DBowman's Def 4

[Jim Green <JMGreen@SISNA.COM>]

I agree with both John Mallinckrodt and David Bowman -- This revelation
will likely be met with mixed feelings <g>:

In sum, both seem conclude that the difference between Q and W is that Q
changes the entropy and W does not -- Name  them what you will.

David, I think that I understand your post. Nevertheless there may be a
couple of problems:

1) The only situation where this matters is the ubiquitous adiabatic
cylinder and piston which is operated reversibly. I don't know of any other
cases where "macroscopic" work doesn't change the entropy (ie is not both Q
& W). I would be delighted to be shown others where this can be
analytically demonstrated. This situation leads John Denker and me to worry
about the value of the First Law.

2) The difficulty on this list comes in the paragraph which might follow
your masterful elucidation. No mention is made of the mechanism for W or Q.
You seem to say that it doesn't matter, but this then brings up the common
language diffugalty of thermo with "stuff" flowing. You do eliminate the
assumption that Q depends on a temperature difference across the system
boundary and I wholeheartedly agree. But I would be even more supportive if
you at least said that both Q & W are actions leveled upon the system.
And if you emphasized that U is inside the system.   It is the terminology
and the concomitant pedagogy that the list argues about not the equations.

3) This level of stat mech is clearly too much for any intro student, for
most HS instructors, and, alas, for many on this list. Further, it seems to
do away with classical thermodynamics: Carnot, et al and even Gibbs. Not a
great loss in my opinion, but the chemists and engineers would be totally
lost without their convoluted equations and their books of tables. I think
that John Denker would not mind either as the First Law is not universally
very helpful.  But you then seem to be restricted to a text the likes of
Kittel -- pretty staunch except for the physics majors at Georgetown.

In sum your Def 4 does not disagree with Def 3 and is the position which
has been taken on my web page for many years. There I have tried to
simplify and to make this palatable to the majority of readers --
apparently without much success.  Maybe my lack of mathematical elegance
hinders.

So I think that the list is back to arguing over language usage.

A summary of David's post follows:

> The total finite energy change for the process is the
> integral sum of the individual dU's over the sequence of the process
> as it unfolds. The integral sum of each of the infinitesimal
> first-term contributions *is* the heat Q for the process, and the
> integral sum of each of the infinitesimal 2nd-term contributions *is*
> the (macro)work W done by the system during the process. Thus,
> delta-U = Q + W.
>
> Since the Q is the sum of all the infinitesimal first terms,
> and since they are all due to changes in the probability
> distribution for the system's microstate (for the current
> macrostate at that stage for each infinitesimal contribution), we see
> that the heat Q is (according to def. 4.) "the integral of the
> infinitesimal contributions to the differential change in the
> macroscopic energy expectation due to a change in the probability
> distribution for the system occupying its various microscopic
> states." Furthermore, since the entropy is also determined by the
> {P_r} distribution, any change in that distribution will "typically
> be associated with a change in the system's entropy resulting from a
> change in the system's distribution of microstates which are
> accessible to the system's microscopic dynamics over the time
> interval that the changes occur."

Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen