Re: Why do we care about heat?

[John Denker <jsd@MONMOUTH.COM>]

At 11:41 PM 10/31/99 -0800, Leigh Palmer asked, tongue in cheek:
> Are questions about entropy
> real physics/engineering questions? Does the name of an engineer
> called Sadi Carnot bring any applications to mind?

Hmmmm.  Lemme see.  Maybe one or two.....

> It certainly does matter that one understands the difference
> between work and heat.

Indeed.

1) There is a difference between a taut spring and a hot spring.

2) The difference does not much depend on how things got that way
(isothermally or adiabatically, quasi-statically or suddenly, ...).

3) In some cases there can be minor contingencies about how much of the
energy should be called thermal, to wit:

3a) If something unusual like a spin-echo experiment is going on, entropy
must be defined by conditional probabilities rather than unconditional
probabilities -- conditioned on how much you know about the system.

3b) Equilibrium is when the fast things have happened and the slow things
have not.  So if the timescale is not obvious from context, it is helpful
to make a conditional statement such as "If we look on timescale xxx, the
entropy is yyy."

3*) ... But I mention these quibbles only to minimize their importance in
real-world applications.  I spent years of my life in a research lab where
people did serious thermodynamics for a living:  designing, building, and
operating refrigerators that went down to millikelvin or sometimes
microkelvin temperatures.  I assure you that in order to build this
apparatus and do these experiments, it was necessary to have a consensus
about the meaning of "work" and "heat" and "entropy" -- and there was *no*
difficulty achieving this consensus.

> ... the classical meaning of entropy is the one
> which is fundamental here. One can certainly prove that the
> Boltzmann interpretation set in a quantum mechanical frame is
> also correct, but the first applications of the concept were
> to engineering and chemical problems.

I agree that classical thermodynamics
  a) is one of the all-time great intellectual achievements, and
  b) stands on its own, independent of mechanis.

But this in no way disparages quantum staticstical mechanics, which
  a) is also a great achievement, and
  b) sheds additional light on classical thermodynamics, providing
principled explanations for certain notions that classically had to be
postulated.

> Solution of such problems
> relies heavily on the distinction between heat and work in
> ideal models.

Indeed.


______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com