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Re: Explanation of def. 4 of Q (long)



John Denker has pointed to a putative weakness in the definitions
of heat and work I have offered. I would suggest, however, that
the issue he raises is a red herring for the following reason:
He has constructed a system possessing a large amount of energy in
a single mode which, like bulk translational kinetic energy, is
uncoupled from other energy storing modes and, therefore, not
subject to the dictates of the equipartition principle.

(Actually, I think any reasonably practical model of the inner
wall of his toroidal box *would* end up coupling the rotational
energy to the other modes and would, as a result, change the
occupation numbers of those modes, the temperature, and the
entropy of the gas. Thus, I would classify the energy change as
heat. But this is all beside the point.)

More generally, I think the weakness JD has exploited is easily
remedied with the addition of a few words that I hope most of us
would agree *could* have gone without saying, but probably
shouldn't have. I would simply add the stipulation that the
change under consideration be from one thermal equilibrium state
to another and that forms of energy that are decoupled so that
they do not participate in the process of equilibration don't
count.

Finally I would offer my opinion that JD's "flywheel" arguments
are generally invalid on their face because they incorrectly treat
rotational energy as if it were a form of (what some people like
to call) "thermal energy"--that is, a form of "internal energy"
that is on the same footing as other forms like molecular motions,
rotations, and vibrations. To the extent that bulk rotational
motion is decoupled form those other modes and populated with far
more than its fair share (a la the equipartition principle) of the
system energy, it is simply not subject to the rules of classical
equilibrium thermodynamics.

Indeed, just yesterday I explained why I generally like to
consider rotational kinetic energy and bulk vibrations as
"internal energy" even *though* they should clearly *not* be
considered to be (what some like to call) "thermal energy."
Specifically, I wrote:

... "bulk" vibration modes can easily be populated
with FAR more than their fair share (a la the equipartition
principle) of the system energy and, therefore, probably should
not be considered when talking about the type of energy some like
to call "thermal energy", however, it is not obvious how to draw
the line between "bulk" vibrations and "thermal" or "microscopic"
vibrations so I'd just as soon include *all* vibrations as
contributors to "internal" energy. If I do that, I feel
inclined to do the same thing with rotational energy which seems
to be the same "kind" of energy as bulk vibration.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm