Essex on Entropy, Hydrodynamics, Radiative Transfer, Steady State, Thermodynamic Equilibrium

Posted: July 22, 2014 by tchannon in atmosphere, radiative theory

A seminal moment came 1984 when three papers were published by Christopher Essex on thermal radiative transfer and thermodynamic equilibrium. This year, 2014, Essex joined the GWPF advistory council.
Given the ongoing heated discussions on the Talkshop on broadly this subject, perhaps this adds light. Fat chance!

Here is one of the papers (another can be found, third is paywalled)

Minimum entropy production in the steady state and radiative transfer

Essex, C.
AA(Department of the Environment, Canadian Climate Centre, Ontario)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 285, Oct. 1, 1984, p. 279-293. (ApJ Homepage) 10/1984

An extremum principle is developed for radiative transfer in a gray atmosphere by using a purely thermal example from Planck’s (1913) work on heat radiation. Entropy is accounted for, as is Prigogine’s (1947, 1967) theorem describing equilibrium as a thermodynamic state of minimal entropy.

An extremum principle is developed for radiative transfer in a gray atmosphere by using a purely thermal example from Planck’s (1913) work on heat radiation. Entropy is accounted for, as is Prigogine’s (1947, 1967) theorem describing equilibrium as a thermodynamic state of minimal entropy. Attention is given to cases where thermodynamic equilibrium is not present. An isothermal black slab heated on one side is considered. The extremum is shown to be an unconstrained steady state and a minimum. The steady state is also demonstrated not to be equilibrium and a countering force on the slab is modeled. The discussion is extended to local thermodynamic equilibrium and to absorption by two isothermal gray slabs. Energy balance conditions for the latter are calculated in order to obtain a generalized extremum. Constraints on the equilibrium are found using irreversible thermodynamics. The problem of a gray atmosphere is then approached in terms of a continuum of isothermal slabs.

Paper at SAO/NASA ADS

Wikipedia has an article which commences

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with thermodynamic systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium; …

This concept, real systems are not in a final state, are in a state of change is fundamental to earth studies.

Post by Tim

Comments
  1. AlecM says:

    One of the good guys. I have developed his work of 30 years ago.

  2. Tenuc says:

    “This concept, real systems are not in a final state, are in a state of change is fundamental to earth studies.”

    This why the output of all climate models fail to get anywhere near to being able to predict future direction – they cannot even hind-cast well!

    Complex non-linear systems, such as climate have no trends, because climate mechanisms work in concert to dynamically alter their trajectory in response to the constantly varying energy input from the sun, the rest of the solar system and the galaxy.

    Climate is a highly intransigent system and we have yet to develop the mathematical toolkit necessary to deal with it. Long-term forecasting of is just not possible.

  3. If it doesn’t generate the well-known vertical temperature lapse rate structure of the Standard Atmosphere troposphere–which is simply derived from the hydrostatic condition–it is simply more wrong theory. If it doesn’t explain the Venus/Earth temperature ratio I found, over the range of Earth tropospheric pressures, it does not “add light” to the debate.

  4. Because of the cyclic heating and cooling of any location. No actual equilibrium can be established.
    However a cyclic repeatable near equilibrium is possible along with a quite deterministic heat flux from equator to poles. Question is how close to equilibrium need occur, before some of the knowledge of equilibrium, like the equibrium requirements of Kirchhoff’s law of radiation, be correctly applied to this atmosphere.
    Huffman’s question is similar. Why is the atmosphere not considered to have a thermostatic, pressure and temperature gradiant, maintained by gravitational forces. At the same time for thermodynamics, where neither sensible heat, or latent heat are affected by position in a gravitational field, at least in the troposphere. That troposphere is to be considered thermodynamically as both isothermic, and isobaric. Why generate unnecessary thermodynamic processes when no transfer of energy occurs, except for out of equilibrium noise.
    Roger, I wish to identify only scientific stumbles, with the knowledge I have no problem.

  5. That should have been “no transfer of energy between masses occurs”

  6. Sera says:

    @ Will Janoscka:

    Sounds like my steam engine- it works, but it is never in equilibrium. It might pass through equilibrium from time to time, on the way up or down, but it can not stay there- too many factors.

    It’s a pain in the ass to get going, but fun to play with when it works.

  7. Sera says: July 23, 2014 at 5:53 am

    @ Will Janoscka:

    ‘Sounds like my steam engine- it works, but it is never in equilibrium. It might pass through equilibrium from time to time, on the way up or down, but it can not stay there- too many factors.
    It’s a pain in the ass to get going, but fun to play with when it works.’

    This is what is needed to combat the CAGW scam. Much more poking at the planet and measuring the result, then learning. This learning, can possibly counter the arrogant academic SCAM.

  8. Have not read the papers but in the above abstract at least he mentions surfaces for which the S-B equation applies. Prof Hoyt Hottel developed equations from measurements for heat transfer from and to gases (particularly from flames in furnaces). Hottel was the world respected Professor of Chemical Engineering at MIT. From all my reading there is no scientist (particularly so-called Climate scientists) that fully understands thermodynamics and heat transfer -these are engineering subjects underpinned by empirical results not some wishful thinking or thought bubbles I have seen in papers and on blogs from AGW alarmists and sceptics. (Note Baron Joseph Fourier, one of the founders of heat transfer theory from his own experiments could be called an engineer as he was a Prof at the French technical university Ecole Polytechnique – Stefan used Fourier experimental data to work out the Stefan-Boltzmann equation. Fourier also developed the engineering maths, dimensional analysis which scientists, particularly so-called Climate Scientists do not understand with their references to forcing)

  9. Sera says:

    I also have a Stirling engine (toy). And as a scotsman myself, I would like to personally beat the crap out of the man who invented it. Yes it is efficient, and it uses any heat source, but it is the most picky and frustrating piece of hardware ever made.

    Btw- does anyone know whether the atmosphere is still expanding?

  10. tchannon says:

    The Essex work is consistent with reality so any other consistent with reality will agree.

    As it happens I wrote much more than appears in the article but then simplified by cutting all of it. Part of the cut was a parallel with heat engines as several commenters mention but this is universal, all heat engines, they can’t work in an equilibrium world.
    Now someone will show I am wrong, one reason for minimising article content.

  11. A. Ames says:

    tchannon says “The Essex work is consistent —”

    Please, can you explain what aspect of the atmosphere is consistent with isothermal slabs whatever their radiative properties? I would think that downward solar, upward IR cannot
    have a unique temperature.

    Thanks,
    AA

  12. tchannon says:

    Ah, fair question.
    Deleted my initial reply, it is best I minimise what I say, others are more knowledgeable.

    At least two ways of putting this. When a trio of papers are seminal, upsets the apple cart but are accepted there is no conflict, it fits.

    Another way of putting it which I am reluctant to give because it extends much further. Two separate origins (one engineering, one science) for a dual to the usual way of handling heat transfer have become a viable alternative to how things are done. This uses the grey body and layer concept. Consistent with that way of considering things but not consistent with the alternate way. (probably sheds darkness)

    This paper might help or be a leap too far
    http://arxiv.org/pdf/1101.3173

  13. tchannon says: July 26, 2014 at 10:47 pm

    “Ah, fair question.
    Deleted my initial reply, it is best I minimise what I say, others are more knowledgeable.”

    “At least two ways of putting this. When a trio of papers are seminal, upsets the apple cart but are accepted there is no conflict, it fits.”

    Nicely stated and informative! Thanks for the paper. If the climastrologists, used layers of constant emissivity/absorbtivity but varying temperature intervals, the process would be faster, more informative, and more easily checked. I guess this is why they do not.

  14. A. Ames says:

    Tim:

    Thank you very, very much for this interesting thread.

    Before looking at the merits of the papers I had to review the notion of Maximum Entropy Production (MEP) and related ideas. A lot has changed since Prigogine, or even 1984 (no, the other 1984).

    Among references that might be of interest are Paltridge: http://www.mdpi.com/1099-4300/11/4/945,
    Hogg: http://dspace.mit.edu/bitstream/handle/1721.1/26841/27777410.pdf, and Dewar: http://www.mdpi.com/1099-4300/11/4/931.

    The conclusion seems to be that MEP is not a scientific principle, but rather a tool like non-linear Newton-Raphson (NR) — sometimes successful, sometimes not, maybe depending on how you use it. If MEP were a scientific law would such things as steel or glass exist? I refer to NR because it might be an alternative to MEP: from wherever you find yourself, go down the steepest slope.

    How you evaluate the papers depends in part on your view of the status of MEP.

    In your Herbert et.al. reference, excluding weight factors, is the radiation handling essentially the classical Schuster-Schwartzchild two flux approximation?

    Thanks,
    AA

  15. tallbloke says:

    AA: from wherever you find yourself, go down the steepest slope.

    This calls to mind the constructal law, stated by Bejan in 1996 as follows: “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.”

    This evolution of a system (eg Earth) within the larger system (the universe) could be viewed as anti-entropic; i.e. shedding the Sun’s energy at a fast enough rate to prevent a rapid shortcut to a much more entropic state. Currently, the steadily maintained 20% oxygen component (a highly reactive gas) of the atmosphere is an indication that Earth is far from being in a state of ‘maximum entropy’

  16. tchannon says:

    The reason for the article here was a quick filler post at a choice moment to do with discussions on other threads. Sometimes this is picked up and works. In this case not.
    The origin of the article is a body of work towards a more complete article, including pointing out the significance of Essex associating with GWPF.

    Upshot this is a fragment. I know too little about the subject.

    I agree over dispute on whether there is a law or not, this though feeds in to the broader problem related to 1/f noise / flicker noise / pink noise which is found very widely in nature. This too is in dispute although I see it more as something awkward, put on blinkers. In addition there is the oddity that summing 1/f sources then looks like gaussian. However for processes a constancy vs. rate implies rising energy via rate and that is going to break basic laws.

    Returning to the problem of a dynamic world where nothing is in a terminal state, is in transition to, there is a limbo state where practice and simplistic theory differ. Entropy of argument anyone, is that MEP?

  17. A. Ames says:

    tallbloke:

    20% is a clue, isn’t it. Part of why this thread is interesting is because the planet is ridiculously far from equlibrium, yet we talk about it as if it were, (black body radiation is just the start), run models assuming equally ridiculous average steady state, then wonder why the predictions don’t work.

    While the idea of Constructionism is fascinating, are you aware of any implementation? I contrast this with Mandlebrot’s fractals which have influenced civil engineering, polymer science, computer graphics, and handling of real-world statistics.

  18. tallbloke says:

    AA: No. It is illustrated by examples such as evolving river meanders and the like (shortest route downhill isn’t always the best way to shed energy). I think ideas about equilibrium can inform our understanding of the climate system though. The output of the Sun, the mass of the atmosphere, the force of gravity and the heat capacity of the system are all pretty stable.

    In systems involving negative feedback, there is always oscillation either side of ‘optimal’, and this is the general characteristic of the system. At one level the alarmists in the debate worry and fret over a +/- 0.5K oscillation. At the level of glacial/interglacial epochs we are looking at a +/- 2K oscillation. At the level of geological timescales we are looking at a +/- 4K oscillation.

    You can easily encompass that variation by travelling a couple of thousand miles north or south, so I stopped worrying about ‘climate change’ long ago, after realising current changes are well within the range of natural variation.

  19. A. Ames says:

    tchannon says:
    “—the broader problem related to 1/f noise / flicker noise / pink noise which is found very widely in nature.”

    You are correct that you see such things in systems far from equilibrium. Noise in semiconductors is a classic example. There are many distributions for which all higher moments do not exist. The more samples (or longer integration time) the larger the variances get. This means that the “central limit theorem” has failed once again, and may be true for “climate” as well.

    I recommend a few nights with Maldlebrot or Feder, if you can find them. There may be more modern books on fractals, but the originals are pretty good.

  20. oldbrew says:

    FYI: ‘Fibonacci Numbers and the Mandelbrot Set’

    http://fractalfoundation.org/OFC/OFC-11-4.html