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[Phys-l] thermodynamics of dissipation

On 01/11/2010 09:24 AM, LaMontagne, Bob asked:

... What does one do when
external "paddle" work is done on the system? For example, If I treat
a can of paint as the system and I stir the paint with a stick or a
small fan-like stirrer. I no longer have a term that I can add that
can be formulated with state variables.

OK. That is one of the great foundational questions.

The topic can be traced back to the exciting "Boring"
paper of 1798 (Rumford).

The good news is that we all understand what is going
on here. We understand it physically, conceptually,
qualitatively, quantitatively, et cetera. You stir
the paint with a paddle. Your arm gets a little bit
tired and the paint gets a little bit warm. We can
quantify the energy as it goes in via

dE = F•dx

We can measure the temperature by sticking a thermometer
in the paint.

We can quantify the entropy since we know the "heat"
capacity of the paint, which in this case is for practical
purposes really the entropy capacity:

∂ S |
Cp = --------|
∂ ln(T) | P

which can be generalized to

∂ S |
Cx = --------|
∂ ln(T) | X

for almost any thermodynamic potential X, including X≡P
or X≡V among others.

We know the energy and the entropy and the temperature.
So at this point each of us should be as content and smug
as an old cat on a warm rug.


The only problem is that the standard textbooks ask us
to divide things up in ways that don't make sense, and
ask us to encrust the physics with terminology and
concepts that don't make sense ... such as heat.

This is what I call the thermodynamic catch-22:

-- Anybody who thinks they have a clear, unambiguous
understanding of "heat" is confused.
-- Anybody who thinks "heat" is a confusing chimera
has got the right idea.

Constructive suggestion: There is a third way: Don't
worry about the "heat". You don't need to grasp the
nettle. You don't need to sit on the cactus.

If you can quantify the energy and the entropy, you don't
need to worry about "heat".

I used to be bothered by inconsistent and unworkable
definitions of "heat", but not anymore. The definitions
are just as inconsistent and unworkable as ever, but I
don't let it bother me.