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Re: [Phys-l] Temperture profile in a graviational field




Preliminary note: It must be emphasized that in general, stability
is not the same as equilibrium.

On 01/18/2012 09:33 AM, Christopher M. Gould wrote:
let's distinguish between what happens when we _first_ connect
your air column with your copper column, and the _steady_state_.
If the bottoms were already thermally connected ahead of time, then
it is clear that initially thermal energy has to flow from the top of
the copper into the top of the air, warming it, but after enough energy
flows into the air, an isothermal profile in the air will be set up.
As students of atmospheric physics well know, if the environmental
lapse rate is less than the saturated air lapse rate, the column is
absolutely stable

I thought we were talking about thermal equilibrium. Dynamic stability
is something else entirely.

As students of atmospheric physics well know, an _inversion_ (where
the gas is hotter at the top than at the bottom) is even more stable
than the isothermal case. Let's be clear: dynamical stability does
not imply thermal equilibrium.

On 01/17/2012 03:46 PM, Christopher M. Gould wrote:
The general principle is that any system in mass transport equilibrium
has a uniform chemical potential. If there are no external forces then
that means the temperature will be uniform. Here, with an imposed
gravitational potential, air at the top of a column will be colder than
at the bottom.

If that is the "general principle", it should apply to thermal equilibrium,
should it not?

So how would you describe thermal equilibrium?
-- In thermal equilibrium, is the gas is colder on top?
-- Or isothermal?

===============

A dynamically-stable column of air may require a verrry long time to
reach thermal equilibrium (by diffusion or whatever). I say that if
equilibrium were not isothermal, you would be able to build a perpetual
motion machine. It might run verrry slowly, but even a slow PMM is a
gross violation of the laws of physics.