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

["LaMontagne, Bob" <RLAMONT@providence.edu>]

It appears we have two groups talking past each other. Gravity is a major factor in setting the adiabatic lapse rate. An insulated piston containing air will have a temperature drop when the pressure is reduced - and in the atmosphere gravity is responsible for the pressure decrease with altitude. Hence dT/dh = -g/Cp = -10 degC/km. A simple sketch of this for air can be made from Tds=dh-vdP:  dh =  Cp dT and dP = - rho g dh and ds = 0 (adiabatic).

However, the original proposal added the condition of holding both top and bottom of the column at the same temperature - which changes the situation considerably.  One cannot have the same temperature top and bottom while simultaneously having an adiabatic lapse rate. Everyone appears to be correct - just solving different problems.

Bob at PC



________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of Bernard Cleyet [bernardcleyet@redshift.com]
Sent: Tuesday, January 17, 2012 8:39 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Temperture profile in a graviational field

On 2012, Jan 17, , at 16:38, brian whatcott wrote:

> On 1/17/2012 5:43 PM, John Denker wrote:
> > 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>
> Ah, yes: not accomplished on vertical air masses (as far as I know) ,
>  but certainly done on vertical sea masses.
>  Not a mobile perp., however, just a heat engine of the ordinary kind.
>
> Brian W


Can the temperatures be the same, each top and bottom, but the top one lower than the bottom w/ g?

bc

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