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From: firstname.lastname@example.org [mailto:phys-l-
email@example.com] On Behalf Of Folkerts, Timothy J
Sent: Tuesday, January 17, 2012 9:05 AM
To: Forum for Physics Educators
Subject: [Phys-l] Temperture profile in a graviational field
Here is an interesting question that I have been seeing in the context of
climate science and the "Greenhouse effect". (I may have more points to
make later, since this topic is interesting and important -- for science and for
Suppose you have a perfectly insulated column of air. Let's minimize
concerns about IR by making the inner walls of the container highly reflect
and making the gas N2 (which emits/absorbs minimal amounts of IR).
Suppose the column is a few km tall, with the base at the surface of the
1) What will be the temperature profile? Certainly there is a pressure
gradient and a density gradient in the column. I would say there is a
temperature gradient as well. On a microscopic scale, between every
collision, if the molecule gains altitude it will gain PE and lose KE (ie it will
cool). Any molecule moving downward will warm. On a macroscopic level,
this can discussed in terms of the "dry adiabatic lapse rate".
http://en.wikipedia.org/wiki/Lapse_rate#Dry_adiabatic_lapse_rate and the
In either case, it is clear to me that the equilibrium condition (both in this
ideal column and in the real atmosphere) would be a temperature gradient
(cooling ~ 10K/km). Do others agree?
2) If this is true, how can this best be squared with the 2nd law of
thermodynamics? If the top and bottom of the column were held at a the
same temperature, there would be a continuous flow of energy from top to
bottom, even though they are the same temperature. Even if the top were
slightly cooler than the bottom, there would be a downward flow. This
would violate a standard statement of the 2nd law, since we have
spontaneous heat from cool to warm.
I've been trying to think of a good way to explain that this is not indeed a
violation. I suspect the best explanation will have to involve the more
fundamental statement of the 2nd law -- that entropy tends to a maximum.
The adiabatic lapse rate leads to an isentropic gas and a constant potential
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