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

["John S. Denker" <jsd@MONMOUTH.COM>]

John Mallinckrodt wrote:
> 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.

I agree with about 5% of that.  I agree that a flywheel (gaseous or
otherwise) contains energy that is non-thermal.  That's the whole
point.  That's why I keep bringing up flywheels as counterexamples
whenever somebody erroneously assumes that all internal energy must be
thermal.

I do not consider this a "red herring".

I do not agree that the flywheel's energy is in a "single mode", since
we are not assuming that it has zero temperature.  In my previous note,
I explicitly mentioned the Maxwell-Boltzmann distribution in order to
make this clear.

> 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.

It is not safe to assume that macroscopic objects never have internal
springs or internal flywheels.  Such an assumption does not go without
saying.

There are many things that are true in certain toylike model systems
that are not true in general.  When an alleged definition is presented
in very formal, sophisticated, and emphatic terms, we generally assume
it is valid in general. If the definitions are in fact limited to
certain toylike model systems, these limitations do not go without
saying.

> 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"--

This opinion is without foundation.  I never treated rotational energy
as thermal.  I never said that.  I never intended that.  I never
imagined that. Indeed the whole point of the example was to treat
rotational energy as nonthermal.  I do not know how I could have made
this more clear.

> that is, a form of "internal energy"
> that is on the same footing as other forms like molecular motions,
> rotations, and vibrations.

Well, certainly internal energy is internal energy.  I treated in in
terms of states, as required by the definitions that JM offered.  I
cannot imagine what other footing could have been used.

> 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.

I'm sure many practitioners will be disappointed to learn that the
Maxwell-Boltzmann distribution is "simply not subject to the rules of
classical equilibrium thermodynamics".

Feynman said "equilibrium is when all the fast things have happened and
all the slow things have not".  I assert that there can exist a
timescale such that the flywheel has established a well-defined
temperature but has not lost its rotational motion.  If somebody can
prove (using physics, not just opinions) that such a timescale cannot
exist, I will be very interested to see the proof.  Meanwhile, until
such a proof appears, I will continue to believe that my flywheel
arguments are valid examples of real physics, not red herrings.

==================

Furthermore, and more importantly, I continue to assert that the effort
to define entropy in terms of equilibrium thermal distributions is very
misguided.  Entropy is well defined even in situations where the
temperature is zero, or undefinable, or unknown, or irrelevant.
Example:  shuffling a deck of cards introduces 226 bits of entropy.
  http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-second-law