Re: Definition of heat [and S]

[John Denker <jsd@MONMOUTH.COM>]

At 07:50 AM 11/27/99 -0500, Ludwik Kowalski wrote:
> Let me paraphrase JohnD (see below) in order to be corrected,
> if necessary.

OK, here goes.

> There are no advantages in emphasizing that heat is "energy in
> transfer".

That's one of my points.

>   Heat is a form of energy. Thermal energy is heat.

I recognize *two* definitions of heat.  I don't happen to like one of them,
but I recognize that they both exist.  Thermal energy is one of the two
definitions.  Heatflow is the other.

> It is not wrong to say that the heat lost by an object A is later
> present in objects B or C.

Let's be careful how we say it.  It's not wrong to say it happens if it
happens.  It might happen, but it's not a law of physics.  In general, the
thermal energy lost by A might show up as thermal energy in B or C, or it
might show up as nonthermal energy in A, B, and/or C.

> The caloric analogy is not totally wrong.

IMHO it's wrong enough to be irrelevant.  To my mind, the defining property
of caloric was that it was *separately* conserved, as opposed to the modern
notion that energy is conserved while its various sub-types are not
separately conserved.

>Heat can flow but it is not a material substance.

Yes.

According to the heatflow definition, heat can flow and that's *all* it can
do.  According to the thermal energy definition, it can flow and/or be
converted to nonthermal energy.

> There are more important issues to deal with; some students
> are not aware of the fundamental difference between heat and
> temperature.

This has to do with the nontechnical definitions of heat and is independent
of the aforementioned problems with the technical definition.

There are dozens of nontechnical uses of the word "heat".  In accordance
with the usual ironic rule, problems arise not from the dissimilar ones,
but rather from the ones that are similar but not identical.

Many (perhaps most) technical terms have nontechnical meanings that are
close enough to be confusing.  Examples such as "energy", "elastic", and
"lift" spring to mind.  In this regard thermodynamics is neither much
better nor much worse off than any other field.

> Trying to avoid dS=dQ/T may be challenging to
> some creative thinkers but many teachers are used to it.
> They need to be persuaded to abandon this ....

I hope that isn't meant to be a paraphrase of something I said.  I would be
surprised to learn that it is possible to discuss thermodynamics without
invoking dS=dQ/T.

> They need to be persuaded to abandon this macroscopic approach.

dQ is a macroscopic concept.  T is a macroscopic concept.  dS=dQ/T is a
macroscopic concept.  I would not dream of persuading anybody to abandon
this; it seems like the linchpin of all thermodynamics.

Z (the partition function) is based on quantitative microscopic
concepts.  Z stands for Zustandsumme (sum over states).  S=log(Z) is a
microscopic concept.  The study of such things is called statistical
mechanics in contrast to classical thermodynamics.

BUT (!) -- Macroscopic versus microscopic is not exactly the defining
difference between classical thermodynamics and stat mech.  Carnot was able
to do thermodynamics without making any *quantitative* microscopic
arguments, but he was quite clear about qualitative microscopic statements
such as

  Heat is simply motive power, or rather motion which has
  changed its form.  It is a movement among the particles of bodies.

IMHO it is not helpful to avoid such qualitative microscopic statements in
a course (especially an introductory course) on classical thermodynamics.

Trying to construct a purely macroscopic theory of classical thermodynamics
is a ridiculous exercise anyway.  It's like trying to be more Catholic than
the Pope, if you'll forgive the expression.  (1) We have seen that Saint
Sadi used microscopic concepts when convenient, and (2) we know (because of
the black-body paradox etc.) that sooner or later microscopic concepts are
indispensable.