An Introduction to Thermal Physics

Daniel V. Schroeder, Department of Physics, Weber State University

Suggestions for Course Plans

Ideas for a One-Semester Course

As noted in the Preface, the book is too long for a one-semester course. You have many choices for what to cover and what to omit, but here are a few suggestions.

Here at Weber State University, my one-semester course omits Sections 1.7, 4.3, 4.4, 5.4-5.6, the Sommerfeld expansion from Section 7.3, and all of Chapter 8. This choice of topics gives somewhat more emphasis to statistical mechanics applications than to thermodynamics.

A very different option would be to start at the beginning of the book and work your way through, stopping when you run out of time. I've never tried this, but I think that in one semester you would probably have to stop at the end of Chapter 6. This selection of topics would emphasize applications to chemistry, earth science, and everyday life. If there's a bit more time, you could cover the beginning of Chapter 7, or jump straight to Section 7.4 on blackbody radiation (possibly followed by 7.5 on Debye theory), or cover either section of Chapter 8.

On the other hand, if the main emphasis of your course is on statistical mechanics, you can go straight from Chapter 3 to Chapter 6. The catch is that you need to come back and pick up most of Sections 5.1 and 5.2 sometime before Section 6.5. If you omit the rest of Chapter 5, all of Chapter 4, and Section 1.7, you may be able to make time for all of Chapters 7 and 8.

A Summary of Inter-Section Dependences

In designing other syllabi, it may be helpful to know exactly what depends on what. Here is a summary:

Nearly everything in Part I is essential, with the exception of Section 1.7 on transport processes which is entirely optional. You might be tempted to skip or skim Section 2.5 on the ideal gas, but the results are used repeatedly later in the book. Section 3.3 on paramagnetism could be postponed until before Chapter 6; if you do this you should also postpone the discussion of magnetic cooling at the end of Section 4.4. Section 3.5 (chemical potential) could be postponed until after Chapter 4.

Nothing later in the book depends on Chapter 4, so you can omit it entirely if you wish. Within Chapter 4, however, there isn't a lot of flexibility; each section builds on those that precede it, except for some of the material on low-temperature physics at the very end.

Sections 5.1 and 5.2 are pretty essential; free energy is needed in Sections 6.5, 6.7, and 8.1, and is mentioned briefly in 7.4. The rest of Chapter 5 isn't really needed in later chapters, though phase transformations are mentioned in places and the van der Waals theory is referred to in Section 8.1. Chemical equilibrium comes up briefly in Section 7.4, but this reference can be easily skipped if necessary.

Within Chapter 5 the logical relations are complex. Practically everything else depends on Sections 5.1 and 5.2, and on the first half of 5.3. Nothing else in the chapter depends on the van der Waals subsection. The concept of mixing entropy from the beginning of Section 5.4 comes up in both 5.5 and 5.6, but the rest of 5.4 could be skipped. The second and third examples in Section 5.6 depend on the first subsection of 5.5, but the rest of 5.5 could be skipped. To cover chemical equilibrium only in ideal gas reactions (not in solutions), you need to cover the beginning of 5.4 but you can omit the rest of 5.4 and all of 5.5 (as well as most of 5.3). If your main goal is to get to the Saha equation, however, the approach of Section 7.1 might be a better option; see Problem 7.3.

The first four sections of Chapter 6 can be read any time after Chapter 3, but Sections 5.1 and 5.2 are prerequisite to the rest of Chapter 6. Sections 6.1 and 6.2 are essential for everything that follows, although the worked examples on atomic hydrogen, paramagnetism, and rotating molecules are not essential in themselves. Sections 6.3 (equipartition) and 6.4 (Maxwell distribution) are optional; either or both could be skipped. Sections 6.5 and 6.6 are needed in 6.7 (ideal gas), which in turn sets the stage for the discussions of quantum gases in 7.2 and nonideal gases in 8.1.

Sections 7.1 (Gibbs factors) and 7.2 (bosons and fermions) are both essential for 7.3 (Fermi gases) and 7.6 (Bose-Einstein condensation). But Section 7.4 on blackbody radiation could be read any time after Section 6.2, if you omit the subsection on "photons" which depends on 7.2. Section 7.5 on Debye theory depends on 7.4 but not on the rest of Chapter 7 (or on the later parts of Chapter 6). The subsection on density of states in Section 7.3 is needed in Section 7.6, but the Sommerfeld expansion is completely optional.

Sections 8.1 and 8.2 are completely independent of Chapter 7 and of each other. Section 8.1 (weakly interacting gases) does depend on nearly all of Chapter 6, while 8.2 (Ising model) could be covered any time after 6.2.

Longer Courses

If you're lucky enough to have more than one semester, you can cover essentially all of the book (though not all of the problems!).

In a two-quarter sequence, covering the whole book would be doable but not trivial. Perhaps the trickiest question is how to divide the material into two equal halves. If the first quarter is intended to emphasize thermodynamics and the second quarter statistical mechanics, then I think I would try to get to the end of Chapter 5 in the first quarter. To do this I would postpone Section 3.3 (paramagnetism) until the beginning of the second quarter, just before Chapter 6; the material on magnetic cooling in Section 4.4 would also have to be postponed. Still, the schedule for the first quarter would be tight.

If you have two full semesters, you should have plenty of time for a leisurely treatment of Chapters 1-5 in the first semester. In the second semester you could cover the rest of the book, possibly including parts of the appendices and some of the more advanced problems from Chapters 7 and 8.


I won't try to list all the ways in which problems depend on earlier problems, or on earlier sections that are otherwise optional. I hope that most such dependences are clear, at least to instructors, from the statement of each problem. In some cases, if you want to get to a particular problem or set of problems, you need to plan in advance by working certain problems in earlier chapters. The problems on black hole thermodynamics (2.42, 3.7, and 7.53) build on each other in this way, as do the problems that develop and apply the grand free energy (5.23, 7.7, and 7.75). Problem 1.16 on the exponential atmosphere is prerequisite to Problems 1.40, 3.37, 5.44, 5.45, and 6.14. The most intricate example is the set of problems that develop partial-derivative trickery for thermodynamic relations, beginning with Problem 1.7 on thermal expansion, continuing with Problems 1.46 and 3.33, and ending with the problems on Maxwell relations on pages 158-159.

In a few cases the results of problems are used later in the main text. The most important example of this is the microcanonical treatment of an Einstein solid, Problems 3.24 and 3.25, which is referred to in Chapters 6 and 7 and is also essential to the completeness of Chapter 3. Problems 6.16 and 6.44 are also in this category, though both are quite short. The result of Problem 2.38 is used in Section 5.4. Problem 1.17 on the virial expansion is optional in the context of Chapter 1, but is recommended before covering the van der Waals model in Section 5.3, and is almost essential before covering Section 8.1. Problem 6.51 is also prerequisite to Section 8.1.

Last modified on January 9, 2013.