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,
For a discussion of how the book was produced,
If you have a question or comment that isn't addressed here, please e-mail me
- 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 Uthermal, 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 = dNR = 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 Gl and Gg 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
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.