Since there has been so much discussion of thermodynamics on this list,
I thought some of you might be interested in the following two items.
First, Tom Moore (of Pomona College) and myself have recently finished
a paper, to be published in American Journal of Physics, entitled
"A Different Approach to Introducing Statistical Mechanics". A preprint
is available (from me) on request. Here is the abstract:
The basic notions of statistical mechanics (microstates, multiplicities)
are quite simple, but understanding how the second law arises from these
ideas requires working with cumbersomely large numbers. To avoid getting
bogged down in mathematics, one can compute multiplicities numerically
for a simple model system such as an Einstein solid--a collection of
identical quantum harmonic oscillators. A computer spreadsheet program
or comparable software can compute the required combinatoric functions
for systems containing a few hundred oscillators and units of energy.
When two such systems can exchange energy, one immediately sees that
some configurations are overwhelmingly more probably than others.
Graphs of entropy vs. energy for the two systems can be used to motivate
the theoretical definition of temperature, T = (dS/dU)^-1, thus bridging
the gap between the classical and statistical approaches to entropy.
Further spreadsheet exercises can be used to compute the heat capacity
of an Einstein solid, study the Boltzmann distribution, and explore the
properties of a two-state paramagnetic system.
Second, I have recently finished typesetting the lecture notes for my
junior-level thermal physics course, formatting them into something that
looks like a 150-page book, titled "An Introduction to Thermal Physics."
Someday I may expand this into a real book for publication. For now,
though, I very much need advice and feedback on the book, especially from
instructors who have taught such a course. If any of you would be willing
to look it over and give me your reaction, I will happily send a copy free
of charge. Here is an outline of the contents, for those who might be
interested:
1. Energy in Thermal Physics
A fairly standard overview of temperature, ideal gases,
equipartition, and the first law.
2. The Second Law
Fundamental statistical ideas applied to two-state systems
and the Einstein solid model; analysis of two interacting
Einstein solids, leading to second law; multiplicity of an
ideal gas; definition of entropy.
3. Interactions and Applications
Definitions of temperature, pressure, and chemical potential
as partial derivatives of the entropy; prediction of heat
capacities and other thermal properties of paramagnet, Einstein
solid, and ideal gas (all microcanonical).
4. Engines and refrigerators
Derivation of limits on efficiency, followed by some discussion
of real engines and refrigerators.
5. Free Energy and Chemical Reactions
Definitions and applications Helmholtz and Gibbs free energies;
chemical equilbrium (law of mass action); phase transformations
and the Clausius-Clapeyron relation.
6. Boltzmann Statistics
Boltzmann factors and partition functions, including applications
to calculation of thermal averages, equipartition theorem, Maxwell
distribution, ideal gases.
7. Quantum Statistics
Gibbs factors; Fermi-Dirac and Bose-Einstein distributions;
degenerate electron gas; blackbody radiation; Debye theory.
If you are interested in either of these items, please send me an e-mail.
(Send it to me personally; do not reply to the list.) Be sure to include
your snail-mail address.
Dan Schroeder
Physics Department
Weber State University
Ogden, UT 84408-2508
dschroeder@cc.weber.edu