Copyright © 2010 jsd

Some Observations on Devoe,
Thermodynamics and Chemistry
John Denker

1  Notes

Here are my notes on reference 1:

Howard DeVoe
Thermodynamics and Chemistry (second edition)

I never got around to writing a full-fledged review.

Page 17: We are told the subject of the book is classical thermodynamics. We are not told how this differs from modern thermodynamics.

This is a Big Deal, because classical thermodynamics has been obsolete for more than 100 years. Students need to be warned that it is obsolete.

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 naïve student is unlikely to understand or even notice the distinction.

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 intensive.

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 simply regions.

This heretical definition of «phase» can be seen again on page 127.

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 «detectable».

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 this notion.

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 «Cartesian».

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:

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 equilibrium states.»

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 and incomplete.

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 gradient.»

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:

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 process.

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

Sstat = k ln W + C

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 it.

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 ground.

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 chain rule.

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 unhelpful.

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 ... In other words, the osmotic pressure of a solution ... is the additional pressure that would have to be exerted on the solution to establish transfer equilibrium ....»

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» things. By way of analogy, we do not «define» gravity in terms of the upward force the floor exerts on your feet.

2  References

Howard DeVoe Thermodynamics and Chemistry (second edition)
Copyright © 2010 jsd