Does Gravity Cause a Temperature Difference?
Most recent answer: 07/28/2012
- Steven Flarity (age 57)
Phoenix, AZ, USA
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
- Doug Cotton (age 67)
Syney NSW Australia
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
- Gary Tiani (age 67)
Lexington, MA
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)