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

["Carl E. Mungan" <mungan@USNA.EDU>]

John Mallinckrodt reminded us:

> David has provided a thorough "parsing" of his definition of heat.
> I believe it may amount to what I wrote on October 28 in the
> "ENERGY WITH Q" thread":
>
>  "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.'"

Yes, I immediately connected these two emails and appreciate David's
explanation. Just to clarify a couple of small points:

* David did not use the adjective "quantum" anywhere in his
explanation. Would it be fair to say his discussion includes the
possibility that we are doing classical statistical mechanics?

* It would be nice to have some actual examples of how these
definitions of heat and work can be applied. The obvious example is a
collection of up and down spins. The energy spacing between the two
states depends on the magnetic field, which takes work to alter (via
the magnetic susceptibility). Heat changes the relative population of
the two levels. But I'm unclear and even nervous about other
examples. Isn't it possible to do irreversible work (which must
therefore change the entropy)? I am thinking of sliding friction,
Joule's paddle wheels, etc. Equating entropy changes to heat only
holds in defn 2 (heat = thermal energy) and not in defn 1 (heat =
energy transfer due to a temperature difference).

This also leads me to some puzzlement over several recent postings
where folks claim that there is not necessarily a contradiction
between defns 1 and 2. Consider an adiabatic compression of an ideal
gas. Let the system be the gas. Suppose the walls and piston have
negligible mass so we can ignore their internal energies. The gas
warms up, yes? Either an explanation of this process involves heat
(defn 2) or it does not (defn 1). Since I go with defn 1, when I am
teaching thermo I would NEVER say to students that the gas "heats"
up. I would either say it warms up or, better yet, its temperature
rises. A complete explanation would involve the ideal gas law, the
concept of internal energy, and kinetic theory but nowhere would I
mention the terms heat or thermal energy.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/