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Re: [Phys-l] T dS versus dQ

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: [] On Behalf Of John Denker []
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

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

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

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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