Re: ENERGY WITH Q

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

At 07:00 PM 10/22/01 -0400, Ludwik Kowalski wrote:
> One can declare that S=0 at T=0 (an arbitrary reference level, like for
> PEgrv) and observe that S is always positive.

I would not recommend declaring this, since it's not true.  S is not
arbitrary.  S is not generally zero at T=0.  That's a fact, and piling up a
large number of high-school physics books that say otherwise isn't going to
change this fact.

Put 500 pennies in a shoebox.  Shake vigorously.  There will be 500 bits of
entropy, because you won't know which ones are heads and which ones are
tails.  Put the shoebox in the refrigerator.  Get it as cold as you
please.  The coins will _not_ anneal themselves into the all-heads state,
or any other ordered state.  S=500 bits right down to T=0.

If you want more entropy, something on the order of 10^23 bits, i.e. enough
to show up in a macroscopic calorimetry experiment, there is something
called a _spin glass_ that behaves just the same as those pennies.

> This offers an opportunity to introduce entropy
> (dS=H/T) whose unit is J/K.

This is unsatisfactory for two reasons.  Obviously, this causes trouble
when T=0.

What's worse, at the point where this was introduced, Ludwik's exposition
has not provided a sufficiently-clear distinction between thermal energy
and nonthermal energy.  We were looking forward to getting one.

It's like saying that
        boojum depends on temperature
and then defining
        snark := boojum divided by temperature
The student still has not the slightest understanding of the snark concept
or the boojum concept, and cannot derive one from the other.

If I were doing it, I would define entropy _first_.  I would give a
_nonthermal_ definition of entropy and use that to explain the difference
between thermal and nonthermal energy.
  http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-second-law