Mathematical and conceptual prerequisites of thermodynamics

[naele]

I'm a biochemistry major entering my junior year. After completing the requisite general physics course, I found that I quite enjoyed it and I wanted to take more advanced physics classes. I've set aside my junior year to take math classes necessary to be competent when I take my university's thermodynamics sequence.

So my question is, what mathematics tools do I need to be competent in, as well as what foundational concepts are needed before entering a thermodynamics course?

 

[Andy Resnick]

The mathematics of thermodynamics isn't much more than differential calculus and algebra. Thermodynamics has a notoriously poor mathematical structure, which can cause students to get confused.

For an introductory thermodynamics course, there are not too many difficult concepts, besides entropy. As a biochemistry major, you may have encountered the free energy already; if so, you are further along than many of the physics students.

Fermi's book "thermodynamics" is a great introduction- and it's a Dover book, nice n' cheap. Also hit the school library for a intro the thermo book and browse through it.

 

[Count Iblis]

It's better to study statistical physics which includes thermodynamics. The book by F. Reif, URL="https://www.amazon.com/dp/0070518009/?tag=pfamazon01-20 here[/URL] treats this subject in this way. It starts with statistical physics and thermodynamics is treated later on in the book as soon as the funbdamental concepts like entropy and temperature are defined. That's the most natural way to explain it.

 

[naele]

It's better to study statistical physics which includes thermodynamics. The book by F. Reif, URL="https://www.amazon.com/dp/0070518009/?tag=pfamazon01-20 here[/URL] treats this subject in this way. It starts with statistical physics and thermodynamics is treated later on in the book as soon as the funbdamental concepts like entropy and temperature are defined. That's the most natural way to explain it.

Thanks for the replies. I took a look at the Reif book when I was in the library. Would you consider it useful to either take an appropriate statistics/probability class or get a book and study it on my own? If so, is there a classic text for this purpose?

 

[atyy]

I agree with Andy Renick that elementary calculus is essentially all you need. Also I don't think you need to do statistics and probability separately. I think the only important idea from multivariable calculus that you need is that in general, the integral of a function is path dependent, and only certain functions have integrals that are path independent. In thermodynamics, the former correspond to processes like heating and doing work. The latter correspond to variables describing the state of the system such as energy and entropy.

I agree with Count Iblis that statistical physics is easier, and Reif is one of my favourite books. It's also good to learn thermodynamics the classical way, just to have another approach. I did find this material difficult until I learned statistical physics, but the logic of thermodynamics is beautiful. Our text was Castellan, which I think is clearly written.

Eric Poisson has good notes for thermodynamics as well as statistical physics:
http://www.physics.uoguelph.ca/~poisson/research/notes.html

I also like Mehran Kardar's notes 8.333 notes very much, which are useful if one has read stuff at the level of Reif:
http://ocw.mit.edu/OcwWeb/Physics/index.htm