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What are some good advanced textbooks for thermodynamics and statistical mechanics for an undergraduate physics student?

It's important that the book is for physics students and doesn't follow an engineering or chemistry approach. Also I am willing to get a full grasp on the subject and spend a lot of time. So it should not only cover the shallow basics.

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You may like starting with Fundamentals of Statistical and Thermal Physics by F. Reif. There is also a good book on Thermodynamics by Enrico Fermi, you might want to get a glimpse of his views on the subject. Then, there is Heat and Thermodynamics by Mark Zemansky. But, keep in mind. These books which I have mentioned are more than sufficient for a fundamental & physical understanding of thermodynamics, these are also the books which I found useful for myself. So, may or may not prove to be useful to you. But, remember, solve sufficient conceptual problems also to reinforce your concepts. After you are done with all these, do check out Landau and Lifshitz's book on Statistical Physics.

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There are many good textbooks you can go for, if you want to build up basics you can use any good university physics to understand heat and the basics of thermodynamics.

After that, you may go through the books like "Statistical Mechanics" by R. K. Pathria and P. D. Beale and/or "Fundamentals of Statistical and Thermal Physics" by F. Reif.

Though I know that the book by Pathria is widely hated in some communities, but after you get through the initial pages of the book, you feel it's quite good unlike the book by Jackson, which maintains the incomprehensibility.

On the other hand, the aforementioned book by F. Reif is a widely accepted book not only for the Statistical Mechanics, but for the Thermodynamics also.

After that, you can obviously go for "Statistical Physics (Course of Theoretical Physics, Volume 5)" by L. D. Landau and E. M. Lifshitz.

Another good book (or the one that I prefer the most) is the book by Prof. Mehran Kardar, "Statistical Mechanics I: Statistical Mechanics of Particles". He delivered his lectures at MIT, which are very closely related to the book and are very well explained; he first taught the basics and then discussed about the Statistical Mechanics for fields. This book (or the lectures) is also easy to comprehend and has good examples and questions as well.