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

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

Several people have commented approvingly of what John Mallinckrodt wrote
at 12:54 PM 11/14/01 -0800, namely:
> "Any energy change in a system that is associated exclusively
>  with an alteration in the occupation numbers (rather than the
>  energy levels) of the allowed quantum states *will* alter the
>  entropy of the system and ought, therefore, to be considered
>  'heat.'
>
> "Any energy change in a system that is associated exclusively
>  with an alteration in the energy levels (rather than the
>  occupation numbers) of the allowed quantum states will *not*
>  alter the entropy of the system and ought, therefore, to be
>  considered 'work.'"

That uses elegant and sophisticated language, but alas the notion it
expresses is not consistent with any reasonable definitions of "heat"
and/or "work".

By way of counterexample, consider particle-in-a-box states.  Make the box
toroidal, perhaps by joining a hose to itself end-to-end to form a hollow
hoop.  Populate the states of this box with non-interacting particles to
form an ideal gas.  Start with the gas at some temperature T, but with no
net momentum and no net angular momentum.  Then perform the following
change:  Set the gas in motion flowing along the hose, around and around in
the hoop.  The box is unchanged, so the states _per se_ are not changed.
However, significantly different states are occupied.  The energy is
changed.  If you do it in the ordinary way, the temperature will _not_ be
changed.  A Boltzmann distribution has been changed into a
Maxwell-Boltzmann distribution.  This scenario is constructed to satisfy
the premises of notion #1 above ... however, contrary to the claims quoted
above, the entropy has _not_ increased and it would be foolish to say that
any heating had occurred.

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

People who have been following my recent postings may have noticed a
pattern: flywheels are very useful for refuting a large class of
misconceptions about thermodynamics.  This note just describes the gaseous
version of a flywheel.

Entropy lies at the core of thermodynamics.  Simple "mechanical" statements
about what constitutes entropy and what doesn't constitute entropy are
usually wrong.  For some more-constructive comments on what entropy is, see
  http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-second-law