Page 17: We are told the subject of the book is classical
thermodynamics. We are not told how this differs from
This is a Big Deal, because classical thermodynamics has been obsolete
for more than 100 years. Students need to be warned that it is
Page 17: The emphasis on matter and «energy» to the neglect
of entropy is quite a bizarre way for a thermodynamics
book to define thermodynamics.
(The concept of entropy is not introduced until page 102.)
Page 21: The concept of "amount of substance" is archaic.
Page 24: The discussion does not explain the difference between
units and dimensions. The discussion uses the words correctly,
but the naive student is unlikely to understand or even notice
Page 27: «Classical thermodynamics looks at macroscopic
properties of matter. It deals with the properties of aggregates of
vast numbers of microscopic particles (molecules, atoms, and ions).»
This fails to mention that modern thermodynamics applies to microscopic
as well as macroscopic systems.
This is a Big Deal, because if the first law is not strictly enforced
for small systems as well as large, then the law is unenforceable and
meaningless. Ditto for the second law.
Page 28: There are two definitions of «adiabatic» in common use.
Only one is mentioned here.
Page 28: It says here that the surface area of a solid is an extensive
property. That’s not true. In fact, it is neither extensive nor
Page 30: The definition of «phase» in terms of a
«region» is quite heretical. This definition is inconsistent
with what is conventionally considered a phase change. Instead, such
regions would conventionally be called subsystems or parcels ... or
This heretical definition of «phase» can be seen again on page
Page 31: The assertion that «detectable flow occurs in any
material under shear stress of any magnitude» is simply false.
In a very wide range of practical situations, the flow (if any) is not
Page 38: The definition of «pressure» seems awkward.
Page 52: The notion of «inexact differential» is (according
to Schroeder) a “crime” against the
laws of mathematics. It is also quite unnecessary, as
we can see from the fact that folks including Pippard, Schroeder, and
Moore have written thermodynamics books that do not use
I emphasize that the problem is with the fundamental idea, not the
notation. Changing the notation doesn’t help at all. Writing
ð with a slash through it is just a way of saying “we know
this is wrong but we are going to do it anyway”.
Expressions such as «heat capacity ≡ ðq/dT» (as in
equation 3.1.7 on page 63) prove that the crime is fully intentional,
and that writing ð instead of d is a transparent disguise,
i.e. a distinction without a difference.
Page 52: It says «The value of a state function refers to one
instant of time; the value of a path function refers to an interval of
time.» This statement makes no sense.
Page 53: It is unwise to assume that every reference frame is
Page 53: It is silly to suggest that things like the altitude and
velocity of a fluid parcel relative to the lab frame «are not
properties of the system». Daniel Bernoulli would have
been very surprised to hear this.
Page 56: As a matter of common courtesy, authors
should number all the equations.
Page 56: The equation that is designated the «first
law of thermodynamics» is not the first law of anything. It’s not
even true in general.
It would be much wiser to formulate the first law as a straightfoward
statement of conservation of energy. This idea is touched on in
passing on page 57, but is de-emphasized.
Page 58: The distinction between «contact force»
and a «gravitational force» is very unorthodox. It makes a mockery
of the laws of physics. This may at first seem similar to the
aforementioned confusion between state variables and internal energy
(item 14) ... but it’s not really the same.
As I see it:
- There is a valid distinction to be made between the total system
energy and the “internal” energy.
- There is a valid distinction to be made between things that
are functions of state and things that are not.
- There is a valid distinction to be made between short-range
forces and long-range forces.
However ... these are not the same idea! These are three different
ideas! They are not even particularly closely related.
Page 63: It says «Thermal energy has no exact
definition» but then proceeds to assign a meaning that is quite wrong
even by that low standard. In a typical solid, neglecting the
contribution of potential energy to the thermal energy would
lead you to underestimate the heat capacity by a factor of 2.
Page 64: The alleged requirement that a
reversible process proceed through a «sequence of equilibrium
states» (and not otherwise) is quite unnecessary.
I am not misinterpreting this passage, and I am not picking on an
isolated slip of the tongue. On page 66 it says clearly that «A
purely mechanical process is not reversible, for its states are not
Page 66: The example in Figure 3.2 is a fine
example in terms of common sense and real physics. However, it is
alas not consistent with the approach to thermodynamics taken in this
book. The example cannot be analyzed in terms of heat, work, and/or
internal energy. It is the perfect example for demonstrating
the weakness and incompleteness of the “classical” approach.
People who understand thermodynamics celebrate its power and
generality. In contrast, the approach taken here is needlessly weak
Page 67: It says «We may sometimes wish to treat the
temperature as if it is discontinuous at the boundary, with different
values on either side. ... The temperature is not actually
discontinuous; instead there is a thin zone with a temperature
Alas this is not necessarily true in any practical sense. Consider
two chunks of metal at different temperatures, separated by a gap,
with a rarefied gas (Knudsen) in the gap. The dominant issue is not
the temperature gradient in the metal or the temperature gradient in
the gas. The dominant issue is that the gas has no well-defined
temperature at all.
Page 121: Commendable clarity in specifying
the domain of validity of the expression for ΔS, in this case
a reversible process in a closed system.
Page 122: The indented digression
needlessly confuses two different concepts, namely (a) the concept
of integrating factor and (b) the uniqueness (or lack thereof)
of the labels of the adiabatic surfaces. These are two
wildly different concepts. Any invertible function of S would
be sufficient to label the surfaces; this is certainly not
restricted to constant-proportionality functions.
There are many requirements on the entropy function beyond
being a function of state and being suitable for labeling
the adiabatic surfaces.
Page 122: It says: «We may need
to evaluat the entropy of a nonequilibrium state. To do this,
we imagine imposing hypothetical internal constraints that change the
nonequilibrium state to a constrained equilibrium state.»
This is a mixed bag. On the one hand, it exhibits commendable clarity
about what is being assumed. All-too-many other books make this
assumption (or a similar assumption) tacitly, thereby leaving a huge
hole in the structure of the argument, i.e. leaving the readers to
guess how we should define the entropy of a non-equilibrium state. On
the other hand, even in this book we have a problem, because the thing
being assumed is not necessarily true. Counterexamples include:
- Consider the Knudsen gas mentioned in item 21.
- In the context of pulsed NMR experiments, of the kind routinely
performed by chemists, imagine starting with a highly polarized spin
system and applying a π/2 tipping pulse. I know how to quantify
the entropy of the resulting state (and its successor states) using
modern statistical mechanics, but there is not – so far as I can tell
– any way to do it using classical thermodynamics. There is not
any way to reach these states, even approximately, by any combination
of reversible operations and equilibrium states.
Page 123: Here the book utterly fails to heed its own advice.
Previously we were warned that heat and work are not state functions,
even though the entropy is a state function. Here
the book starts talking about the entropy change between two
states A and B, which is OK up to this point, but then
it immediately asks «whether or not there is work during the
process». Since the path has not been specified, we have
no hope of knowing how much work was done along the path.
Specifying the endpoints of the path does not specify the path.
You might hope that the intent was to consider a variety of paths, as
opposed to a single path or «process», but this hope is dashed when
it talks about an infinitesimal path element of «the» irreversible
Page 130: It deprecates the idea of entropy as
disorder. This is commendable.
Page 130: It assumes that accessible microstates
«of equal energy» are equally probable. It then writes
where «W is the number of accessible microstates». The problem
is, the requirement for constant energy has been dropped. Canonical
(not just microcanonical) ensembles are explicitly mentioned. Alas,
this invalidates equation 1 ... yet the book continues to
refer to the equation, to the exclusion of more-general expressions.
Page 130: The discussion of statistical mechanics is so
sketchy that even if it were correct, an ordinary student would have
no chance of understanding it or being able to do anything useful with
This book spends a single sentence connecting the statistical
definition of entropy with classical thermodynamics. This stands in
contrast to other books that spend many pages covering the same
There are apparently no exercises involving the statistical definition
of entropy, which is further evidence that this whole section is no
more than window-dressing.
Page 131: The book grovels before Lambert and Leff,
suggesting that entropy can be interpreted in terms of «spreading»
of energy. This is a bunch of hooey. It is just as invalid as the
interpretation in terms of disorder.
In statistical mechanics, entropy is not defined in terms of energy or
vice versa. There are plenty of examples where the entropy changes
without any energy-spreading whatsoever. Indeed there are plenty of
examples where entropy is well-defined and important while the energy
is completely irrelevant.
Page 134: The book gives a short list of potentials,
and asks us to classify all state functions as either «independent»
or «dependent» variables. This approach is remarkably unmodern,
unsophisticated, and unhelpful.
It would be better to treat all state functions as ... well ...
functions of state. Here the state is an abstract vector.
The state is not «defined» by the state functions, but rather
the other way around.
See also item 32.
Page 135: The discussion of differentiation is
basically sound, although the terminology is messed up. The equation
that is called the “total derivative” would be more appropriately
described as having a differential on one side, and on the other
side an expansion based on the chain rule. Most of the
discussion centers on the chain rule. The concept of differential was
previously introduced; I see no reason to rename it, or to rename the
Much of the general discussion that occurs in section 5.2 would more
logically belong in section 5.1.
Page 137: The notion of «natural variables»
is another thing that we must consider unmodern, unsophisticated, and
As an example, one of the most familiar and elementary ideas in
thermodynamics, namely the heat capacity, comes from differentiating
the energy (or enthalpy) with respect to an “unnatural” variable.
This is probably related to item 30. In many cases,
both problems come from not visualizing thermodynamic state space as a
space, with spatial and topological properties.
Page 145: The thing that is here called the
«Helmholtz energy» is more conventionally called the Helmholtz
potential, the Helmholtz free energy, or simply the free energy.
Page 145: The thing that is here called the
«Gibbs energy» is more conventionally called the Gibbs potential,
the Gibbs free enthalpy, or simply the free enthalpy.
Page 373: It says «The osmotic pressure of the solution,
Π, is defined as the additional pressure the solution must have,
compared to the pressure p’ of the pure solvent at the same
temperature, to establish an equilibrium state ...»
That may be an OK way to measure the osmotic pressure, by seeing
how much non-osmotic pressure coming from outside is needed to balance
the osmotic pressure coming from inside ... but it is not a smart way
to «define» osmotic pressure. By way of analogy, we do not
«define» gravity in terms of the upward force the floor exerts on