Q & A: does gravity cause a temperature difference?

Q:
Does gravity generate a temperature gradient in a column of motionless gas? When a molecule is flying upwards, won't gravity slow it down? Therefore, molecules that are higher will see a lower average temperature of collisions that hit it. It's a little easier to visualize if you have two vertically separated solid objects in a partial vacuum. I claim you should see a slight temperature difference between them.
- Steven Flarity (age 57)
Phoenix, AZ, USA
A:
Nope. Trying to think of it from your starting point, as molecules go up they do tend to lose kinetic energy. On the other hand, as you look higher up you won't find the molecules which started with low energy, they won't make it that high. So which effect wins? Neither. In equilibrium the temperatures at different heights are exactly the same.

This is not an accident due to particular properties of the ingredients. It follows from the fundamental nature of thermal equilibrium. Equilibrium mean that entropy (S) is maximized. For our purposes here, we can treat the total entropy of the high and low regions as simply the sum of the two: SA+ SB. Let's say that these two regions can trade energy, U. If either one has a bigger derivative of entropy with respect to its U than the other, U will flow to the region with higher derivative. Equilibrium will be reached when the two derivatives are equal: dSA/dUA=dSB/dUB.

So what does that have to do with TA and TB?  The definition of T is1/(dS/dU). So we must have TA=TB for any two regions in equilibrium, regardless of what they're made of or what the gravitational field is.

Mike W.

(published on 07/28/2012)

Follow-Up #1: crackpot thermodynamics

Q:
I have written a paper on this. It is not about "thermal" equilibrium. It is about "thermodynamic" equilibrium. The Second Law of Thermodynamics says thermodynamic equilibrium will evolve with a state that has maximum accessible entropy. This implies isentropic conditions which thus imply a thermal gradient. It has also been demonstrated empirically in over 800 experiments.
- Doug Cotton (age 67)
Syney NSW Australia
A:
I read the paper to which you referred. Watching you take a few swings trying to connect with sophomore thermodynamics answered a question I've long wondered about.
What would it look like if I tried to hit big league pitching?

Mike W.

(published on 02/05/2013)

Follow-Up #2: gravity and temperature

Q:
There are two sides to the temperature gradient problem. The "crackpot" side says there is a temperature gradient and the "educated" side says there is no temperature gradient. It's just plain silly to deny the obvious fact that temperature keeps dropping as elevation increases (with slight variation in extremely thin atmosphere). The physics calculations that show otherwise remove the heated Earth from the equations. The Earth is a massive body that is being constantly warmed by the sun. Of course the air is warmer at the surface of the Earth since the Earth is warm and colder at higher altitude since space is cold. If a physicist wants to calculate the presence or absence of a temperature gradient then at least include the heat from the planet Earth into the calculations otherwise the results of the calculations are the exact opposite of a simple observation.Gary
- Gary Tiani (age 67)
Lexington, MA
A:

Yes, the Earth and its atmosphere are very far from being an equilibrium system. There's energy input from the hot Sun, which mostly warms the Earth's surface. Then that energy flows out to cold space, mostly in the form of infrared light. Part of this pattern is that the atmosphere generally gets colder as you get farther from the surface. There are parts of the stratosphere, however, that are hot because they absorb ultraviolet light from the Sun.

So everybody knows there are big gradients in the temperature of the atmosphere, although they aren't monotonic. Only crackpots think that gravity makes temperature gradients in equilibrium.

Mike W.

(published on 01/02/2016)