Re: entropy - motivation for definition

[John Denker <jsd@AV8N.COM>]

Bob LaMontagne wrote:
> For lack of time, I'll just give a quick example:
> Isentropic flow of an incompressible fluid. A simple
> analysis of the entropy flow equation for a control volume
> gives that the work done by a pump driving the fluid is the
> sum flow work (v delta p), kinetic energy change and
> potential energy change. That's a use of entropy that
> hardly fits a statistical mechanics approach. I don't think
> this really qualifies as something an engineer doesn't
> "need" to know.

I appreciate the effort, but the example doesn't seem
to answer the question.  The problem (work/pressure/flow)
can be solved just fine by someone who has never heard
of entropy.  It's a mechanics problem.  So if this
characterizes the "needs" of the customers, we can meet
their needs without teaching 'em thermo at all.

> From meteorology: The  Potential Temperature of a parcel of
> air is an isentropic parameter. Statistical analysis
> doesn't give insight into this quantity - traditional Q/T
> does.

That's a better example, in the sense that "adiabatic"
and "entropy" are related concepts ... but again this
problem can be solved by rote application of the "gas
laws" (or in fancier language, the equation of state).
You can take the equation of state to be an observed
fact, in which case you can solve this problem without
knowing anything about entropy ... or you can try to
derive the equation of state from scratch, in which
case you are going to need _statistical mechanics_
since non-statistical thermodynamics won't help you
understand the heat capacity (etc.) of diatomic gasses
under the relevant conditions.

==========

Also, if we're talking about meeting the needs of
engineering students, there's a very good chance that
they'll get a job in a communications-related field or
in computer science, where the statistical notion of
entropy will be far more valuable to them than all the
Q/T in the world.  For that matter, librarians refer to
the mis-shelving of books as being "entropic".

And chemical engineers are very commonly called upon to
work high-stakes design-of-experiment problems, where
notions of entropy and information are central, as I
mentioned in my analysis of the twelve coins problem.
  http://www.av8n.com/physics/twelve-coins.htm

> my comment was simply about using techniques appropriate to
> the audience.

Nobody's opposed to the idea of using appropriate techniques.
The question is what's appropriate, and why?

> To decide as physicists that our way is the
> only way to do things smacks of arrogance.

Which is why I make connections to electrical engineering,
cryptology, gaming, machine learning, chemical engineering,
et cetera.