Re: [Phys-l] T dS versus dQ

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

What characteristic of the final equilibrium state would tell me if stirring occured or not?

While you reject the temperature-entropy relation I wrote, do you also disagree with the final T value after the waves die out being determined by the well defined energy input - in this particular example? I'm trying to get through this one step at a time.

Bob at PC

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker [jsd@av8n.com]
Sent: Sunday, January 17, 2010 6:17 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] T dS versus dQ

On 01/17/2010 03:22 PM, LaMontagne, Bob wrote:
> If the energy input is well defined,

Yes, the energy is well defined.

> isn't the final equilibrium
> increase in the temperature of the gas well defined?


> After waves have
> dissipated, there doesn't seem to be any other way for the energy
> input, mgh, to manifest itself - leaving S = k lnT the same.

The entropy is not k ln T.  Not even close.

I would have said

           S         V/N     5
         ----- = ln ----- + ---          [1]
          N k        Λ^3     2

where Λ depends on temperature.  For details, see
  http://www.av8n.com/physics/thermo-laws.htm#eq-sackur

On the RHS, neither the volume nor the temperature is
a function of energy alone, so even using equation [1]
doesn't tell us the entropy as a function of energy
alone.

Stirred is not the same as unstirred.

Each of E, T, S, P, and V is a function of state.  But
the state vector is not one-dimensional.  Knowing any
one function of state does *not* suffice to tell you
the others.

Restricting the problem to "isothermal" eliminates one
of the variables, which might permit a one-dimensional
analysis ... but the problem of interest is not isothermal.

Alternatively, restricting the problem to "thermally
isolated" and "non-dissipative" would make the
problem isentropic, thereby eliminating one of the
variables ... but the problem of interest is not
isentropic.  Bottom line:  the problem cannot be
reduced to a one-variable problem in any reasonable
way.

Real-world thermodynamics is highly multi-dimensional.

Misconceptions about this run wide and deep.  Students
have spent years doing one-dimensional experiments such
as heat capacity measurements.

You need a multi-dimensional state space to describe any
sort of heat engine or refrigerator, i.e. anything that
involves a thermodynamic cycle ... and also for anything
that involves dissipation.

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