’s the zeroth law. It defines the thermal equilibrium of two systems as the condition where no heat flows in between them, and establishes the transitivity of equilibrium:
Zeroth Law: If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then system A is in thermal equilibrium with system B.
This law is the basis of the thermometer, system C in my example. If we know the thermal properties of system C so that we can transform its equilibrium state into a linear scale of temperature (I will skip the historical process that lead to not only managing this but establishing the absolute or kelvin temperature scale) we can make it into a thermometer, and use it to predict whether system A and B, brought into thermal contact, would exchange heat.
The first and second law are also important in this process. In order for the systems in question to be in equilibrium, we have to manage energy flow into and out of them. First law states that we can’t have heat flow in or out (adiabatic) or work coming in or out, although it allows for a quasi-static progression through a set of states with the same temperature that takes in heat and transforms it directly into work (isothermal expansion). This kind of process can occur, but cannot be made into a cyclic process that “just” makes heat into work. The Second law establishes (among other things) the direction of heat flow. It always flows from the hotter to the colder system when they are placed in thermal contact so that they can exchange heat. Heat can never flow from the colder to the hotter system, nor can a single system evolve in time into a thermal equilibrium with different temperatures at different places as long as heat exchange is possible between those places.
So now imagine a supposed column of air that has spontaneously separated into a low temperature at the top and a higher temperature at the bottom because gravity has compressed the fluid until it is in static mechanical equilibrium. From the zeroth law, this means that if you put your thermometer in the top it will read T_t, and if you put your thermometer in at the bottom it will read T_b, where T_b > T_t.
Now imagine taking a thermally insulated silver wire that is exposed at the top and the bottom so that it is in thermal contact with the fluid there and only there. Place it into the fluid vertically, so that the top of the wire is in contact with gas at T_t, the bottom of the wire is in contact with the fluid at T_b. What will happen? Well, now you’ve got a piece of silver (an excellent conductor of heat) with a temperature gradient across its ends. Obviously, heat will flow out of the fluid at the bottom and up to the fluid at the top, cooling the bottom, warming the top. You must now use your common sense and experience of the world to predict which of the following will be true:
a) Heat will flow forever — as fast as it is delivered to the top, gravity will somehow re-sort the energy so that it flows back to the bottom and keeps it warmer than the top, to be picked up by the silver and conducted back up to the top, to fall to the bottom, to be conducted to the top, to fall to the bottom…
b) Heat will flow until the top and bottom are, in fact, in thermal equilibrium. They were not in equilibrium before. Only when the temperature of the top and the temperature of the bottom are the same will heat stop flowing in the wire, and once that is established the system is truly in equilibrium.
In the latter case, of course, you don’t need the wire. The gas itself conducts heat. In general, you never need “a wire” within a system. If you imagine using your thermometer to measure the temperature of any two neighboring coarse grained chunks of fluid (big enough to internally be in “thermal equilibrium”, small enough to be considered differential chunks as far as calculus and secular changes in gravitational potential and so on are concerned), the only way that heat will not flow between the two chunks (that are in thermal contact) is if the thermometer reads the same thing when it is in contact with each chunk separately. Otherwise if you connect them with an imaginary silver wire (that really only represents the process of heat conduction), heat would flow.
That’s the importance of the zeroth law in this discussion. Thermal equilibrium is isothermal, period. Otherwise it literally contradicts the simplest and most ubiquitous of our experiences of heat — that it flows from hot to cold, that it only flows if things aren’t at the same temperature, that thermal equilibrium is transitive (so we can build devices that measure equilibrium and quantify it as a temperature).
So much for Jelbring. No, under no circumstances will an isolated fluid establish an eventual equilibrium with a thermal gradient. But what about N&Z?
There I have no real idea, because when I read their paper (well, poster) originally, it didn’t describe how compression was supposed to heat, only made noises about density, pressure, and temperature in an open (non-adiabatic) system being heated by the sun. Really, in a whole series of such systems — all of the planets and moons with atmospheres, supposedly. I still don’t feel particularly warm and fuzzy about their assertions, though. There are two things at issue.
First, there is the real physics of the adiabatic lapse rate. This physics presupposes a planetary surface that is continuously being warmed, so that heat is continuously flowing outward from the dense, high pressure atmosphere at the bottom to the near vacuum, low density atmosphere at the top. There are many mechanisms that enable this heat flow — convection, conduction and radiation — and all three obey the simple rules for thermodynamics — heat flowing from hot to cold, not the other way around, for example. Given certain assumptions — primarily that moving a chunk of air quasi-statically up and down in the atmosphere (where it expands and cools to match its local density along the way) is an approximately adiabatic (reversible) process — adiabatic expansion, the same kind of thing that turns heat directly into work — one can derive a density/temperature gradient for the air column, the so-called adiabatic lapse rate.
This physics is not new, is not due to N&Z, and is thermodynamically valid reasoning although a particular idealization of the real atmosphere that isn’t necessarily or generally satisfied as anything like a law within our atmosphere. It is more like a semi-quantitative argument for understanding the thermal profile of the troposphere, even though one knows that if one actually measures the thermal profile via a sounding above any given spot on Earth, it will probably not match this rate. Again, in climatology all of this is well understood, and anyone who wants to understand and is willing to slog through some physics (some of it nontrivial but none of it beyond what physics majors typically learn in their first three intro/review courses in physics — mechanics, E&M and modern physics — before starting in on the real work of learning it in detail) can read Caballero’s online book on physical climatology and come to understand it and even understand wet air and precipitation and stable vs unstable atmospheres and how buoyancy and thermal driving at the bottom create and sustain heat transport within the atmosphere both vertically and horizontally.
Second, there is the suggestion in N&Z that there is something else going on, that gravity somehow creates either a heating or trapping of energy so that the bottom of an atmospheric well will always sort itself out to be hotter on the bottom, hotter in some predictable way compared to the top. In this picture — and again, here I’m very uncertain because nobody I communicate with understands N&Z any better than I do as they do not really explain mechanism in their paper in an understandable way — the heating of the atmosphere on the bottom isn’t important — you can heat it on the top if you like — and the greenhouse effect isn’t important as long as the planet is in radiative balance: the bottom of the atmosphere will be warmer than the top in a predictable way that depends only on the base density of the atmosphere. The clear implication is that this gravity-driven “process” (whatever it is) is somehow responsible for some fraction of the warmer temperatures on the surfaces of planets than one would expect for an ideal superconducting perfect absorber zero albedo blackbody.
Here I cannot really comment on the physics. I’d have to have a clue as to what the physics being asserted is to comment. But my bullshit detectors are out full force, as their argument sounds a lot like a reworking of Jelbring, and the final state that they describe sounds like it could be heated on the outside, and hottest on the inside in steady state even when the heat isn’t actually being differentially delivered to the bottom.
This, as the argument above should make clear, cannot be correct in any sort of equilibrium system, and it violates a variety of very simple physical principles — Gauss’s Law for a vector description of energy flux, for example — unless some very interesting structuring of the energy flow occurs, energy flow that I think violates all sorts of physics. Heat, recall, can never spontaneously flow from cold to hot (not even with gravity around, not even “on average” in convection) unless something is doing continuous work on the system. Gravity cannot do continuous work. Radiation heating of the top of the atmosphere cannot do continuous work that carries heat down to make the bottom warmer than the top because the heat equation is not a wave equation, it is the wrong order and requires that thermal gradient to establish a net flow.
To put it another way, in an optically thick atmosphere, the only way the inside well inside the optical path thickness of the atmosphere can maintain an outward directed thermal gradient is if there is net production of heat inside! Heat always flows from hot to cold, so if there is a thermal gradient, heat is flowing out from hotter to colder. That’s what heat does. This flow removes heat from the interior of a closed sphere. The energy content of that sphere therefore decreases (first law) unless one is continually adding or releasing energy inside of it.
In collapsing protostars, gravity is in fact doing work and adding net energy inside any given concentric spherical volume, some of which does squeeze out as heat and is given off as radiation, gradually raising the temperature. This goes on a long time, because the protostar isn’t in equilibrium. Wait long enough, and either you find a black dwarf — all of the heat squeezed out, the star cooled, and it is now at equilibrium with no thermal gradient — or it gets hot and dense enough at the center to ignite fusion, and you get a real star with a real heat source at the center that burns until the fusion fuel is exhausted and then follows one of several paths to the eventual heat death of the Universe (neglecting global things like opened vs closed that might intervene a few hundred billion years hence).
In a big (gas giant) planet like Jupiter, there may still be some collapsing action at the center to explain how its center is giving off heat.
In the case of the Earth and the smaller rocky planets, this isn’t still happening, not to any significant extent. Yeah, the core is giving off some heat from natural radioactivity and tidal heating and is still molten from its original formation, but the crust is thick and a poor conductor of heat, most places. I’m not seeing any reasonable way for there to be a temperature gradient due “just” to atmospheric compression as heat cannot flow from cold to hot without a source of work pushing it.
rgb
Robert Brown says:
Second, my comment about egregious violation of the laws of thermodynamics were specific to Jelbring, who (IIRC, I’m not looking at his article again as I type this) explicitly asserted a column of fluid with no energy inputs, and then claimed that in equilibrium it would exhibit a thermal gradient. No, it wouldn’t.
Hi Robert,
I think the laws of thermodynamics talk about energy, rather than temperature or heat, but there are several formulations of them, so maybe we’d better discover who is using which definitions. We’d better do this, because in the application of classical mechanics to energy distribution in the model atmosphere, as defined by Hans Jelbring, there will indeed be a thermal gradient, as confirmed by Graeff’s empirical experimental data (Which should be replicated by an accredited laboratory).
“if A and B are placed in thermal contact, they will be in mutual thermal equilibrium, specifically no net heat will flow from A to B or B to A.” That’s the zeroth law.
Assuming your A and B have at least some dimension, then a thermal gradient across them would mean that the top surface of A will be at the same temperature as the bottom surface of B where they contact. Therefore no heat will flow. Even so, the average temperature of the whole of body A will be higher than that of B. QED.
http://www.emc.maricopa.edu/faculty/farabee/biobk/biobookener1.html
Laws of Thermodynamics
Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work. Thermodynamics is the study of energy.
First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. Click here for another page (developed by Dr. John Pratte, Clayton State Univ., GA) covering thermodynamics.
The Second Law of Thermodynamics states that “in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state.” This is also commonly referred to as entropy. A watchspring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it.
———————-
I’m not seeing the words ‘heat’ or ‘temperature’ in these definitions, so please could you clarify. Thanks.
I’m not looking at his article again as I type this
Maybe you should. This is one of Jelbring’s chief complaints. People answer what they think he said, instead of answering what he actually said.
No takers on my Gibbs energy approach. I’m disappointed.
Let’s again return to my imaginary planet. It has an atmosphere of ideal gasses. The pressure at the planet surface is 1 bar. The conditions at the edge of the atmosphere are the conditions of outer space (To, Po). The planet has been there for a few billion years; the atmosphere is at equilibrium. Z is the vertical direction from the surface of the planet to the top of the atmosphere.
Equilibrium is, by definition, when Gibbs free energies are equal. Thermodynamics thus requires that there be no Gibbs energy gradient: dG/dz = 0. But dG = -SdT + VdP. Doing some simple math we find that dT/dP (constant G) = V/S. Because our atmosphere is an ideal gas, we can express V in terms of P and T. S is not so simple. More on that later.,,
At this point, we can already see that, for my imaginary atmosphere at equilibrium, a gravity imposed pressure gradient requires a temperature gradient.
It seems to me.
But I could be wrong. Would love to hear how. You guys seem smart enough to fitgure it out.
Now returning again to my imaginary planet. I have a governing equation for the equilibrium temperature profile: dT/dP = V/S. V=RT/P (ideal gas), but what to do about S. Well dS = (dS/dT)dT + (dS/dP)dP, and after employing a maxwell relationship, integrating, and inserting my top at atmosphere conditions (To and Po) this tells me that S = So + Cpln(T/To) – Rln(P/Po). I can evaluate the last two terms, but I’m still stuck with the integration constant So, which is the entropy at (To,Po), or the entropy of outer space.
I now have a system I can almost solve for the surface temperature: dT/dP = (RT/P) / ( So + Cpln(T/To) – Rln(P/Po) with the boundary condition that at the planet surface P = 1bar. This would give me the non-greenhouse gas ATE (for my imaginary planet anyway). All I need is the absolute entropy of outer space. Put another way, if I could find a decent model planet and measure the surface conditions I could calculate the entropy of outer space…
Well, hope you’ve enjoyed this journey to my imaginary planet.
Would love to hear where to go from here, or what I did wrong along the way.
@ Stephen Wilde
“A non GHG atmosphere is not transparent to conduction.”
The concept of transparency to conduction seems of doubtful meaning.
“The conductive energy exchange betwen surface and atmosphere must be accounted for”
Why?
If the atmosphere is transparent, all radiant exchange with space occurs at the surface, which means that the presence or absence of the atmosphere makes no difference to the mean planet-wide surface radiant emittance or, therefore, the mean planet-wide surface temperature.
I do understand that the atmosphere will act as a thermal buffer, cooling the surface during the day and warming it at night, but I am concerned only with planet-wide mean temperature.
Elevator speech for Willis’s parameters, with a zero gas atmosphere, verses a non GHG atmosphere.
At its most basic only two things can effect the heat content of any system in a radiative balance. Either a change in the input, or a change in the “residence time” of some aspect of those energies within the system. (David’s Law) ++NOTE
The addition of a non GHG increases the residence time of the specific heat at the surface, thereby increasing the specific heat above the S-B equation.
There done. Now to add a few further basics for a longer elevator ride.
++ note, adding an atmosphere changes the system to a different system with increased volume requiring more energy to have an equal T, which is naturally attained over time when the atmosphere molecules reach their specific heat with the surface per the second law, which here , just like with radiation, is net flow from higher to lower.
A zero atmosphere surface cools strictly through radiation, which is very fast. The specific heat of the BB surface reaches a certain level determined by the S-B law, at which point the radiating temperature, radiates the heat away to match the insolation.
The existence of an atmosphere adds a second method of cooling and warming the surface. That method is conduction.
Now the surface has two methods of cooling. These methods are not additive, (they do not accelerate the cooling) They are subtractive. (Now less of the specific heat is radiating from the surface, as some of the specific heat is now conducting.) Conduction is slower then radiation.
The dry adiabatic lapse rate is g / Cp, where g is gravity and Cp is the specific heat of the atmosphere The lapse rate may be constant, but it is a constant VARIATION, which appears to be predicated on g and Cp. (IE, the greater the gravity in an otherwise equal atmospheric content of non GHG, the higher the specific heat content of the atmosphere) What does “specific heat emanate from? If specific heat, which is “heat capacity per unit mass of a material”, then the more mass per volume, the greater specific heat per volume. Therefore an atmosphere of denser mass, (caused by either more atmosphere same gravity, or more gravity same atmosphere) will have a higher specific heat content then a thinner atmosphere. The lapse rate will be the same in all atmospheres, just the starting point or temperature will be different. The individual non GHG molecules do not vibrate at a higher specific heat, but due to the fact that there is more per M2 the T is raised. This is just the opposite of some molecules at the top of the atmosphere which, subject to very high energy SWR, individually vibrate at a very high T, but the actual air T is low because there are so few per M2.
So, with greater bottom of atmosphere residence time of conducted specific heat, (both down dwelling and upwelling), due to increased mass per volume as a result of more atmosphere or gravity, the flow from the surface is delayed due to the decreased gradient between the surface and the atmosphere, plus there is backflow, or “back conduction” to the surface, thereby increasing the surface specific heat above the S-B equation.
Conduction, just like radiation from a GHG flows both ways, just net warm to cold. Some of this conducted heat flows back to the surface, and slows the flow of heat from the surface, raising the temperature of the surface above the S-B law. And the densest air being at the surface (due to gravity) that air insulates the surface for longest, thus raising the surface temperature, effectively delaying the loss of energy to space so that energy builds up in the atmosphere until a new higher temperature equilibrium is attained.
Both this and GHG do the same thing, increase the residence time of energy in the earth, ocean atmosphere system allowing additional accumulation of energy relative to S-B and the earths albedo. Either both are breaches of the Laws of Thermodynmics or neither are.
kdk33
very impressive, I’m sure you can run rings round most of us. So do you agree with my basic outlining of the classical mechanical situation which results in a thermal gradient as i gave it in the original post?
CanSpeccy says:
January 18, 2012 at 5:07 pm
@Stephen Wilde
““outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at surface of the planet, which means that the mean surface temperature must be the same with an atmosphere as without.”
S. W responds
Not so, because the atmosphere decouples the surface from space.Outgoing has to match Incoming at top of atmosphere but NOT at surface.”
============================
CanSpeccy responds
I understand that the atmosphere decouples the surface from space. But we are talking about mean planetwide radiation.
All radiation from the surface of the planet must emerge from the top of the atmosphere, because the atmosphere is transparent, and, at equilibrium, outgoing radiation at the top of the atmosphere must match incoming radiation at the top of the atmosphere (if scattering is ignored), so my contention stands: the mean surface temperature must be the same with an atmosphere as without
=============================================================
@ Can Speccy The surface does not lose all of its T through radiation, much of it is conducted to the atmosphere, some of that to a non GHG, which may, higher up in the atmosphere conduct it to a GHG, where, from there some of that energy is radiated to space, some back towards the surface. Much of the radiation to the TOA occurs throughout the atmosphere. If the surface radiation must match the TOA, and it is also losing energy to the atmsophere through conduction, then it must be greatly elevated above S-B by the presence of any gas to which it conducts.
TB,
I don’t think I can run rings around anyone. I’m sure I’m making terrible errors, just don’t know what.
This part of your original post stand out to me:
[So is that why its cold at high altitude and warm near the surface? Ira Glickstein said it only works once, when the air is first pulled down and compresses, then the heat dissipates back to being the same temperature everywhere again.
That’s one way of looking at it, from the point of view of the classical mechanics of the microscopic scale. Ira is right in one sense, but wrong in another. Although initial heating caused by sudden compression dissipates, the ongoing action of gravity as a force keeps the air compressed more near the surface. This means air is denser at low altitudes, and that means more molecules are having collisions more often, thermalising energy.]
I would change this to say: after initial compression, the atmosphere returns to equilibirum. But the equilibrium condition is not equal temperature, it is equal Gibbs energies. Since there is a gravity imposed pressure gradient, the equal Gibbs energy constraint requires that there also be a temperature gradient (which was the starting point for my math).
The difference boils down to the definition of equilibirum. I say it is no Gibbs energy gradient. Ira says it is no temperature gradient. The force of gravity the imposes the pressure gradient.
@David
“the surface does not lose all of its T through radiation, much of it is conducted to the atmosphere, some of that to a non GHG, which may, higher up in the atmosphere conduct it to a GHG, where, from there some of that energy is radiated to space, some back towards the surface.”
But in my example the atmosphere is transparent, i.e., without GHG so mean planet-wide radiant emission at the surface will be the same as at the TOA.
And if my model is valid, it precludes a gravitational effect on surface temperature.
In fact, any non-transient heating effect of gravity would result in a planetary inequality between radiant emission and absorption, which is not, I believe, what is observed.
kdk33 thanks, I’ve worked your rephrasing into the original post. Now, I need to study your algebra, and remind myself which letter represent what… I’ve got a bout 3/4s of them in my head.
Help us out with a list please.
TB,
I’m thinking you should check my maths and my logic before changing your post. I’m a rank amateur (seriously), and don’t want to be responsible for any mistakes…
I do like to play around and appreciate your interest. Let me know what you think.
P = pressure
V= volume
T = temperature
S = entropy
G = gibbs free energy
Cp = heat capacity (in this case, ideal heat capacity)
R = gas constant
To = temperautre of outer space
Po = pressure of outer space
Thanks kdk33. Wiki says this about Gibbs free energy:
In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy[1] to distinguish it from Helmholtz free energy) is a thermodynamic potential that measures the “useful” or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure (isothermal, isobaric). Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings. Gibbs energy is the capacity of a system to do non-mechanical work and ΔG measures the non-mechanical work done on it.
I’m not sure that matches the classical dynamics case I’m trying to capture, so I’ll think some more. Clearly it is linked into the picture, but seems to apply to the macroscopic rather than microscopic description.
Sadly, I think the Gibbs energy approach is incorrect. Some more reading and I now understand this:
Gibbs energy equality is the equilibrium criteria for system at constant temperature and pressure. It is useful for vapor liquid equilibrium calculations (it underpins the clausius clapyron equation) and chemical equilibrium in reacting systems. (I think I knew this in my school days.) It is the wrong criteria for my imaginary planet.
I mis-applied it as a more general equilibrium criteria. I initially thought I could derive DALR from it. The math was interesting, and it looked like it indicated a gravity induced temperature profile. sighhh….
One the bright side, I learned something, and had some fun with calculus. I solved the DE in Mathematica, which was kinda fun too.
I like your blog. Hope you don’t mind if poke around from time to time.
Robert Brown,
Thanks for your comments about the Jelbring paper. I don’t know if you had a chance to read my previous post of 1/17/12, but here is a link:
I believe it fairly outlines the science behind Jelbring’s paper and is the basis for my response to you.
Your discussion perfectly illustrates the paradigm shift that must take place for atmospheric thermodynamics to be properly understood. The recent online discussions at Tallbloke and WUWT are totally representative of the battle of paradigms described in Thomas Kuhn’s book “The Structure of Scientific Revolutions”. Before getting into the details I would like to throw out a few quotations from that book so that we are on the same page with Kuhn:
“When examining normal [established] science….we shall want finally to describe that research as a strenuous and devoted attempt to force nature into the conceptual boxes supplied by professional education.” (Page 5) [Note added by me]
“Therefore, paradigm-testing occurs only after persistent failure to solve a noteworthy puzzle has given rise to crisis. And even then it occurs only after the sense of crisis has evoked an alternate candidate for paradigm.” (Page 145)
First, you talk extensively about “thermal equilibrium”. But I believe we should be talking about “thermodynamic equilibrium”. Thermal equilibrium is but a subset of thermodynamic equilibrium. A system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium and chemical equilibrium. Thermodynamic equilibrium equals thermal equilibrium only when a system’s internal energy can be described by
U = CvT (1)
In this case the system’s internal energy is thermal energy and thermal equilibrium is all that matters. Your statement “Thermal equilibrium is isothermal, period” only applies to such a system. But that is not the system of a planetary atmosphere under the influence of a gravitational field.
Second, we need to better define where the classical laws of thermodynamics and equilibrium are valid. They are valid with a homogeneous system where all the locally defined intensive (e.g., per unit mass) variables are spatially invariant. But a system is not homogeneous if it is also affected by a time invariant externally imposed field of force, such as gravity. Thus in a gravitational field the laws of thermodynamics have to be applied to reflect the external field. This is a paradigm buster.
Third, the thermodynamics of an atmosphere cannot be described wholly through considerations of heat transfer only (Trenberth diagram, anyone?). The atmosphere must be treated as a system undergoing both heat and mass transfer. Mass transfer is the reason that gravity is so important in understanding atmospheric thermodynamics. This gets to the mechanical equilibrium part of thermodynamic equilibrium.
Fourth, chemical equilibrium is also very important in atmospheric thermodynamics but that involves latent heat and is beyond our discussion here.
Thus, as I explained in my previous post, the proper formulation of the first law of thermodynamics for a “dry” atmosphere under the influence of a gravitational field is:
dU = CvdT +gdz – PdV (2)
The first energy term, CvdT, is the only variable that deals with thermal energy (temperature). The other two energy terms, gdz (gravitational potential energy) and PdV (mechanical work energy), deal with mass transfer. Thus temperature reflects only one variable in the energy composition of the atmosphere. As Tallbloke has pointed out, for the first law to apply energy can be transformed from one form of energy to another, but total energy content must remain constant (dU = 0). The temperature profile through the atmosphere is dependent on the mix of energies at any given point.
The temperature profile resulting from a dry adiabatic lapse rate is covered in my previous post. And that profile reflects an isentropic system in steady state dynamic equilibrium described by:
CpdT + gdz = 0 (3)
The same system in static equilibrium can be described by the equation of state:
CpT + gz = constant (4)
But for an isothermal temperature profile to exist in an atmosphere in a gravitational field both CpT and gz must increase with altitude. Thus internal energy (U) is not a constant but must increase with altitude. The only way that could be achieved is if work was being done to the system. And such a system would not be in thermodynamic equilibrium.
The zeroth law only applies to a homogeneous system and the atmosphere under the influence of a gravitational field is not a homogeneous thermodynamic system. And equation (3) does not violate the second law since the process equation reflects an isentropic (constant entropy) process.
The Jelbring hypothesis holds up perfectly from a thermodynamics standpoint.
Your insertion of an insulated silver wire into the discussion makes for an interesting mental exercise, but it has nothing to do with the thermodynamics of a planetary atmosphere. You have just added a non-existent subsystem to the existing system. And the wire does not reflect conduction since vertical conduction is almost non-existent in a gaseous system in a gravitational field. Vertical diffusion is inhibited due to the deceleration of upward (z axis) moving molecules (and acceleration of downward moving molecules).
As for the N&Z hypothesis, I too have no firm opinion as yet. I am awaiting Part 2 of their submission that deals with the detailed thermodynamics. But if that is based on a premise similar to the Jelbring hypothesis, I will be pleased.
I would like to add one more quote from Kuhn to wrap things up:
“Because the unit of scientific achievement is the solved problem and because the group knows well which problems have been solved, few scientists will easily be persuaded to adopt a viewpoint that again opens to question many problems that have previously been solved.” (Page 169)
Bill
Kdk33,
I think you may be on the right track looking at free energy. I have also played around with the concept with respect to the dry adiabatic lapse rate. I am at the point where I am not sure whether the Gibbs free energy or the Helmholtz free energy is the best fit. The atmosphere is constant pressure at the surface but the pressure decreases along the adiabatic curve. I am also not quite sure how to handle the gravitational field in the equations. But I haven’t tried very hard as yet. I would be very interested in any ideas you may have.
Bill
“vertical conduction is almost non-existent in a gaseous system in a gravitational field. Vertical diffusion is inhibited due to the deceleration of upward (z axis) moving molecules (and acceleration of downward moving molecules)”
Doesn’t the reduction of weight of a package of warmed and expanded non radiating air overcome that gravitational restriction ?
Conduction goes hand in hand with convection and on a rotating sphere with an uneven surface there is going to be a heck of a surface temperature difference between night side and day side when one considers how fast a radiatively transparent atmosphere allows a surface to cool down.
More than enough circulation to carry conducted energy around the planet and up into the upper atmosphere against any gravitational restraint.
I just saw Willis’ new post on WUWT concerning Robert Brown’s thread on gravity.
I have read the post but not completely absorbed it as yet. It is way past my bedtime but I look forward to exploring this further. Sounds like my above post was timely. Exciting stuff!
Bill
Posted at WUWT
Willis,
Firstly, thank you for the courtesy of your response. It is encouraging that we are able to set aside non-scientific issues that hang between us and conduct scientific debate rationally and reasonably.
Some preamble, and then some science.
You said to Lucy that
“time is what you don’t have. The clock is running, the elevator speech for N&Z is way overdue.”
Nobody is king of the clocks. Lucy and I are not sales people with obligations to meet targets within timeframes or elevators. Paradigms don’t change overnight. Resistance to the theory of plate tectonics continued for as long as the old guard were in tenure at their institutions. Time must be spent in evaluating new theories properly, not concertina’d into a gish gallop of instant rebuttal and ‘counterproof’.
A more relevant example than plate tectonics is the Loschmidt vs Maxwell and Boltzmann debate regarding thermal gradients matching the theoretical dry adiabatic lapse rate in equilibrium atmospheres subject to a gravitational field. It’s been going on for over a hundred years without resolution and we don’t need to force a conclusion within the next few days just because it has been thrust to the centre of the stage at the moment.
OK thanks for reading that, lets address some science.
Willis Eschenbach says:
January 19, 2012 at 6:26 pm
If an energetically isolated system is in its lowest energy state, it cannot perform work.
Agreed
If the isolated atmosphere in Jelbring’s thought experiment is warm at the bottom and cold at the top, I can stick a thermocouple into it and use the temperature differential to generate electricity to perform work.
Excellent, a proposed experiment. Let us know the result. I think you’ll find that even as a thought experiment it doesn’t work out though. Peter Berenyi emailed me that argument and I sent him my disproof. He hasn’t got back to me in the two days since. I’ll post it in a separate comment if you are interested.
As Tallbloke points out, the second law says an isolated system can only move towards a lower energy state. That means Jelbring’s thought experiment must inexorably move towards the isothermal condition as its equilibrium state.
No, as we’ve been saying all along, as have other people on this thread, at the lowest energy state, molecules at the top of the atmosphere have the same total energy as those at the bottom, but less of the total is available as kinetic energy which manifests as heat via collisions because more of the total energy is locked up as gravitational potential energy.
Since Jelbring claims an adiabatic state will obtain at equilibrium, his hypothesis is falsified.
If my statement above is correct, or if the equivalent macroscopic arguments provided on this thread and by Jelbrings 2003 paper are correct, then this statement is false.
Willis Eschenbach says:
January 19, 2012 at 9:21 pm
Jeremy says:
Gravity has NO AFFECT ON TEMPERATURE.
How many times must it be said.
You people are reading science fiction.
You have to do WORK to create a change in temperature – this is basic thermodynamics!!!!
If an object falls in a gravitational field then potential energy will be converted to kinetic energy which will create heat. However a stable column of air in equilibrium does not create any energy or heat.
Thanks, Jeremy. You are a hundred percent correct, gravity can’t do ongoing work to change the temperature
Jeremy and you are 100% wrong. Work is done by energy. Gravity is not a type of energy, it is a force. It cannot and does not need to “do ongoing work”. Nor is a change in temperature under discussion. Gravity, via the pressure profile it induces in an atmosphere, and considering the compressibility of the medium, causes the denser per unit area of the atmosphere near the surface to be warmer than it is at higher altitudes. g/Cp
If you are fighting basic ignorance of science, you will be deluged with ignorant people. Not much I can do but just keep putting the facts out there.
Certainly there are a host of much more sophisticated threads, and those tend to attract a more scientifically literate commenter. But when you are discussing “gravito-thermal” theories …
This is an ad hominem attack which has no place in scientific discourse.
kdk33: no worries. I’ve reverted the text in the original post. Stick around and keep thinking. 🙂
Roger,
I am puzzled why neither you nor anyone else will respond to this seemingly simple piece of logic:
“At equilibrium, planet-wide outgoing radiation at the top of the atmosphere matches planet-wide incoming radiation at the top of the atmosphere. But if the atmosphere is transparent (i.e., without significant GHGs), outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at the surface of the planet, which means that the mean surface temperature must be the same with an atmosphere as without.”
If that is correct, it means that gravity does not account for the greenhouse effect.
If it is incorrect, for the reason Jelbring contends, i.e., that gravity causes an atmospheric temperature gradient that accounts for the greenhouse effect, then planet-wide radiation at the top of the atmosphere must exceed planet-wide incoming radiation, meaning that the planet is luminous. However, we know that the planet is not luminous.
QED
CanSpeccy,
An observation.
We are dealing with some kind of approximation to isotropic flux sources.
If there are concentric circles then comparing a flux at different distances and finding it the same is troubling.
“If there are concentric circles then comparing a flux at different distances and finding it the same is troubling.”
That’s not relevant, to “planet-wide” fluxes, which is what I was speaking of. They are independent of the surface area of the sphere at the point of measurement.
CanSpeccy,
I’m sure you have been told already but the surface will not radiate at the same rate as top of atmosphere if there is an energy exchange going on between surface and atmosphere.
It is the same principle as the proposed GHG Greenhouse effect. The ATE is exactly the same in principle but from differing causation.
Where the atmosphere is transparent it is a matter of conduction and convection between surface and atmosphere rather than downward radiation from GHGs.
“the surface will not radiate at the same rate as top of atmosphere if there is an energy exchange going on between surface and atmosphere”
I spoke of mean planet-wide radiation, to which your objection is irrelevant.
If the planet is in equilibrium with the rest of the universe, and has no internal heat source, outgoing radiation must equal incoming radiation.
CanSpeccy,
The only way to have the scenario you describe is to remove the atmosphere. Only then would you be right.
A planet with an atmosphere is never in equilibrium with just the universe. It also must be in equilibrium with its own atmosphere.
The surface has to be warm enough to provide energy for both exchanges in parallel.
“A planet with an atmosphere is never in equilibrium with just the universe. It also must be in equilibrium with its own atmosphere.”
It’s a matter of time scale. Over the course of a year, the Earth is, to the closest approximation, in equilibrium with the universe.
I understand that the atmosphere acts as a thermal buffer. Thus during the day, heat is transferred from the surface to the atmosphere, thereby cooling the surface and reducing its radiant emission. However, at night the reverse is the case. The atmosphere transfers energy to the surface, thereby increasing its radiant emission.
Similarly, hemispheric and season differences balance out over the course of the year.
And, of course, the Earth’s crust and oceans act as thermal buffers, moderating the surface temperature, lowering it during periods of summertime high isolation, raising it during periods of winter darkness. But that is no reason to doubt that the Earth is in thermal equilibrium with the universe.
Night and Day, Winter and Summer do not average out to zero. They average out to about half of the daily or seasonal input and output so on average globally there is always an energy exchange between surface and atmosphere which is never in equilibrium.
A portion of surface energy needs to be allocated to that exchange process.
That portion is in addition to the portion needed to match incoming solar with outgoing longwave.
Exactly as with the GHG based greenhouse effect but actually in my opinion due to the ATE which is caused by gravity, pressure and mass acting with solar input.
The Earth plus atmosphere could be said to be in equilibrium with the universe at 240W/m2 in and 240W/m2 out but the surface/atmosphere relationship is separate.
“The Earth plus atmosphere could be said to be in equilibrium with the universe at 240W/m2 in and 240W/m2 out but the surface/atmosphere relationship is separate.”
Yes, exactly as I said, except for the numbers which I cannot vouch for.
“there is always an energy exchange between surface and atmosphere”
Also, exactly as I said.
“A portion of surface energy needs to be allocated to that exchange process.”
This is new physics!
Energy is not lost in the exchange process, although entropy is gained.
You are evading the point, which is that the thermo-gravitational hypothesis, implies a higher radiant flux at the surface than at the top of the atmosphere (after adjusting for area differences) even if the atmosphere is transparent. This has to be so, because there would otherwise be no GE effect. But this is self-evidently impossible. The atmosphere is transparent, therefore, whatever is radiated at the surface must emerge at the top of the atmosphere.
“Energy is not lost in the exchange process”
Of course not. At equilibrium the transfer each way is equal. It is retained within the system to increase system equilibrium temperature just as proposed for GHGs but in fact the exchange is not radiative but conduction and convection.
So no need for outgoing at top of atmosphere to match the surface outgoing because the difference is accounted for by non radiative processes of conduction and convection retained between surface and top of atmosphere.
You keep applying radiation only principles. That is wrong.
You said “A portion of surface energy needs to be allocated to that exchange process”
Now you’re saying “Energy is not lost in the exchange process.”
Looks like a contradiction to me.
“no need for outgoing at top of atmosphere to match the surface outgoing because the difference is accounted for by non radiative processes of conduction and convection retained between surface and top of atmosphere.”
But outgoing at TOA must match outgoing at the surface because the atmosphere is transparent.
“applying radiation only principles. That is wrong.”
That sounds like a mantra, not an argument.
I’ve done my best for you CanSpeccy. If you don’t get it yet that isn’t my problem.
Well, Stephen, I’m not sure I can go with your mantra,
“applying radiation only principles… is wrong.”
But anyone interested in my fuller reflections on the Jelbring hypothesis, will find an early draft, with probably some typos, here.
Tallbloke: Here is an interesting thought experiment that might shed some light on whether gravity alone can produce a temperature gradient in a column of gas.
Imagine a horizontal sealed cylinder of gas 1 m2 in area, 20 km tall, containing 10^4 kg of nitrogen located 10 km above the surface of a planet like the Earth but with no atmosphere. Although it isn’t necessary, the quantities were chosen to mimic the earth’s atmosphere, which has 10^4 kg of weight above every m2 and 99% of its atmosphere is below 20 km. We can pick a particular temperature and calculate the pressure if we want. Now we want to rotate this cylinder about its center of mass to the vertical position, but to keep the gas from moving during rotation, let’s imagine that removable barriers or pistons of negligible thickness are present every 1 m or less while we rotate. Once vertical, we remove the barriers, or if we want a totally reversible process, we allow the pistons to slowly move to an equilibrium position before we remove them. SInce we are pivoting around the center of mass on a frictionless pivot, rotation can be done without doing any work or changing internal energy.
Does anyone have any doubt that most of the gas in the cylinder will “fall” to the bottom and create a pressure gradient with altitude similar to that on earth? Does anyone believe that the kinetic energy acquired while falling will not make the gas at the bottom of the cylinder warmer (at least temporarily) than the gas at the top? Have we violated the 2LoT by spontaneously creating a temperature gradient where none existed before? Since: 1) I’m fairly confident it will be hotter at the bottom than the top, and 2) I doubt we have violated the 2LoT, and 3) we haven’t done any work on the system, I conclude that the entropy of a gas depends on more than just temperature in this system. One can find expressions like the one below that suggest that pressure also plays a role, but I don’t have a clear understanding of when or how to apply this equation:
S2 – S1 = Cp * ln ( T2 / T1) – R * ln ( p2 / p1) http://www.grc.nasa.gov/WWW/k-12/airplane/entropy.html
Now let’s imagine a thin layer of gas anywhere in the vertical cylinder enclosed by two frictionless pistons, each having a pressure sensor facing the thin layer of gas. The pressure at the bottom of the layer differs from than at the top of the layer by the weight of the gas in the layer. BUT, according to the kinetic theory of gases, pressure is actually created by collisions between gas molecules and the walls, piston and pressure sensor. Usually we assume that the pressure is the same everywhere inside a container and that 1/3 of the kinetic energy is directed along the x, y and z-axes, but this isn’t true in a gravitational field. If the pressure at the top of the thin layer is less than the pressure at the bottom, then the gas molecules moving upward to strike the upper piston must be moving slower than the gas molecules moving downward to strike the lower piston. The decreasing pressure as one goes up the cylinder is caused by gas molecules converting kinetic energy to potential energy!
In his WUWT post, WIllis cites Brown saying that at equilibrium, the same number of molecules in a column of atmosphere are moving up and down (which is correct). If the temperature in the column is uniform, Brown says that the molecules moving up have the same kinetic energy as those moving down. That appears to be wrong; the molecules that move up have less kinetic energy than those that move down to take their place. Those moving up converted kinetic energy to potential energy and got slightly colder and those moving down did the opposite. In Brown’s column of atmosphere, the pressure will not change with altitude!
So an answer appears to be very simple: If there is a pressure gradient in a column of air, the kinetic theory of gases tell us that there should also be a temperature gradient. Both pressure and temperature are associated the velocity of molecules (temperature with mean kinetic energy. pressure with the impulse transfered). This conclusion doesn’t require any assumptions about convection, radiation, the optical properties of the gas.
Frank, thank you for that. It is very noticeable that people who are thinking for themselves are coming to this conclusion, whereas the people who insist that there will be a thermal equilibrium are making appeals to famous names or abstruse statistical arguments to support their contention.
The huge kinetic energy of the earth’s angular momentum is very slowly being expended as the universe winds down. The evidence that considerable work is continually being done as a result is manifested in the very fact of weather in all its forms. At a glance the relevant numbers appear commensurate, viz mass of earth 6×10^24 kgs; age of universe 5×10^12 days.
Interesting comment Simon. Kind of reminiscent of the Virial Theorem. However the Earth speeds up as well as slows down, on timescales of several decades. I discovered that changes in Length of Day (LOD) correspond quite closely to changes in the distance between the Sun and the centre of gravity of the solar system in the z axis. Ian Wilson independently discovered the same is true in the x,y plane too.
Trying to understand the cause of this relationship has been a major theme of this blog since it started. See the very first post. And this plot:
It looks like Hans just skewered Willis on his WUWT thread 🙂
Hans Jelbring says:
January 20, 2012 at 5:53 pm
Trick says:
January 20, 2012 at 3:33 pm
Willis says at 1/20 2:19pm:
“I say the column will be isothermal, meaning all at the same temperature top to bottom.”
“This violates the 2nd law, KE + PE = constant at each h in the presence of an inexplicable gravity field in the gaseous cv of interest, namely an adiabatic (no gain or loss of heat from CV) GHG-free air column.”
Many thanks for your insight.
Tallbloke: Someone needs to publicize the fact that people are misusing the kinetic theory of gases. Is there no peer-reviewed publication discussion this situation?
In a laboratory setting, we say that the pressure is the same in all directions and therefore that the kinetic energy associated with movement of molecules (thermal diffusion) is the same in all directions. On a planetary scale, we say that pressure change is associated with the weight of gases overhead, and forget to consider what this means about the behavior of molecules. If there is a pressure gradient with height, it can only be caused by molecules moving upward more slowly than they move downward. The obvious reason for this is that the molecules moving upward are converting kinetic energy to potential energy (and cooling when we consider a large enough group to treat mean kinetic energy as temperature). The opposite is true for molecules moving downward.
I’m not sure how the 2LoT applies to this situation, but rotating the above cylinder from horizontal to vertical persuades me at spontaneous formation of a temperature gradient in a gravitational field won’t violate this law. If I placed a single molecule in an empty vertical cylinder and watched it move, no one would complain about interconversion of kinetic and potential energy. Why should things suddenly be different when I consider a large number of such molecules in the cylinder, so that LTE exists, mean kinetic energy is proportional to temperature and the 2LoT applies?
Frank, thanks, I will use some of that in reply to Robert Brown, who to his credit has at long last replied to my short proof that the zero’th law of thermodynamics does not preclude an thermal gradient in an energetically equilibriated column in a gravitational field:
Robert Brown says:
January 21, 2012 at 2:22 pm
tb says:
However, Robert still hasn’t addressed my short proof that no heat has to flow in a gravity induced thermal gradient at energetic equilibrium.
Here it is again if he feels like getting round to it.
Robert says:
“if A and B are placed in thermal contact, they will be in mutual thermal equilibrium, specifically no net heat will flow from A to B or B to A.” That’s the zeroth law.
tb:
Assuming your A and B have at least some dimension, then a thermal gradient across them would mean that the top surface of A will be at the same temperature as the bottom surface of B where they contact. Therefore no heat will flow. Even so, the average temperature of the whole of body A will be higher than that of B.
rgb
Sure, and in return you can address the actual topic of the thread, which is how any system that spontaneously generates a thermal gradient violates the second law of thermodynamics and thereby enables the construction of PPM2K’s, including the trivial thermocouple example in the previous post.
First of all, what you offered is not a proof. You simple restate your conclusion. You postulate two systems in thermal contact, one at a higher average temperature than the other, and then say “no heat will flow” as long as the boundary in between them is at some (presumably intermediate) temperature.
The problem is that temperature is a meaningless concept for a two dimensional surface. What you’re saying, in a nutshell, is that you have two volumes neither of which is in thermal equilibrium (if they were, they’d have the same temperature throughout each volume.
But let’s see if I can come up with a simple, simple argument that will convince you.
Go into your column of air with its imagined lapse rate. Get perfectly insulating jar and fill it with air from the top. Get a second jar and fill it with air from the bottom. By hypothesis, these jars are in thermal equilibrium, but have different temperatures. Note that once you fill the jars, you can move them up or down all you like — the gravitational field doesn’t vary (by enough to matter). You’ve simply replaced the fluid that was supporting the air with the jar walls — nothing else changes. Which, incidentally, is why your entire argument is wrong — no gravitational potential energy is involved in heat exchange or energy balance. You move the jar slowly up, move it slowly down, nothing in the jar knows that it has been moved at all!
Now put the two jars in thermal contact. I don’t care how — move them together, use an insulated silver conductor of heat to couple their otherwise adiabatic walls without moving them up or down — it doesn’t matter, does it. What happens? Well, they are at different temperatures, so heat flows. If you change the temperature across any jar heat flows. There is nothing special about the heat flow. It will flow up or down or side to side to neutralize a thermal gradient no matter what you do to the otherwise unaltered jars of air.
The existence of the jar itself doesn’t matter. Put a side-insulated silver rod into the air column and heat will flow in it forever. Put a heat engine into the air column and you can run it off of that temperature difference forever.
The point is that your air column isn’t in equilibrium. Heat can easily be conducted through the air — the equilibrium distribution of the air (and its temperature) isn’t just determined by convection. Once it settles down into a density profile, heat will flow throughout that profile until the temperature is the same because the air at the top cannot tell any difference between heat that arrives through the intermediary air and heat that arrives through a silver rod. The point is that heat spontaneously flows from hot to cold, never the other way around, in the absence of something that does continuous work to push it the other way.
Nothing about the density of air in a jar tells you its temperature. Heat is perfectly happy being conducted uphill, downhill, or sideways. Warmth has no mass, and objects placed in gravitational fields do not spontaneously separate into warm side down. Indeed, in general it is rather the other way, at least at first! But equilibrium is always isothermal in a case like this with no meaningful constraints.
rgb
I’ll be replying to this after some careful thought about maximising the potential fruitfulness of further interaction with Robert.
My reply to Robert:
Hi Robert, and thanks again for your reply. I’m going to split my response into two halves. the first will deal with your statements and claims about my position. The second half will deal with the argument you feels sufficiently addresses the matter in hand.
You say that:
“The problem is that temperature is a meaningless concept for a two dimensional surface. ”
Well, I was only trying to address your ‘slices’ argument from the original post, so I humbly submit that you are the one who started it with the surfaces malarkey.
and you say that I should:
“address the actual topic of the thread, which is how any system that spontaneously generates a thermal gradient violates the second law of thermodynamics”
Well you can’t define us out of existence. Total energy = KE+PE. The second law I’m working from (feel free to define the one you’re using) tells me that in a gravitational field, the higher up you are, the less Kinetic Energy you’ll have and the more Potential Energy you’ll have. Total energy must be conserved. Everyone is agreed on that one, so, less KE = less heat high up.
Now, I’m aware that there are some very sophisticated arguments about this stuff which use statistical mechanics, but as Joe Born will tell you, he’s been through the math in the Coombes and Laue paper, and the Valesco et al paper, and he has found the reason they come to the isothermal conclusion. It doesn’t work. They are playing with limit cases which don’t relate to the mechanical behaviours of actual atmospheric gases.
“and thereby enables the construction of PPM2K’s, including the trivial thermocouple example in the previous post.”
The only viably well specified machine I’ve seen in this thread fails the logic test quite quickly. keep trying though.
“What you’re saying, in a nutshell, is that you have two volumes neither of which is in thermal equilibrium (if they were, they’d have the same temperature throughout each volume.”
Your problem here is that you keep going back to your own preconceptions instead of following our argument. KE+PE is constant, so as we go up, PE increases. Therefore KE (and temperature) falls. So an air packet is in energetic equilibrium when the temperature gradient across it is such that it matches the lapse rate defined by gravity and it’s specific heat at constant pressure. Loschmidt held it should be that way for solids too by the way, so your silver rod may not behave as you’d expect.
Now, your capturing of gases in jars argument seems hopelessly confusing to me. That may be my fault or yours or just that we’re seeing things differently. Try this explanation of why we have ended up with differing interpretations and see if it makes sense to you.
H/T Frank
“In a laboratory setting, we say that the pressure is the same in all directions and therefore that the kinetic energy associated with movement of molecules (thermal diffusion) is the same in all directions. On a planetary scale, we say that pressure change is associated with the weight of gases overhead, and forget to consider what this means about the behavior of molecules. If there is a pressure gradient with height, it can only be caused by molecules moving upward more slowly than they move downward. The obvious reason for this is that the molecules moving upward are being slowed down by gravity and converting kinetic energy to potential energy (and cooling when we consider a large enough group to treat mean kinetic energy as temperature). The opposite is true for molecules moving downward.”
Now from what I read in an earlier comment, someone claimed that you’ve said that the KE of molecules won’t be affected by gravity. If that’s so, please could you explain why they are exempt from the law of gravity. What goes up must lose velocity. If it’s mass stays the same, it ends up with less KE. QED
Thanks
TB.
tallbloke wrote:
It might just be, that in common with much of the rest of climate science, the averaging of averages has been taken a step too far, and ended up smearing the gradient into isothermal conformity…
I believe that is the case here.
I think I understand Robert Brown’s commentary based on the MB distribution and net flow. I’d like to thank Joe Born for challenging me to think it through on the Loschmidt thread.
I’ll focus on the distribution of velocities in a gas in a gravity well. This is somewhat simplified, for the purpose of conveying the concepts.
My example has a box with non-interacting molecules (very sparse) of an ideal gas. There is a thermal reservoir at the bottom. At the bottom, the molecules will have exactly the MB distribution. The bottom of the box is assigned height z=0.
To visualize what I’m saying, draw vx and vz axes on a piece of paper. Now draw a circle around the origin representing ithe maximum probability for the MB distribution at z=0. This is our reference point, and the reservoir will maintain that distribution.
Let’s consider at another height, za > 0. At za, some molecules will be going up, and some will be going down. I agree with Robert Brown that the number going up must be exactly equal to the number going down. In other words, the distribution remains symmetic across z.
Not all upwards bound molecules had enough z velocity to reach za, so draw a horizontal line above the vx axis to exclude them. Those that did had their velocity reduced by the same amount.
Similarly, not all downwards bound moleclues (to z=0) had enough z velocity to have passed through height za, so draw another horizontal line below the vx axis, mirroring the line above.
Molecules between the two lines are those that lack the energy to reach height za. Those outside the lines have energies reduced. At height za, those with exactly enough z velocity to reach za will now have vz=0. Draw new axes, with the new reduced populations, shifted inwards towards the vx axis.
This is how gravity distorts the Maxwell-Boltzmann distribution, by compressing the vz axis. Maintaining a perfect MB distribution in a gravity well is one averaging too many.
I’m familiar with the math Robert Brown cites for saying that a column of gas is isothermal. I believe that it follows directly from ignoring the effect of gravity on the MB distribution.
In other words, if gravity has no effect on the MB distribution, then our column of gas is isothermal. If it does have an effect, then it’s not isothermal.
Gas molecules follow ballistic trajectories between collisions.
I just posted this on WUWT and figured I would cross post it here before it got deleted.
Bill Hunter says:
Your comment is awaiting moderation.
January 21, 2012 at 6:34 pm
I think I see a logic here with convecting air. The relationship with kinetic energy and temperature has been confusing to say the least.
Perhaps the problem is in the way its been explained.
OK so as a gas rises it does not lose kinetic energy thats whats been said about the adiabatic “process”.
But at the same time we are told it loses temperature.
One logic would be the kinetic energy always equates to a certain temperature in a single kind of material.
And when air rises it also mixes with other air. The mixing lowers the average temperature of the mixed gas, which is all we can read with measuring devices; but it takes a while for the kinetic energy of individual molecules to come to equilibrium as you need collisions or radiation or something of that nature for them to dump their kinetic energy.
If I can adopt that idea then I can see my way through this morass a bit more easily.
Here I can see an isothermal atmosphere and a lapse rate created by the fact the convection/conduction system fails to keep up.
It really fails to keep up during the cooling cycle as it might require a lot of years for conduction to work its way through the atmosphere. Convection on the other hand might only take a few days or a week or so to catch up (though that last nth of a degree could be long extended as convection slows to a crawl so slow a snail looks like a speeding bullet.)
So since this equalization in effect is in fact determined by a combination of gravity and atmosphere mass that makes Jelbring basics right (just his equilibrium is wrong). And to prove Jelbring was wrong about the equilibrium, his critics were required to resort to an argument that proved the essence of this theory was right that convection and conduction would eventually catch up and equalize the temperature of the atmosphere. (or at least I can think of no other means for the surface to be normal temperature and have a need for it to be the source of warming the upper atmosphere. So in the end Jelbring’s model proves beautifully useful.
Now one more step! If the reason we have a lapse rate is this delay in equalization of the atmosphere it follows that the longer the delay the hotter the surface and the cooler the upper atmosphere and viola we are back in business with a lapse rate and an explanation for why the surface is warmer than its expected blackbody temperature. Or at a minimum we have a concrete theory it at least partially explains it. Then the correlations across planets with disregard to GHG begins to explain why it might be a very large part of it.
I am feeling pretty comfortable with that. Does somebody have a pin to puncture my balloon?
The energy of a molecule of gas is not the same as the temperature of the gas. The amount of energy in the space will give the temperature. As a gas is compressed into a smaller space the temperature is increased but the energy levels of the molecules is not changed. As the molecules rise the pressure decreases and the temperature decreases, energy does not change. Only the amount of energy in the space changes. Energy of the molecule can only change by direct contact,( conduction), or radiation. When energy is, charged or discharged, changed by Radiation, there is a rebound, You know action, reaction, that causes the apparent dance of collisions. This dance is cute but has little to do with the internal energy level of the molecule. That is increased by the adsorption of the correct frequency radiation or lost by the same means.
Gravity does not increase the internal energy level of the molecules. It just changes the amount of compression and the space that the molecule and it’s energy occupies. Ergo! gravity causes heating but does not add energy! AS to the nit pickers about the energy of acceleration, deceleration, in that cute little dance. I can assure you that it is very small. pg
I think it doesn’t matter to the base gravity/mass theory if the atmosphere at equilibrium isothermic or stablizes with a lapse rate.
But I think Jelbring’s theory is cleaner and more intuitive if the atmosphere does stabilize at an isothermic condition.
If incoming and outgoing radiation is prohibited that means the equalizing of the atmosphere has to be internal. Thus the lower atmosphere has to be the source of warming the upper atmosphere proving that at equilibrium the lower atmosphere would be cooler.
Thus gravity and atmosphere mass are the main functions and the delay claimed by the isothermal crowd for equilibrium that conduction and convection are behind schedule on is in fact evidence of this relationship.
Jelbring’s model is ideal for teasing this out whether or not the atmosphere stabilizes at the lapse rate or continues to isothermic.
tallbloke says:
January 22, 2012 at 1:23 am
Tim Folkerts says:
January 21, 2012 at 5:15 pm
There are really only two possibilities.
1) The second law works and thus the temperature must be uniform.
2) KE + PE is constant, so the particles cool as they go up, and thus the temperature drops.
The laws of thermodynamics have been stated in terms of energy rather than temperature for over a hundred years. The news hasn’t reached Duke University it seems.
I can give the “elevator speech” for why #2 is suspect. For any given trip, the KE + PE is indeed constant, but for different trips, the value is different (ie the boltzman distribution). If you look near the top, the “low energy tail” never gets that high, so you are only looking at self-selected particles that started in the high energy tail. These originally-high-energy-particles have indeed lost some KE on the way up, but they started with extra on average. This can (and does) leave this SUBSET of particle with the right average energy to be at the same temperature as the WHOLE set was at the bottom.”
I think this is wrong because of the very short mean free path length between collisions. Maxwell did a fair bit of work on that when he was considering the collisions and distributions of various sized gravel (analogous to differing KE in molecules) in the rings of Saturn (also sorted by gravity) and this is what led him to develop Clausius’ statistical mechanics. I’ve been reading up on this at the library in my University and will be writing an article sometime in the next few weeks.
I certainly haven’t proven this rigorously in this non-mathematical paragraph. However, it is clear the “lose KE and lose temperature” argument has a huge hole in it. Those who want to pursue this line of reasoning IN THE FACE OF STRONG COUNTER-ARGUMENTS, would need to determine the distribution of energies of particles at any altitude, and show that those remaining particles are indeed lower KE then the whole set was at the bottom. I am sure they can’t do this because I am sure they are wrong.
Well, do the maths and see if you get the same answer as Joe Born and Valesco. I’m certainly willing to concede the possibility that the gravito-thermal effect we are outlining might not account for the whole of the dry adiabatic lapse rate, but a substantial part of it. There may be some room in there for radiative effects too. It’s current ongoing work. Real science in real time.
William Gilbert says:
January 21, 2012 at 7:42 pm (Edit)
Robert Brown,
I have been following your posts both here and at Tallbloke’s blog. Unfortunately I have not read all of the posts here at WUWT (although I have covered a lot of them) so I hope what I say is not a repeat of what others may have said.
First, you talk extensively about “equilibrium” and “thermal equilibrium”. But I believe we should be talking specifically about “thermodynamic equilibrium”. Thermal equilibrium is but a subset of thermodynamic equilibrium. A system is in “thermodynamic equilibrium” when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium and chemical equilibrium. Thermodynamic equilibrium equals thermal equilibrium only when a system’s internal energy can be described by
U = CvT (1)
In this case the system’s internal energy is thermal energy and thermal equilibrium is all that matters. Your statement “Thermal equilibrium is isothermal, period” only applies to such a system. But that is not the system of a planetary atmosphere under the influence of a gravitational field.
Second, we need to better define where the classical laws of thermodynamics and equilibrium are valid. They are valid with a homogeneous system where all the locally defined intensive (e.g., per unit mass) variables are spatially invariant. But a system is not homogeneous if it is also affected by a time invariant externally imposed field of force, such as gravity. Thus in a gravitational field the laws of thermodynamics have to be applied in a manner that reflects the external field. This is a paradigm buster in itself.
Third, the thermodynamics of an atmosphere cannot be described wholly through considerations of heat transfer only (Trenberth diagram, anyone?). The atmosphere must be treated as a system undergoing both heat and mass transfer. Mass transfer is the reason that gravity is so important in understanding atmospheric thermodynamics. This gets to the mechanical equilibrium part of thermodynamic equilibrium.
Fourth, chemical equilibrium is also very important in atmospheric thermodynamics. But if you assume uniform molecular diffusivity in a horizontal layer (gravitational potential energy handles the vertical diffusion) we are left with latent heat and that is beyond our discussion here.
Thus, as I explained in a previous Tallbloke post,
the proper formulation of the first law of thermodynamics for a “dry” atmosphere under the influence of a gravitational field is:
dU = CvdT +gdz – PdV (2)
The first energy term, CvdT, is the only variable that deals with thermal energy (temperature). The other two energy terms, gdz (gravitational potential energy) and PdV (mechanical work energy), deal with mass transfer. Thus temperature reflects only one variable in the energy composition of the atmosphere. As Tallbloke has pointed out, for the first law to apply energy can be transformed from one form of energy to another, but total energy content must remain constant (dU = 0). The temperature profile through the atmosphere is dependent on the mix of energies at any given point.
The temperature profile resulting from a dry adiabatic lapse rate is covered in my previous post above. And that profile reflects an isentropic system in steady state dynamic equilibrium described by:
CpdT + gdz = 0 (3)
The same system in static equilibrium can be described by the equation of state:
CpT + gz = constant (4)
But for an isothermal temperature profile to exist in an atmosphere in a gravitational field both CpT and gz must increase with altitude. Thus internal energy (U) is not a constant but must also increase with altitude. That violates the first law. The only way that could be achieved is if work is being done to the system. And such a system would not be in thermodynamic equilibrium.
The zeroth law only applies to a homogeneous system and the atmosphere under the influence of a gravitational field is not a homogeneous thermodynamic system (as defined above). And equation (3) does not violate the second law since the process equation reflects an isentropic (constant entropy) process.
The Jelbring hypothesis holds up perfectly from a thermodynamics standpoint.
Your insertion of an insulated silver wire into the discussion makes for an interesting mental exercise, but it has nothing to do with the thermodynamics of a planetary atmosphere. You have just added a non-existent subsystem to the existing system. And the wire cannot be a metaphor for conduction since vertical conduction is almost non-existent in a gaseous system in a gravitational field.
As for the N&Z hypothesis, I too have no firm opinion as yet. I am awaiting Part 2 of their submission that deals with the detailed thermodynamics. But if that is based on a premise similar to the Jelbring hypothesis, I will be pleased.
I would like to provide one quote from Thomas Kuhn’s book “The Structure of Scientific Revolutions” to wrap things up:
“Because the unit of scientific achievement is the solved problem and because the group knows well which problems have been solved, few scientists will easily be persuaded to adopt a viewpoint that again opens to question many problems that have previously been solved.” (Page 169)
Bill
Scot Allen says:
January 22, 2012 at 12:27 am (Edit)
Robert Clemenzi says:
January 21, 2012 at 10:43 pm
When a molecule moves either toward or away from the center of the Earth, it will undergo an acceleration for some time (dt). If the change in velocity due to gravity is a significant part of the average speed, then there should be a measurable induced lapse rate. However, I suspect (I have not computed this) that the gravitationally induced change in velocity will be at least nine orders of magnitude less than the average velocity (mainly because dt is extremely small). As a result, the gravitationally induced lapse rate will not be significant with respect to the current models.
Average speed of N2 at surface is 500m/s.
It has kinetic energy (ignoring rotational energy)
1/2 * 28 * 1.66 x 10^-27 kg * (500 m/s)^2 = 5.81×10^-21 J.
Average distance between molecules at surface is 10^-5 cm.
28 * 1.66 x 10^-27 kg * (9.8 m/(s^2)) * 10^-5 cm = 4.56×10^-32 J of kinetic energy change over 10^-5 cm.
Seems small, but a molecule at the bottom of the atmosphere transferring energy to another above and so on up to 10km gives 4.56×10^-21 J KE to PE change. That’s significant.
Stephen Rasey says:
January 21, 2012 at 10:06 pm
William Gilbert says: 7:42 pm
dU = CvdT +gdz – PdV (2)
The first energy term, CvdT, is the only variable that deals with thermal energy (temperature). The other two energy terms, gdz (gravitational potential energy) and PdV (mechanical work energy), deal with mass transfer.
It seems to me that you have given insufficient consideration to the mechanical energy changes in Pressure P as a function of z and T. And doesn’t this formula apply to a constant mass? Therefore the volume is a function of pressure which is a function of z.
So far I’ve been taking the view that a column of air would become isothermal over time despite a gravitational field but that there would be more mass per unit volume at the lower levels.
Then the ATE arises when an external energy source is provided.
Does it matter then whether there is or is not some lesser gravitational effect involved ?
If there is then is it significant in relation to ATE ?
Stephen Wilde wrote:
Does it matter then whether there is or is not some lesser gravitational effect involved ?
My take is that if the gravitational lapse rate is on the order of (or equal to) the dry adiabatic lapse rate, then something close to Jelbring is required. However, the isothermal column does not disprove Jelbring.
TB
William Gilbert comment about “Thermodynamic Equilibrium” not being only a “Thermal Equilibrium ” here: https://tallbloke.wordpress.com/2012/01/16/the-gravity-of-some-matter/#comment-14958 is a very important aspect to consider.
I think it schould not be buried in the comments. May be you could persuade William to do an sepparate article or I can persude you to make a summary of what William says.
[Reply] See this thread where William’s paper is linked.
Take gravity and call all of the atmosphere molecules, these little buggers get attracted and are thus compacted near the surface, old sol heats the surface including our ocean surfaces. The little buggers get all hot and bothered and puffed up by sucking in heat when they contact the warm surface of the earth. Thus they start elbowing one another much like a bar room brawl, being all puffed up they become bouyant like a cork in the ocean, and rise, they will continue to rise until one of two things happens.
They will establish equalibrium in a sea of the same density, or they will be impacted by a molecule of much lower temperature but of higher potential energy on its way down under the force of gravity.
This does two things it gives both molecules around the same temperature and energy and they are both attracted back to a lower altitude, thus keeping the heat from escaping.
This is the basis of the lapse rate and the so called green house effect. Non of it is rocket science.
Frank,
I think you have just described the DALR. The pressure temperature relationship of an ideal gas at constant entropy.
But what brings the DALR about? I think it is convection. If you do not have a convecting atmosphere, then gas won’t move up and down the pressure gradient to experience the compressions and expansions.
I think the constant entropy constraint works like this. In an environemnt where convection is the dominant mode of heat transfer, the temperature gradient cannot return to zero. Instead, it returns to the DALR, as isentropicity requires.
High in the atmosphere, convections ceases to be the dominant heat transfer mechanism (I suppose radiative heat transfer takes over). At this point the atmosphere can return itself to equal temperautre so the temperature gradient becomes less than the adiabatic lapse rate. Eventually approaching zero, I suppose.
Otherwise, if the atmosphere were isentripic into outer space, I think the temperature at earth’s surface would be enormous.
How do you refer to prior posts without numbers? Anyway, there is a post dated Jan 22 9:37AM that seems to be from TB, but I think is actually from William Gilbert. So, a note to William Gilbert.
That was an interesting post. You seem to be applying constant entropy as an equilibrium criteria for the atmosphere. I also think it is constant entropy, but have a slightly different understanding – I think it is the constraint placed on convective heat transfer. But my question is slightly different.
If constant entropy applies, then Cp ln(T2/T1) = R ln(P2/P1). R is the gas constant and we can approximate ideal gas heat capacity as 5/2 R. If you solve this equation from the tippy top of the atmosphere to the bottom I think you’ll calculate an enormous surface temperature. So, it seems to me that the isentropic assumption must breakdown somewhere. My question to you is:
1) Do you agree with my algebra (a wholly isentropic atmosphere requires an enormous surface temperature)?
2) If I haven’t made an algebra mistake, where do you think the isentropic assumption breaks down?
3) Or do you see it a different way?
kdk33,
Can you give me some background as to where your equation comes from? Do you have a derivation? I have seen it before (recently I think) but I can’t remember from where.
Thanks,
Bill
It seems to me that Robert Brown’s silver wire is a bad design for PMM2.
A better design would be to use two gases, one light gas with a high boiling point, and one heavy gas with a low boiling point.
Place a reservoir of the light gas in liquid form at the bottom of the column. At the bottom of the column, it will be in equilibrium with its gas form. At all higher elevations, the heavy gas will produce a temperature gradient sufficient to cause the lighter gas to condense. A series of basins and catchments can collect the condensate.
I wonder if anyone else has thought of this.
-God
I am comfortable with isothermic for basically the same reasons compressed air in an air compressor cools down without exchanging gas molecules. Dr Brown points out inversion layers occur overnight. Thats occurring without convection yet overriding the lapse rate and more.
Wind aids the process or they would not get so high in the atmosphere and instead remain a few inches height off the ground if conduction were the sole vehicle.
Further viewing an atmosphere profile suggests somewhat an isothermic influence with warming slopes of alternate layers about the same as the others but opposite signs.
And after thinking originally this would be an important issue I have changed my mind because in a sense it is out of bounds.
Jelbring’s world was created to study internal processes that occur in the presence of a sun but without confounding internal processes with external processes. What it does exclusively in imaginary environments is really not applicable nor do we have any good reference points to work with.
So it seems pretty irrelevant though at some point it might aid in fine tuning some numbers. However, conduction is so slow through still air compared to moving air (ratio roughly 18 to 20:1) that it isn’t all that important.
N and Z is proposing that the actual greenhouse effect might be 80% off and thats not due to maybe a 5% error in failing to consider the system seeks an isothermic equilibrium after convection has ceased.
And finally I don’t see how this issue has anything to do with the basic conclusion that gravity is the cause for what N and Z call the ATE. Convection is the vehicle for the ATE (as we can conclude from the flow diagrams in a higher thread here) and convection is unique to an environment with gravity. So Willis might have stumbled into a valid criticism but its like hitting the target on its outermost ring. You can’t qualify as a rifleman in the service putting your shots there thats because you need to hit vitals to stop the guy your are shooting at not just shoot off his shoulder battalion badge.
The 1365 watts is the relevant figure to work with.
Note they mention the moon surface soars to 390K. For a .89 emissive PBG thats the equivalent of 1365 watts solar with about 50 watts still be absorbed by storage.
William Gilbert,
My equation describes the temperature pressure relationship of an ideal gas in an isentropic process. There are several derivations. Wiki (the fount of all knowledge, it seems) has a decent writeup – Google: isentropic expansion (http://en.wikipedia.org/wiki/Isentropic_process)
They derive the isentropic relationships and then give some equations for the case of constant Cp, which is the ideal gas case. They give the following:
S2 – S1 = nCp ln(T2/T1) + nR ln(p2/p1)
If the process is isentropic then S2 = S1 and the equation above rearranges to the equation I’ve given. They solve this equation in Table of isentropic relations for an ideal gas. They give
T2/T1 = (p2/p1)^(gamma-1/gamma), where gamma = Cp/Cv
Since Cp-Cv = R, the exponent in the equation above is actually R/Cp (after some algebra).
Anyway, hope that helps.
So, let T1,P1 be temperature pressure at the tippy tippy top of the atmosphere. Let P2 be the pressure at planet surface. You can solve for T2, the temperature at the planet surface. If I use the temperature and pressure of space for initial conditions, and 1 bar for P2, the surface pressure, I calculate an enormous temperature. This makes me think the isentropic assumption breaks donw somewhere – or I can’t do algebra.
Let me know what you think.
kdk33,
Thanks for the reference. I think I see the problem. This equation is derived assuming constant volume (V). Thus the energy used in a constant pressure atmosphere for volumetric expansion is locked up and shows up as pressure. The much higher pressure value is then reflected as a much higher temperature. That additional pressure (or volume expansion in a constant pressure system) is what shows up as gravitational potential energy in the first law equation:
U = CpT + gz
I explain how PV is converted to gz in an earlier post. (Let me know if you can’t find it). But this exercise of yours illustrates the significance of gravitational potential energy in atmospheric thermodynamics. It is far from trivial.
I hope this makes sense.
Bill
William Gilbert,
I think I’m a little confused.
The equations are derived assuming constant entropy not volume. In fact, if you look at the table of ideal gas isentropic relationships you will see that volume changes according to the constraint:
PV^(gamma) = constant.
kdk,
It is all very confusing. I don’t use these relations very often so I always have to look them up again. This reference explains your equation’s derivation a little better,
http://www.grc.nasa.gov/WWW/K-12/airplane/entropy.html
but it still gives me a headache. Your equation which shows the relation of T and P is derived from Enthalpy (H) which is a measure of the internal thermal energy (CpT) plus the work energy that would have gone to expansion (PV). This non-mechanical work energy is defined as VdP. The differential equations are process equations that describe a thermodynamic pathway between two equations of state (each at thermodynamic equilibrium). Your equation is showing the entropy change between two equations of state (1 and 2). Since this equation is based on enthalpy, the energy change will thus be the thermal energy change plus the work energy that would have been produced by expansion on the surroundings. Thus if you calculate T2 from the surface and tropopause pressure you will get a temperature based on thermal energy + work energy (constant volume). T2 will be relatively higher. But in the troposphere the system is constant pressure and that work energy is expended on the surroundings via expansion. The temperature T2 will be considerably lower. The constant entropy assumption comes from S2 – S1 = 0.
I hope that helps.
Bill
Tallbloke: I now realize my January 21, 2012 at 8:40 am post contains an error. I was correct in recognizing that a pressure gradient must – at a molecular level – be produced by a gradient in the impulse being conveyed upwards and downwards. However, there are two ways to produce a gradient in the impulse: 1) By different upward and downward molecular speeds (resulting in a temperature gradient) as described by me above OR 2) By a gradient in the number of molecules colliding. Temperature is the average kinetic energy PER MOLECULE, so temperature won’t decrease if the pressure decrease is caused only by a decrease in the density of molecules.
The Feynman Lectures on Physics Vol I Chap 40 says:
P2 – P1 = n2kT2 – n1kT1 = dP = -nmg.dh
IF T2 = T1, then: kT.dn = -mg.dh
and dn/dh = (-mg/kT)*n
and n(h) = n(0)*exp(-mg/kT) isothermal
substituting gives: P(h) = P(0)*exp(-mg/kT) isothermal
The pressure and the density of molecules will both decrease at the same rate in an isothermal system. Therefore different upward and downward molecular speeds are not required to create a pressure gradient, so different molecular speeds will not perturb an isothermal system. Feynman has not proven that a non-isothermal system will be driven to become isothermal, but it wouldn’t be surprising is this happened by thermal diffusion.
Reading elsewhere, I see convincing arguments that an adiabatic lapse rate will not develop spontaneously due only to a gravitational field. Two insulated columns of gas with different heat capacities (and therefore two different adiabatic lapse rates (g/Cp)) in thermal contact with the ground would have different temperatures on top and this temperature difference could be used to drive perpetual motion.
Sorry for my mistake and I hope it hasn’t caused you any problems.
[Reply] No worries, I’ve debunked four ‘perpetual motion’ machines this week alone. 🙂
Re Leonard Weinstein (January 16, 2012 at 9:21 pm).
On January 18, 2012 at 9:12 am Coldish asked Leonard the following question: “…in an atmosphere containing radiative gases what role do the non-radiative gases play in fixing the mean height of mean out-going radiation and thus the average surface T? None at all? If the amount of N2 (+/- O2) in the earth’s atmosphere was, say, doubled, or halved, or removed altogether (while keeping the content of radiative gases fixed) what effect (if any) would that have on surface temperatures?”
For anybody else still wondering about this problem Leonard Weinstein has now provided a partial answer to this question on Jeff Id’s blog. See http://www.noconsensus.wordpress.com
tallbloke says:
January 24, 2012 at 11:31 am
Joules Verne says:
January 23, 2012 at 4:25 pm
Gravity maintains TWO energy gradients. One kinetic and one potential. The kinetic gradient decreases with altitude and the potential gradient increases with altitude. The two opposing gradients cancel out and the column is isogenergetic. This is how you can have a perpetual temperature gradient yet not be able to extract any work from it for a perpetual motion machine – a temperature gradient can be nullified by an equal but opposite gradient of energy in a different form. You can’t connect the cold and hot sides of the atmosphere without climbing up in a gravity well and the useful energy represented by the change in temperature is exactly used up by the energy required to climb uphill against gravity. The books thus balance and conservation of energy is once again safe from the abuses of junk science.
Neat comment Joules. I can’t wait for the mad inventors to put their money where their mouth is and build one of the erroneously designed machines they propose. Problem is, when it fails to work they’ll come to the equally erroneous conclusion that it failed because the atmosphere is isothermal.
Hope no-one catches a nasty chill while bolting thermopiles together at the top of their 10km high rig. While they’re up there, they might notice how much thinner the air is too. That might give a bit of pause for thought about density and its effect on the ability of air packets at different altitudes to retain the heat of the Sun.
Two gradients in the atmosphere?
I add another one, there is also an electrical gradient.
Lets start this with a 1960 paper
http://dx.doi.org/10.1175/1520-0469(1962)019%3C0226:MOEPGI%3E2.0.CO;2
tchannon, wow, what timing. By chance while exploring my last post to refute wuwt I read it is something like 100 V/m, very very little current but I never expect it to be so large, and many of those chart show it much larger than that, nearing 1000 V/m! Now tell me, I feel sure any atmosphere has such an effect so why do so many swear up and down it is totally impossible to actually have a DALR caused by gravity, not made by gravity, but caused? Sure floors me, except, so few really know gravity and all of its vast effects when speaking of large distances parallel with the field. They need to read the book “Gravitation”, all 1300 pages a few times.
Gravity causes exactly the same warpage as charge fields in atomic structures. Gravity behaves exactly the same as charge fields as to effects over distance. Charge fields are created by gravity.
In a boring week I created a number of gravity batteries of oil, paper and foil. In all cases the batteries were positive on top and negative on the bottom.
The voltage over distance was about .50 millivolts per 10 mils or 300volts over 1 meter. This was dielectric warpage as in a condenser, no current flow measured as this was a device to measure potential created by gravity. Do not confuse voltage potential with current flow! You have to gather the charge bodies as well as develop potential and create a controllable current flow as well as allow for recharge. pg