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Re: entropy - motivation for definition



Mark Sylvester wrote:
... since the (modern) definition of entropy is probabilistic, how
did the early thermodynamicists envisage it? My recollection is that
Boltzmann was so clever precisely because he came up with the
statistical interpretation of the pre-existing concept. Was it a
question of "rigging" something to "explain" the Clausius and Kelvin
versions of the Second Law?

If you're just trying to connect temperature to entropy via
the totem-pole argument (as in my previous note) you don't
actually need to know much about entropy. For reversible
processes, the law of paraconservation of entropy becomes
a law of strict conservation ... so entropy just flows like
a fluid. The totem-pole argument works at the pre-modern
level, needing only a qualitative fluid-like notion of
entropy, not a full-blown statistical definition of entropy.

You also need the famous crucial insight that any
reversible heat-engine has the same efficiency as any
other operating under the same conditions (or otherwise
you could easily build perpetual motion machines).

If that doesn't answer the question, I don't understand
where the question is trying to go, for the following
reasons:

The past is a foreign country.
They do things differently there. (L.P. Hartley)

The past is not as quaint as you might suppose. Mostly
it is just nasty and uncivilized. You don't want to take
your class there, not even for a visit.

I assume "early thermodynamicists" refers to pre-Boltzmann ...
since yes, Boltzmann did use expressions of the form
- Sum P_i log P_i [1]
and did connect them to the entropy ... which was truly a
clever feat, since the sum in expression [1] runs over all
"states", and Boltzmann's work was published in 1896, i.e.
25+ years before QM gave us a firm understanding of what a
"state" was.

OTOH Boltzmann needed a two-volume book full of fiendishly
complicated calculations to explain stuff that nowadays
gets covered in a couple of chapters. I'm not sure I'd be
able to follow his arguments if I couldn't buttress them
with modern concepts as I went along. You don't want to
inflict these "historic" arguments on students.

Things were even worse in pre-Boltzmann days. Carnot
invented entropy while using an *incorrect* notion of
energy. Getting the entropy right under such conditions
is another truly amazing feat. Again, you don't want to
inflict this stuff on students.