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

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

Bob at PC says 
> An insulated piston containing air will have a temperature drop when
the pressure is reduced ... 

But only when the gas is doing work on the piston.  In a free expansion,
the temperature remains the same.  So if we started with all the gas in
bottom 100 m of the column and let it expand freely into the rest of the
10 km tall column, the temperature would not drop.  

Of course, in the atmosphere, it is not a free expansion.  If you take
1m^3 of air at sea level and raise it 10km high, the pressure is lower
and the original 1 m^3 will expand, doing work on the air around it,
causing it to cool.

It would seem then that in the limit where a given parcel of air moves
(rises/fall/blows) without exchanging energy by conduction or radiation
(ie adiabatically), the temperature will be governed by the lapse rate.
In the limit where there is no wind or convection, then the temperature
would eventually equilibrate back to a uniform temperature (by a slow
process of thermal conduction through the air).

All of this, of course, assumes that there are no other energy
sources/exchanges in the system.  The real atmosphere has solar inputs
(eg absorption of UV by ozone) and IR exchange (via greenhouse gases).
Another big factor in the real atmosphere is the
evaporation/condensation of H2O.