An Introduction to Thermal Physics

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

Clarifications and FAQs

This page contains comments, clarifications, and answers to frequently asked questions about the content of the book. For a list of outright errors, click here. For hints on problems that require a computer, click here. For a discussion of how the book was produced, click here. If you have a question or comment that isn't addressed here, please e-mail me at .

• General. Several students have pointed out that many of the problems in the book are difficult, and have asked why there are no answers or hints in the back of the book. In response, let me first say that about 100 of the problems do contain answers or partial answers, while many others contain hints. However, I decided against providing more answers or hints, because I wanted to give instructors the choice of whether to do so. An instructor can always provide more answers, but cannot take away answers that are printed in the book.
  
  If you're struggling with the problems in the book and your instructor is unable to help (or you're using the book for self study with no instructor), you have several options. First, make sure you have read the text carefully, working through every calculation in detail. Second, try working some easier problems before attempting the more difficult ones. Third, try to find other students to study with, so you can check answers and share hints. Fourth, try working some problems out of another book that does provide answers or solutions. Reif (1965) and Zemansky and Dittman (1997) provide selected answers in the back, while Mandl (1988) provides outlines of solutions. Another book that provides solutions is Bowley and Sanchez, Introductory Statistical Mechanics (Oxford University Press, 1996). For much of the material in chapters 1, 3, and 4, you may also wish to consult your introductory physics textbook.


• Sections 1.3-1.6. The term "thermal energy", and the associated symbol U_thermal, are intentionally somewhat ambiguous but nevertheless useful (in my opinion). The idea is that the total energy of the system might contain other contributions, but these do not depend on temperature over the temperature range of interest and therefore they disappear when we consider only changes in energy. For a gas, we normally take the thermal energy to include all kinetic energy (in the center-of-mass frame) plus any vibrational potential energy of the molecules. For a solid, we normally take the thermal energy to be the energy measured relative to its value at absolute zero. Later in the book (for instance, in equation 1.33 on page 25) I've generally dropped the subscript "thermal", hoping that the context indicates which forms of energy are included in U and which aren't. Still, it's good to keep in mind that the U in the first law (equation 1.24) is the total energy, whereas the U that we compute in statistical mechanics is usually just a part of the total energy.


• Section 1.4. The term "heat" causes a great deal of confusion among physicists and physics students. In everyday language, we use the word "heat" in a variety of ways. In physics, we need to adopt a more precise definition, and several have been proposed over the years. My definition of heat as energy that is flowing from one object to another because of a difference in their temperatures follows the usage of Zemansky (see Zemansky and Dittman, 1997, page 73). Currently there seems to be an underground movement among physics teachers to totally abolish the word "heat" used as a noun, substituting phrases such as "energy transferred by heating" or "thermal energy transfer". Although I admit that the everyday word "heat" can be confusing because of its many connotations, my opinion is that there are advantages to having a short (albeit four-letter) word for this concept.


• Section 2.5 (and elsewhere). Note that, for a monatomic gas such as helium or argon, a molecule is the same as a single atom. The word "molecule," in this section and wherever the book discusses gases, is not meant to imply more than one atom per molecule.


• Section 3.3 (and elsewhere). Note that I'm using the symbol M, and the word "magnetization," for the total magnetic moment of the system, not the magnetic moment per unit volume (as is the convention in most electromagnetism books).


• Section 5.2. The discussion on pages 161 and 162 can be confusing if you have in mind a homogeneous, one-component system such as the usual gas-in-a-cylinder. Then, since dN = dV = 0, the quantity (dU - TdS) in equation 5.29 is zero and the whole derivation becomes trivial because the total entropy can't increase--the system is already in equilibrium. The point, though, is that this derivation applies even if the system is considerably more complicated, so it can be in internal disequilibrium even though it is always held at a constant temperature. For example, the system could contain several species of molecules undergoing chemical reactions, or it could consist of two different phases like liquid and gas. In these situations we would need additional variables (besides S, U, V, and a single N) to describe the system's macrostate, so dV = dN_R = 0 does not imply dU = TdS.


• Problem 5.23. The opening sentence of this problem is somewhat misleading, because subtracting mu N from G gives zero, a function that probably doesn't deserve to be called a thermodynamic potential. So really there are only three new potentials to be obtained by subtracting mu N from U, H, and F. (Thanks to T. Clay.)


• Section 5.3. In the derivation of the Clausius-Clapeyron relation beginning at the bottom of page 172, I should have been more clear about the fact that G_l and G_g each represent the Gibbs free energy of the entire mole of the substance, if it is in liquid or gaseous form, respectively. Don't think of the system being part liquid and part gas, with these symbols representing the free energies of the liquid and gaseous portions (which would be ambiguous because each portion could be any fraction from zero to 100%, and the G value would vary accordingly).


• Sections 5.3 and 5.5. Note that the symbol L at the bottom of page 173 denotes an extensive quantity, the total heat absorbed (or more precisely, the change in enthalpy) when the material undergoes the transformation. The symbol L is used in the same way on pages 207-208. However, this use of the symbol L is inconsistent with the use in Chapter 1 (page 32), where I defined L as the heat absorbed per unit mass (an intensive quantity). I should have used a different term, such as "specific latent heat", in Chapter 1, and perhaps a different symbol as well. My apologies.


• Thermodynamic data table (pages 404-405). The data for gases and aqueous solutes can be tricky to interpret, if you are concerned about the fact that real gases are not perfectly ideal, and real solutions are not infinitely dilute. Basically, all the data are such that you get correct results if you naively extrapolate them (assuming ideal/dilute behavior) to the limit of low density/concentration. This means that the numbers are not exact under the standard conditions nominally assumed in the table. Since most gases are fairly ideal at 1 bar, this issue isn't that crucial for gases. Many solutions, however, deviate considerably from "dilute" behavior at the standard concentration of one mole per kilogram solvent, so the data for aqueous solutions can deviate considerably from the true behavior at the standard concentration. For a thorough discussion of these issues, see a physical chemistry textbook such as Atkins (1998).

Last modified on January 9, 2013.