DRAFT Review of Schroeder, An Introduction to Thermal Physics

1  Executive Summary

This book has some good points and some not-so-good points. We all know that writing a book is a tremendous amount of work ... but in this case it seems that with a relatively minor amount of additional work this could have been a much, much better book.

2  Report Card

Here is a list of crucial concepts, with a discussion of how the book handles the each concept.

1. (±) First law : This book blows hot and cold on this issue.

   - On page 18 it offers an equation that does not reliably express conservation of energy but says that it does express conservation of energy. It labels either the equation or the conservation idea – I’m not sure which – as the first law. It refers to the name as «mysterious».

   - On page 111 it defines «thermodynamic identity» which is virtually synonymous with the «first law» equation on page 18. The importance of this identity is grossly overstated. The range of validity is mistated: You can’t say “no other relevant variables are changing”. There are dozens of variables (energy, entropy, enthalpy, free energy, free enthalpy, volume, pressure, temperature, altitude, velocity, magnetic field, chemical potentials, et cetera). You simply cannot hold constant every variable that is not explicitly being differentiated; you to be specific about which ones are being held constant.

   + On page 123 it gets it right: «the first law of thermodynamics tells us that energy is conserved»

2. (−) The second law is not clearly stated anywhere I could find. Indeed, on page 59 it says «it’s not a a fundamental law at all – it’s just a very strong statement about probabilities.» That’s remarkably unhelpful.
3. (+) The book mentions the third law, then correctly points out that it is a crock.
4. (−) Definition of entropy :
   • On page 75 is boldly defined as S ≡ k log Ω ... which is sad, because defining it correctly would have been just as easy.
   • On page 75 it mumbles about «disorder» but does not clearly deprecate the idea.

   This is a problem. I know of physics professors and chemistry professors who are absolutely convinced that S ≡ k log Ω by definition. Then these professors get called upon to teach the thermo course (or the “physical chemistry” course) and the problem spreads.

5. (0) On page 17 it states the global version of the law of conservation, which is true but not especially useful. It toys with the idea of a local conservation law («indestructible fluid») but does not embrace it. There is no discussion of the distinction between conservation and constancy.

   Conservation is such a fundamental idea that inadequate coverage seems like a serious omission, but I rate this a (0) not a (−) because the book doesn’t say outright wrong things about this issue, and supplementing a book is very much more pleasant than contradicting a book.

6. (+) There is no Q such that TdS = dQ. This book calls dQ a «crime» which sounds about right to me.
7. (+) Clear explanation of macrostate versus microstate.
8. (+) Wisely avoids mentioning any alleged “natural variables” such as E(V,S) versus H(P,S).
9. (+) Figure 3.1 is an exceptionally clear explanation of how two subsystems behave in equilibrium.
10. (−) In section 3.1, everything seems to work just fine for systems containing only 100 particles. This is good evidence contradicting the first sentence of the preface, which says «Thermal physics deals with collections of large numbers of particles – typically 10²³ or so.»

    Under the heading of spiral development, here’s another remark: When the number of particles gets down to 2 or 3, additional issues crop up. These issues require a more nuanced understanding of temperature and its relationship to the Boltzmann factor. The way equilibrium and temperature are handled here is entirely reasonable for a first introduction, but there should be at least a hint of the limits of validity, and a hint as to where the next layer of detail might be found.

11. (−) The discussion of equipartition of energy starting on page 14 is seriously oversimplified. It makes predictions that are in error by significant amounts, even for ideal gases at room temperature. See www.av8n.com/physics/thermo/z-particles.html#tab-gamma. It says here that he will «prove» the equipartition theorem in section 6.3 ... not that he will prove it with exceptions, and that even then the significance of the exceptions will be understated.
12. (−) Spiral development: The opening paragraph on page 1 starts out by saying temperature is «one of the trickiest concepts — I won’t be ready to tell you what temperature really is until Chapter 3. For now, however, let’s start with a very naïve definition». To that I say yes, amen, keep it up. The book starts with a naïve approximation, which is OK because it is labeled as such, and because there is a link to the later less-naïve version.

    Alas, the rest book does not uphold the high standard we see on page 1. There are lots of naïve ideas set forth as if they were the last word on the subject.

    It would be a lame excuse to argue that it is not possible to explain the limitations of the approximations being used. This is lame because we see on page 1 that it actually is possible to handle this in a reasonable way.

    More importantly, there is no excuse – lame or otherwise – when the limitations are actually stated, but stated wrongly, as on page 111.

13. (−) On page 212, the book accepts Le Châtelier’s «principle» at face value. This is a crock.

3  Easter Eggs

It is unreasonable to expect that everyone who reads the book will work all the exercises. This is a problem, because some important results are hidden in the exercises:

• Triple derivative identity: Problem 1.46(c). This result should be findable in the index, but is not.
• Heat capacity as entropy capacity :
  • should be findable in the index but is not
  • might logically be in section 3.2 ("entropy and heat")
  • actually is in section 3.4 ("mechanical equilibrium and pressure") as problem 3.33
• The expression

  S = −∑ p log p              (1)

  can be found in problem 6.43 on page 249. The equation is evidently considered so unimportant that it is not even given a number.

4  Miscellaneous Observations

The following items don’t closely correspond to any of the “checklist” items.

(−) On page 19 : exercise 1.26 : As always, we should emphasize ideas, not terminology. Alas, this exercise is at best a question about terminology, and does little or nothing to clarify the ideas. How can any answer to this exercise be graded right or wrong? Experts wage holy wars about the terminology in this area.

(−) Starting on page 149, in the long section on «Free Energy as Available Work», the whole idea is fundamentally flawed. In the expression F = E − TS, the free energy is a property of the system itself, just as E, T, and S are properties of the system itself. However, the «available work» (to the extent that the idea makes sense at all) depends on the temperature of the environment.