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

Some musings:

1) Suppose the atmosphere has some lapse rate - it needn't be adiabatic - just negative. Now set up a long rod with insulated sides - but with no insulation on a region near the top and also at the bottom. Since the bottom is in contact with warmer air than the top, energy will flow up the rod!!??

2) If the temperature of the air is held to be the same at two different heights (resulting in an isothermal atmosphere) then there will be no mass transport because the air will be incredibly stable. Any parcel that rises will cool at the adiabatic lapse rate and will be cooler than the isothermal air surrounding it - therefore falling back to its original position.

Bob at PC


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Tuesday, January 17, 2012 6:43 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Temperture profile in a graviational field

On 01/17/2012 03:46 PM, Christopher M. Gould wrote:
mass transport equilibrium .... Here, with an imposed gravitational
potential, air at the top of a column will be colder than at the
bottom.

<hypothesis>
Let's explore that idea.

To make it more interesting, set up a copper rod next to the
air column. There will be no mass transport in the copper,
just thermal conductivity, so it will be isothermal.

The rod and the air column have the same temperature at the
bottom, since they are both in contact with the heat bath
at that point.

If they have a different temperature at the top, you can
run a heat engine using the difference. Voilà! Perpetual
motion machine.
</hypothesis>

I'm sticking with thermal equilibrium being isothermal, even for a gas in the
presence of the gravitational field.
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