Thermodynamics for math majors

Question

I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis.

I'd like to do some reading into the field of thermodynamics. Would it be best to start with an introductory text given to most lower-division under graduates or should I begin with something with a little more meat on the bones? By meat on the bones, I mean a bit more rigor and explanation for the fundamental theorems and applications. If this is not clear enough please ask for clarification, I'll be glad to provide it.

Answer 1

If you have a solid basis in mathematics, I would go immediately for an advanced book on statistical mechanics. Most of the introductory classes on thermodynamics are very phenomenological and they introduce a lot of math to the math-deprived physicists (been there, done that). Besides, statistical mechanics lies a solid foundations for the more historically motivated thermodynamics. I myself used the book "Introduction to modern statistical mechanics" by D. Chandler, which is a bit old-fashioned, but rather formal and thorough. Good luck with this wonderful field!

Answer 2

I haven't been through it with a fine-toothed comb , but you might check out David R. Owen's A First Course in the Mathematical Foundations of Thermodynamics in the Springer Undergraduate Text in Math series.

Answer 3

In my opinion Thermodynamics is physics, chemistry and engineering. In thermodynamics mathematical operations are used that are unwarranted and would not be acceptable anywhere else. (eg applying a Legendre transform, without solving the differential equation involved.) I would start with 'Cengel and Boles' not with Callen. As Gibbs noted: "A mathematician may say anything, but a physicist must be partially sane."