Re: [Phys-l] The Abysmal Foundations of Thermodynamics

[John Denker <jsd@av8n.com>]

On 12/07/2010 07:31 AM, Rauber, Joel wrote:
> Here is a reference, not really suitable as a textbook for a class;
> but very suitable as a reference for the teacher who is teaching the
> class.
>
> "A survey of Thermodynamics" by Martin Bailyn

As noted, there seem to be two categories of book.  A high-voltage
book is useful:
 -- as a reference
 -- as the text in a review course
 -- as the text for upper-division physics majors at MIT

However, the other 99% of the time what is needed is a low-voltage
text, suitable for an introductory course for students who don't
enjoy "drinking from the fire hose".

A well-regarded book in the high-voltage category is:
  Kittel & Kroemer
  _Thermal Physics_

Returning to the other 99% of the problem, I know of precisely no
thermo books I can recommend in the low-voltage category.

One book that tries to hit this target is
  Sturge
  _Statistical and Thermal Physics: Fundamentals and Applications_

It gets decidedly mixed reviews:  some students love it, some 
students hate it.

I'm not going to write a low-voltage thermo text anytime soon, 
because I don't know how to do it.

The problem is the math.  I don't see any way of expressing (let
alone deriving or understanding) the key thermodynamic ideas except
in terms of probability and multi-dimensional calculus.  However,
there is a need to teach thermo to students who don't have a working
knowledge of these math topics.  Even the students who have passed 
a course that covers probability and div/grad/curl don't have the
math it takes to understand thermo.

If I got roped into teaching such a course, I would get it listed
in the math department as well as the physics department, because
I would spend more than half of the course teaching the required
math.  I would spiral around and around, using the physics to
motivate the math and using the math to explain the physics.

I would do this not out of stubbornness or selfishness, but because
I reckon it would be /easier/ on the students.  Easier and better.
Spending half the course on math means there's only half as much
time to learn the physics ... but using the math you can learn
the physics twice as fast.  More than twice as fast.  Actually
infinitely faster, if you want to actually understand it, which
you were never going to do without the math, no matter how much
time you spent on it.

As icing on the cake, the math involved is useful for other things
besides thermo, so overall this seems like a win/win/win strategy.

Oh, and then there's the prerequisite quantum mechanics.  To me,
thermodynamics is synonymous with statistical mechanics.  It is
predicated on being able to count the microstates.  I am aware
that classical thermodynamics flourished for many decades before
QM was invented ... but personally I don't understand classical
thermodynamics, certainly not the foundations thereof.  Note
that the aforementioned Kittel & Kroemer take an uncompromising
statistical mechanics approach.

If you are teaching physics majors and/or upperclassmen at MIT,
you can assume they know what a quantum state is.  However, as
before, there is a need to teach thermo to students who have 
never seen a quantum state (much less a density matrix).  

I sympathize with the need.  There are lots of engineers out 
there who design refrigerators, piston engines, rocket engines,
et cetera.  They need a good understanding of thermodynamics, 
but might not have any direct need for quantum mechanics.  I 
am willing to believe it is possible to teach things that way,
but I don't know how to do it.

Judging by the number of students who have taken the thermo
course and come away with virtually no feel for the subject,
a lot of other people don't know how to do it, either.

By way of analogy:  A lot of people on this list teach an
"algebra-based" (not calculus-based) introductory physics
course.  It is more-or-less known how to make that work.
About half of the subject doesn't really need calculus, and
there are elaborate circumlocutions that allow us to express
calculus-like ideas without bringing in the heavy mathematical
machinery.

Thermo faces an analogous set of problems, but then the analogy
breaks down spectacularly, because we don't have a solution to
this set of problems.  We don't have the requisite circumlocutions.

Some books take an approach like this: "Here is the entropy.  I 
could explain where it comes from in terms of microstates and 
probability, but we don't have time for that, so you'll just have 
to trust me."  I object to the "trust me" approach on philosophical 
grounds, and also on practical grounds, because virtually all of 
the books that take the "trust me" approach have proven themselves 
to be untrustworthy, in this department as well as others:  they
ask you to believe in a definition of entropy that cannot withstand
scrutiny.