That’s the question posed by Scottish Sceptic here.
When explaining the greenhouse warming effect, I’ve avoided going into the cause of the adiabatic temperature change of the atmosphere as we get higher and instead used a hand waving argument that expanding air is cooler which has been enough to explain the necessary temperature gradient up through the atmosphere (link).
However, this isn’t really the mechanism behind the adiabatic lapse rate.
Then I came across a comment on Roy Spencer’s blog to the effect that the adiabatic lapse rate was caused by the greenhouse effect – indeed driven by it. That seemed to be counter to my understanding. Then another commenter on my blog said it wasn’t due to loss in potential energy as I suggested. So, I decided to think about it more.
First, I should explain that “adiabatic” just means that we are assuming the air does not gain or lose heat to its surroundings (by IR or conduction).
As we know gases are governed by the rule that:
PV = nRT
So, this would suggest that when pressure is reduced, so is temperature. However this is only true of a fixed volume. But when air rises, it expands, so both its pressure goes down and its volume goes up.
So, another way that is used to attempt to explain why the temperature of the gas goes down, is to suggest that it is due to “work done”: because whilst it is expanding it is doing work, this is why it loses energy and therefore heat. That again sounds superficially attractive, but in actual fact when the parcel of air rises it is also gaining potential energy. And moreover, all the surrounding gas is also “doing work” on the other bits of gas around it. So, not only is the parcel of air we are considering doing work against other parcels, but other parcels are doing work against the parcel we are considering. So where is all this “work” going – it can only go into other parcels of air. There can be no net change in energy!
Adiabatic lapse rate is just loss of potential energy
However, once we start thinking about potential energy we have the solution. Imagine if you will a balloon of gas slightly lighter than air (assume the balloon itself is negligible weight). Because the balloon is lighter, it will rise upward. But the gas within the balloon as a finite mass, so in order to make this rise, there has to be a gain in potential energy. But also as the balloon rises, the pressure drops, the balloon expands and the air within the balloon does work (force x distance = work). This work comes from the thermal pressure of the gas. So,, as the air molecules expand they lose heat. And so this is where the potential energy is coming from. If we assume the balloon is big enough to contain 1kg of air, then the transfer of energy per meter is as follows:
Potential energy = energy lost from air = temperature change x specific heat capacity
mgh = T Cp m
(where m is mass in kg, g is gravitational constant 9.8, h is height m, T is temperature C, Cp is specific heat capacity in Joules Centigrade-1 kg-1)
Simplifying we get:-
T/h = g/Cp
The specific heat capacity of air at -50 to 40C is 1.005 kJ Centigrade-1 kg-1
So lapse rate T/h = 9.8/1005
This is the lapse rate of dry air. (Moist air has a different lapse rate because it condenses out water droplets which effectively makes Cp much larger)
Full post with graphics here: What is the adiabatic lapse rate of air? | Scottish Sceptic.
Skipping to the last part…
Greenhouse gases and adiabatic lapse
From this we can conclude:
1. The lapse rate is the rate of loss of energy to potential energy as a packet of air rises.
2. The adiabatic lapse rate will occur naturally in a transparent atmosphere which has no interaction with IR or visible light.
3. If lower layers of the atmosphere are heated, they tend to rise until they encounter a layer at a lower temperature than the lapse rate. So, this mechanism tends to cause convection from the ground up to where the lapse rate breaks down.
4. The lapse rate breaks down because of IR heat loss (or gain). Far from the lapse rate being a result of IR interactive gases (aka greenhouse gases), as has been suggested, greenhouse gases tend to break down the lapse rate tending to move the thermal gradient away from the lapse rate and toward an isothermal region (within the bulk of the atmosphere), but also IR heat loss to space tends to make the upper layers with more of a “window” to the cold of space, colder.
Over to Talkshoppers for discussion.