Copyright © 2007 jsd

1  Overview

This is a review of the following book:

Author:    Arnold Arons
Title:     Teaching Introductory Physics
Publisher:    John Wiley
Date: 1    1996 or 1997
ISBN:    0471137073

This book is a trap. It is superficially attractive, but the more you step into it, the more it reveals itself to be a morass of wrong physics and bad pedagogy. The book contains some good ideas, but they are so diluted by bad ideas that nothing can be relied upon. This makes the book particularly unsuitable for its target audiences, namely preservice teachers and novice teachers (part I) or students (part III).

The book pays lip service to lofty principles, such as the importance of critical thinking, sensitivity to student misconceptions, and the precedence of ideas over terminology. Alas the book by-and-large fails to uphold those principles. An example is its mishandling of the two-fluid theory of electrical charge (item 24).

The book is too much in thrall to the “historical approach”, resulting in needless complexity, confusion, and error. See section 4.

The book goes out with a bang. Chapters III-3 and III-4 are a long discussion of thermodynamics without entropy ... which is like skydiving without a parachute. The book mentions heat, sensible heat, latent heat, caloric, friction, and energy ... without ever mentioning entropy. Ideas such as spontaneity and irreversibility that are intimately connected with entropy are almost-explicitly attributed to energy instead. Also the student is led by detailed historical arguments to a wrong theory, namely conservation of caloric. This will have to be unlearned later. Unlearning is never easy. See item 45.

A relatively minor additional criticism is that the book is inconsistent as to level. It purports to discuss introductory physics, yet it sometimes complains that conventional courses leave students with an incomplete understanding of difficult topics. That’s silly, since incompleteness is natural and unavoidable in an introductory course. For example, see item 32.

2  Facts About Misconceptions

Part I of Teaching Introductory Physics spends a lot of time discussing misconceptions. If this were done properly, it would not be a problem, insofar as Part I is addressed to teachers, not to naïve students. The problems lie elsewhere:

  1. One problem is that the book is often muddled: It discusses all sides of the issue until the reader can’t tell which ideas are being espoused and endorsed, which ideas are being mentioned by way of counterexample on a teacher-to-teacher basis, and which ideas are counterexamples to be presented to the students. Examples of such muddling can be found in item 17 and item 19.
  2. What’s worse, the book explicitly spreads misconceptions. See e.g. item 5, item 24, and item 47.

For some possibly-constructive suggestions on how to deal with misconceptions in the classroom, see reference 1.

3  Specific Observations

In what follows, approving comments are marked (+) and disapproving comments are marked (–).

1.    (–) On page I-23:  It defines «velocity» in an unconventional and unwise way, and then spends several pages explaining how problematic that is. It’s a straw-man argument. If you define velocity in the usual way, it’s not problematic.

2.    (+) On page I-46:  The book rightly recognizes Galileo’s role as the father of modern science. This includes the idea that even when physics says what will happen, it need not (and often does not) say why it happens. This needs to be emphasized, because it is important and because it is not obvious to students.

3.    (+) On page I-65:  PSSC Physics is rightly praised for a «simple, correct, and consistent presentation suitable for introductory levels.»

4.    (–) On page I-67:  It says we «would do better to redefine weight as occasion arises».

I don’t mind making approximations, especially in an introductory course, but to repeatedly redefine the meaning of a single term, back and forth – not just in the direction of progressive refinement – is a very bad practice. It would be much better to put qualifiers on the various versions, such as the subscripts on gI, gL, and gE as explained in reference 2.

In Teaching Introductory Physics, the definition of mg on page I-16 contradicts the definition on page I-66 which contradicts the definition on page I-126.

5.    (–) On page I-76:  It talks about teaching students to distinguish «active» versus «passive» forces. When 700 physics teachers were asked about this, not one thought it was a good idea. Some students spontaneously make such a distinction, but they should be encouraged to discard it.

The fact is, the laws of physics do not care whether a force is «active» or «passive». There are innumerable examples of forces that cannot meaningfully be classified as «active» or «passive».

6.    (–) On page I-85ff:  The discussion of weightlessness is a disaster. It misunderstands Einstein’s principle of equivalence, namely that the definition of g and hence the definition of weight are frame-dependent. They do not depend on the state of motion of the observed object, but rather on the state of motion of the observer’s frame of reference.

Students enter with a qualitative but perfectly correct notion that astronauts are weightless in the frame comoving with the space station. It would be foolish to force them to unlearn this idea in the introductory class, and then force them to relearn it later.

7.    (–) On page I-92:  The section title says «Objects are not “thrown backwards” when accelerated». This is bad pedagogy for two reasons. First of all, it is suboptimal to talk about what doesn’t happen; it would be better to talk about what does happen. Secondly, this continues the practice of not honoring the principle of “idea before name”, in the sense that the title deflects attention from something important to something hardly worth discussing. There are two simple ideas here, and the crucial first step, the sine-qua-non, is to keep track of which idea you are talking about, which the book fails to do.

It is a great disservice to students to teach them the equivalence principle one day and then penalize them for invoking the principle another day.

This is an example where the book compounds a misconception rather than dispelling it.

8.    (+/–) On page I-97:  This is a Jekyll-and-Hyde passage. I agree that there is an important distinction between an equation and a definition. But replacing the = sign with the ≡ sign is not a good solution to the problem, because the ≡ sign is too symmetric. Equality is symmetric, but definitions are not symmetric. It is much smarter to use the := sign for definitions, writing A:=B when A is being defined in terms of B.

The same issue shows up again on page I-185.

9.    (–) On page I-97:  It says «The equals sign in Fnet = ma is not just an ordinary functional equality. it conceals the combination of arbitrary definition and laws of nature....» I’m pretty sure that is not true. It would be unconventional to define net force in terms of mass times acceleration (especially since that would leave us stuck with the task of defining non-net forces). This would contradict the operational definition of force offered by PSSC, which Teaching Introductory Physics seems to endorse. Conversely, it would be absurd to define mass times acceleration in terms of force. Furthermore, there is no reason why «laws of nature» such of this cannot be expressed in terms of plain old equations. Also I do not know what «functional equality» means in this context; I cannot imagine how it differs from any other kind of equality.

10.    (+) On page I-108:  Yes, students should practice adding vectors graphically, tip-to-tail.

11.    (–) On page I-108:  This makes the point that rotations are not well represented by vectors, but fails to suggest how they should be represented. (Hint: bivectors will do nicely. See reference 3.)

12.    (+) On page I-107:  The mention of «additive inverse» in connection with subtraction is always a good idea. Specifically, when introducing vector subtraction, it is a particularly good idea.

(More generally, an introductory physics course must review many ideas that are directly connected to the axioms of arithmetic, and it helps to be explicit about the connection.)

13.    (+) On page I-108:  The point is well made that «vectors are not tied to points». Textbooks often gloss over this important point.

14.    (–) On page I-109:  This needlessly tramples the distinction between a vector and the components of the vector. Vectors exists as geometric objects, whether or not we evaluate their components relative to this-or-that reference frame. See reference 4.

15.    (–) On page I-117:  Although radian measure is conventional in some situations, it is not «natural». It is not even conventional in all situations. Using radians per second is not more «natural» than using Hz.

16.    (–) On page I-118:  The cosine formula is wrong. It needs repairs in two places.

17.    (+/–) On page I-119ff:  The discussion of circular motion makes some good points, but sometimes gets quite muddled. The section on centrifugal force discusses all possible views of the subject, to the point where I don’t know what is being espoused and what is being deprecated.

18.    (–) On page I-125:  After spending many pages trying to set up a formalism that treats circular motion without the use of centrifugal force, we suddenly get a string of problems that practically beg to be analyzed using the rotating frame of reference, i.e. where the students have every reason to put themselves in the role of observers in the accelerated frame.

19.    (–) On page I-127:  In the passage on fictitious forces, it is particularly unclear what is being espoused and what is being deprecated.

20.    (–) On page I-129 and 130:  It repeatedly fails to make the important distinction between the tidal stress and the observed height of the tide. It takes for granted that the observed tide is «semidiurnal», which is simply not the case. See reference 5.

21.    (–) On page I-142:  It takes an unjustifiably narrow view of what “heat” means. It deprecates the idea of «converting work into heat» even though such terminology has been used in the technical thermodynamic literature uninterruptedly since 1798 (reference 6). See reference 7 for more discussion of the various things “heat” can mean.

22.    (–) On page I-146:  It introduces the «first law» (of thermodynamics) in the form

dE = dQ − dW              (1)

which is not a valid equation, because there is no function Q and no function W that could possibly mean what equation 1 requires them to mean.

Furthermore, even if we were to cross out equation 1 and insert something roughly similar that actually means something, such as

dE = T dS − P dV              (2)

this would still be highly suboptimal, because equation 2 is nowhere near general enough to deserve being called the «first law» of anything. It would be much better to formulate the first law of thermodynamics as a simple, direct statement of conservation of energy, as discussed in reference 7.

Compare item 56.

23.    (–) On page I-148:  It alleges that the change in energy can be expressed as «the algebraic sum of the various different internal energy changes»

ΔE = ΔEtherm + ΔEchem + ΔEkin + ΔEpot + ⋯              (3)

A similar equation appears on page III-128.

Let’s see if we can apply this equation to the mechanisms shown in figure 1. The mechanism on the right side of the figure contains just a simple spring. Any F·dx work done by the applied force will presumably result in macroscopic potential energy stored in the spring, and attributed to the ΔEpot term in equation 3. So far so good.

Figure 1: Locrian and Non-Locrian

Meanwhile, the mechanism on the left side of the figure contains a gas of anhydrous acetic acid molecules. If we temporarily (!) approximate this as an ideal gas, any F·dx work done by the applied force will result in kinetic energy in the gas molecules. So arguably this should be attributed to the ΔEkin term in equation 3. But since it is microscopic kinetic energy, not center-of-mass kinetic energy, arguably it should be attributed to the ΔEtherm term. Furthermore, if we look more closely, we see that the acetic acid molecules undergo a reversible chemical reaction, to an extent that depends on pressure, so this is not really an ideal gas, and some of the F·dx work should be attributed to the ΔEchem term. On the other hand, the energy of chemical bonds is entirely attributable to the potential and kinetic energy of the electrons and nuclei in the molecule, so arguably this should be attributed to the ΔEpot and ΔEkin terms in equation 3.

Overall, I have no idea how to make the RHS of equation 3 meaningful. It appears to be mixing things that ought not to be mixed.

24.    (–) On page I-173, 175, 177, 184, and elsewhere:  It says there are «two distinct “varieties” of charge» .... «The choice of the “two distinct varieties” is eventually forced on us by microscopic rather than macroscopic phenomena.» It says that Franklin’s one-fluid model is «fallacious».

That’s just wrong physics. Charge is not matter, and matter is not charge. Electrons and protons are different kinds of charged particles, but they are not the only kinds of particles, and all together there is only one kind of electrical charge. We know how things would look if there really were multiple kinds of charge, by analogy to the nuclear color charge — and electrical charge definitely does not look like that. See reference 8 for details on this.

This is the height of irony: The book preaches “critical thinking” at every opportunity, yet it repeatedly and emphatically rejects the one-component theory, even though there has never been the slightest evidence against the theory.

25.    (–) On page I-199:  I don’t understand the emphasis on batteries and bulbs to the exclusion of voltmeters.

26.    (–) On page I-203:  It says «Joule’s law should be recognized as having an essentially independent status». I have no idea what that means. Independent of what?

27.    (–) On page I-204:  The footnote gives a hopelessly muddled discussion of what “voltage” means. It dances around the issue of electrostatic gauge invariance without properly dealing with the issue. Sometimes it is useful to assign a voltage to a point in a circuit.

28.    (–) On page I-204:  The footnote implies that “voltage” and “potential” are synonymous, which is not the case, as can be proven by glancing at a betatron.

29.    (–) On page I-213/214:  It says «one could, in principle, find the molecular mass µ of the gas from the measurable quantities since on obtains:

µ = 

where Δp represents the pressure....»

Molecular mass? Really?

It goes on to say «Although this is certainly not a useful way of measure molecular mass, able students find the exercise in mathematical physics very instructive.»

Calling it not «useful» is beyond an understatement. Equation 4 cannot possibly measure the molecular mass at all. This should be obvious on theoretical grounds. It should also be obvious from an order-of-magnitude estimate for the quantities involved, considering (say) a 1000-foot-high column of air subject to a one-Gee acceleration.

30.    (–) On page I-229:  Referring to some of Faraday’s hypotheses, it says «The fact that one might perhaps take issue with some of these views and rationalize the observations in some other way is not the point.» Well, it should be the point. We should critically evaluate the evidence, even if Faraday didn’t.

The book touts the importance of critical thinking, but fails to follow its own advice. The historical tail is allowed to wag the thoughtful dog.

See section 4 for more on this.

31.    (–) On page I-249:  It says «The three preceding derivations of wave propagation velocity have been deliberately designed to dramatize the power of an identical approach applied to seemingly very different physical situations.»

There seems to be some dramatic license involved. The approach that works for pressure waves in a tube of air doesn’t work for strings. The calculation on page I-243 only works for a particular chosen point on a particular chosen waveform; the main features (e.g. dispersionless propagation) of waves on a string were assumed on page I-242. They were assumed without proof, not derived.

32.    (–) On page I-257:  It correctly points out that «Like many other phenomena impinging on immediate experience ... diffuse reflection is very complex.» It then goes on to complain that «Since students are rarely, if ever, asked to sketch diagrams in which they themselves show the multiplicity of rays emerging from each point on the object and then select a preferred ray for further tracing, they end up without firm assimilation of the concept.» Well, I wouldn’t expect them to firmly assimilate complex ideas in an introductory course. It would rarely, if ever, be appropriate to require or expect this.

33.    (–) On page I-275:  Replacing one half-truth with another is nothing to be proud of. In the context of the Thomson cathode-ray experiment, the book says «Many students (even graduate students on qualifying examinations) respond that the gravitational deflection is so small because the mass of the particles is so small. They do not immediately invoke what they supposedly learned about the uniformity of g for all objects, and they do not associate the smallness of the [deflection] with the enormous velocity.»

This issue comes up again in question 14.8 in the book’s Section II.

Consider the contrast:

There is a scaling argument that goes like this:

½ m v2 = q V = constant
  v2  1/m
  t = L/v    distance = rate × time   
    since L is constant   
  d  t2    for any free fall

Under the conditions of the experiment, the length of the apparatus L is constant, the accelerating voltage V is constant, and the charge of each particle q is the same. Therefore the velocity scales inversely like the square root of the mass m, the time of flight scales like the square root of the mass, and the gravitational deflection d scales directly like the mass.

So I would not be too quick to pooh-pooh a student who says that the small mass explains the small deflection. Even a student who cannot articulate the details of the scaling argument might have a good “feel” for the right argument … or might simply have correctly identified the mass as the only parameter that could possibly be relevant.

On the other hand, I would be disappointed if the student explained the mass-dependence in a way that violated the equivalence principle, or who thought the cathode ray velocity was small.

The book’s non-recognition of this scaling argument is inconsistent with its remarks in Section 1.2 and elsewhere, which properly extol the importance of scaling arguments.

34.    (–) On page I-286:  It says «(This is not a matter of the complexity of the idea; it is merely a matter of lack of practice on the part of the students.)»

I disagree. It appears that the key idea here is the gauge invariance of electrostatics. Students were not born knowing this idea. Expecting students to re-invent gauge invariance on their own is completely unreasonable. What’s more, depending on how the chassis and vacuum-envelope of the apparatus are constructed, the ΔV in this experiment may not even exhibit gauge invariance. I would say that there are some quite «complex» ideas involved, and furthermore the problem is seriously underconstrained, because the statement of the problem leaves out important information. This goes far, far beyond «lack of practice on the part of the students».

35.    (–) On page I-287:  It seems that ΔV and ΔVS are two different names for the same thing. This just adds to the burdens imposed on the student by item 34.

36.    (–) On page I-301:  The discussion of special relativity places far too much emphasis on Lorentz transformations. It places far too little emphasis on four-vectors and spacetime diagrams. It thereby passes up two opportunities: (1) to achieve a simpler yet more profound understanding of relativity, and (2) to reinforce and deepen the students’ understanding of ordinary vectors, geometry, and trigonometry. See reference 9 and reference 10.

37.    (–) On page I-330:  The whole discussion of «significant figures» is a disaster, for reasons explained in detail in reference 11.

38.    (+/–) On page III-iii:  It’s true that the usual formulation of the second law of motion (and the work/KE theorem) is only valid for point particles. And it’s true that the limitations and provisos are often not adequately emphasized. On the other hand, it is possible to lift some of these restrictions, as discussed in reference 12.

39.    (–) On page III-22:  The argument as to why impulse is path-dependent is fundamentally unsound. The key question is not asked, let alone answered. The question is, what would happen if we chose a different path from state A to state B? The passage imparts quite a serious misconception about what path-dependent means.

It is always possible, but meaningless, to find a seemingly-path-dependent way of calculating a path-independent quantity. See also item 48.

40.    (+) On page III-23:  In the context of momentum and impulse, the student is asked to «Show, from basic definitions, that kg m/s and N·s are completely equivalent sets of units.» That is interesting, because in the context of gravitation, there is a segment of the PER community that insists on emphasizing the distinction between m/s2 and N/kg.

41.    (–) On page III-4:  When discussing one-dimensional motion, the book says one vector is “positive” while another vector is “negative”. Of course positive means greater than zero, and negative means less than zero. So this leads to the equation

v > 0             (6)

In equation 6, note that:

We should distinguish bad pedagogy from wrong physics. For one-dimensional motion, this example does not count as wrong physics, because in D=1 there is an isomorphism between scalars and vectors. However, it certainly seems like bad pedagogy to emphasize on the LHS that vectors are different from scalars, and on the RHS to treat vectors as indistinguishable from scalars.

This is especially disappointing because better alternatives exist, better in the sense that at little or no cost, they establish concepts that can be generalized to higher dimensions. One zero-cost alternative would be to say that one vector is “directed to the right” while the other is “directed to the left”. This makes use of the idea that a vector has magnitude and direction, which is true in any number of dimensions, from one on up. As another alternative, at small cost one could introduce a basis vector γ and say that the first vector is directed in the +γ direction while the other is directed in the −γ direction.

42.    (–) On page III-84ff:  In the chapter on energy, there is a 1.5-page-long section giving examples illustrating the idea of spontaneity and irreversibility. To all appearances, these are meant to illustrate some property of energy. There is one sentence, buried in the middle of a paragraph on page I-86, where the second law of thermodynamics is mentioned, and a Philadelphia lawyer might argue that because of this one sentence, the whole section is technically correct. However, no matter what the technicalities, this section is the epitome of bad pedagogy. It is entirely inappropriate to feature these examples in a chapter on energy. After reading this section, students will be more confused than before ... confused about two of the most centrally important ideas in physics: entropy and energy.

43.    (–) On page III-67:  It says «We shall reserve the word “heat” for a new idea: The interaction we perceive to be associated with temperature changes.» This clearly violates the principle of “idea before name” to which the book pays so much lip service. The name is introduced concurrently with a “definition”.

What’s worse, this is a terrible “definition”, and it is immediately contradicted by the examples on page III-68, and by the redefinition on page III-69. Not until page III-124 do we see the usual textbook definition of “heat” (which itself is not a very good definition, either, by the way).

The book introduces the terms “sensible heat” and “latent heat” without ever giving reliable definitions for them.

44.    (–) On page III-69:  It says «We say that heat is gained by, or transferred to, systems when their temperature increases (or when they melt) in thermal interactions, and we say that heat is lost by, or transferred out of, systems that decrease in temperature (or freeze).» This is yet another definition of “heat”, which contradicts the previous definition (item 43) and also contradicts later definitions (item 52 and item 55).

This misdefinition mentions melting, but fails to mention evaporation, sublimation, demagnetization, et cetera.

45.    (–) On page III-67ff:  The chapter on “Heat” spends many pages offering the student the idea of heat as a conserved quantity. A Philadelphia lawyer would argue that the author didn’t say anything wrong, since he put the wrong ideas into the mouths of Joseph Black and other historical figures ... but the unsuspecting student will not appreciate that distinction.

On page III-71 the book coyly asks the student to explain «Why does Eq. 3.2.4 suggest that the quantity we have invented may be conserved?» Basic pedagogical principles tell us that ideas that students come to on their own are more deeply seated than ideas that are merely told to them. Alas, here the student is asked to form, based on a sizable collection of evidence, his own notion of conservation of heat. It is not until page III-116 that there is a clear indication that heat can be created from scratch. It is not until page III-122 that there is a clear indication that heat can be converted to motion.

Black believed that “sensible heat” and “latent heat” were state functions. The book does nothing to prevent students from believing the same thing.

This seems like the epitome of bad pedagogy. It practically guarantees that students will come away with deep-seated misconceptions about heat.

This is an object lesson in the perils of the twistorical approach as discussed in section 4.

46.    (–) On page III-73:  Heat capacity is extensive. Specific heat is intensive. It is ironic that the book preaches the importance of scaling laws, but fails to apply the most basic scaling checks and dimensional-analysis checks to statements like this.

47.    (–) On page III-81:  It says:
«You can strengthen your insight into these concepts by now returning to the discussion of impulse and change of momentum in Section 1.9. Notice that impulse, like quantity of heat transferred, is path dependent. In order to calculate an impulse, we must know how the force delivering the impulse varied instant by instant (i.e., we must know the "path" of the force with respect to the succession of clock readings). If we have this information, we can evaluate the impulse as an integral (i.e., an area under a graph). The situation with respect to transfer of heat is exactly analogous: Delivery of impulse (which is not a state variable) results in a change in the state variable called "momentum." Transfer of heat (which is not a state variable) at constant pressure results in a change of the state variable temperature.»

The quoted passage has more errors than it has sentences.

One of the central points that this section tries to make is actually valid, if you take it out of context, and re-interpret it in just the right way: It is true that in non-cramped thermodynamics, there is no path-independent value for ∫ TdS.

Alas, Teaching Introductory Physics buries this fact under three layers of wrong physics, plus a few layers of bad pedagogy.

The book does not correctly explain the relationship between TdS (which is a function of state) and ∫ TdS (which is not). This could have been explained using pictures, such as the picture of uncramped thermodynamics in reference 7. See also reference 13.

48.    (–) On page III-81:  The definition of “path dependent” given here is wrong. As discussed in item 39, the key question is not asked, let alone answered.

49.    (–) On page III-81:  The statement (quoted in item 47) about impulse might have been correct if it had considered paths through position-space instead of state-space. In particular, paths through the position-space inside a betatron can produce a path-dependent impulse, since momentum is not a function of position there, as discussed in reference 14.

However, the quoted statement is clearly talking about paths in state-space. That changes everything, because momentum is a function of state ... not a function of position per se, but a function of state. That allows us to carry out the following calculation:

impulse = 

 F dt
     along some path from state A to state B   


 = p(B) − p(A) independent of path in state-space

50.    (–) On page III-81:  Introducing the term «delivery of impulse» violates the principle of “idea before name”. If this term means anything, it presumably is the same as transfer of momentum.

51.    (–) On page III-81:  Saying that impulse is path-dependent is tantamount to saying that the force field is non-grady. As a pedagogical point, just telling students that such a field exists is next to pointless. Students have a strong tendency to assume that every force field is the gradient of some potential. If you want ’em to believe in (let alone understand) non-grady force fields, it will take some serious work, not just a sentence or two here and there. Teaching Introductory Physics doesn’t offer any diagrams of a non-grady field, and doesn’t mention any concrete real world examples (such as a betatron). The analogy to “some” force field is neither concrete nor correct; see item 49. Diagrams would have been a big help, as in reference 13.

52.    (–) On page III-81:  It says «Transfer of heat (which is not a state variable) at constant pressure results in a change of the state variable temperature.» I assume this is meant to be a general rule, since is not restricted to any particular scenario, and no limits to the validity of this statement are given. This rule more-or-less agrees with the “definition” given in item 43, but disagrees with the “definitions” given in item 43, item 44, and item 55.

This rule is inconsistent with basic physics in this context; it is simply not true that heat transfers of the kind considered in this paragraph always result in a change of temperature.

53.    (–) On page III-122:  The book explains that “living force” is an old term for kinetic energy, then quotes James Joule (1847) as being “inclined to believe that both of these hypotheses will be found to hold good — that ... sensible heat will be found to consist in the living force of the particles of the bodies in which it is induced....” Joule was appropriately cautious. The book is not cautious; it boldly says «[Joule’s hypothesis turned out to be correct.]»

Alas, Joule’s hypothesis is not correct. The KE/PE distinction does not parallel the heat/latent-heat distinction. Not all kinetic energy is thermal, and not all thermal energy is kinetic. See reference 7.

54.    (–) On page III-123:  Although the book repeatedly emphasizes the principle of “idea before name”, it introduces the term “thermal energy” without ever explaining what that means. Is it the same as caloric? Is it a function of state? How is it related to “sensible heat” and/or “latent heat”?

55.    (–) On page III-124:  It says «We reserve the term “transfer of heat” to situations in which thermal energy is transferred from a system at higher temperature to a system at lower temperature without any displacements that involve the doing of work by one system on the other.» This is yet another “definition” of heat. This contradicts the “definitions” given in item 43, item 44, and item 52. This pays lip-service to a particular approach that is popular in the PER literature, but is not actually a good idea.

56.    (–) On page III-126:  The book states the first law in the form

ΔE=Q+W       (allegedly)              (8)

which is not a good idea in general. It wouldn’t be so bad if this formula were advertised as an approximate or introductory idea, but on the contrary, the book utterly fails to recognize the weaknesses of this approach. It says equation 8 «always holds». Counterexamples are easy to find, including a wide range of dissipative phenomena, as in item 57 and in the grindstones discussed in reference 7. Another wide class of counterexamples involves advection, also discussed in reference 7.

Compare item 22.

57.    (–) On page III-137ff:  The whole section 4.22 (“Work and Heat in the Presence of Sliding Friction”) is worse than useless. It consists of bad details in the service of a bad goal.

In previous sections the book defined (after a fashion) W and Q and E, and said that the equation 8 «always holds». Many properties of W were explored, including the work/KE theorem.

Now in section 4.22 an impartial observer would see strong evidence that equation 8 does not hold. Rather than analyzing things impartially, the book brutally redefines W so as to make equation 8 hold. The redefinition is based on the assumption that equation 8 should hold, so the result is a meaningless circular argument.

There is no recognition that the redefinition breaks much of the previous development, including the work/KE theorem.

In any situation where dissipation is involved, this approach invalidates the foundations of classical thermodynamics, and leaves us with nothing. In particular it invalidates the idea that there is a meaningful separation between the macroscopic phenomena (W) and thermal phenomena (Q) as in equation 8. Once you start including “some” unobservable microscopic phenomena in W, it is no longer clear what (if anything) is meant by Q.

As an example of what I mean, consider the skin friction drag on the middle car of a long train, as shown in figure 2. We ignore pressure drag and pressure recovery acting on the front and rear of this car (since they nearly cancel by symmetry), which means skin friction drag is the dominant contribution to the drag. It imparts rightward momentum to the leftward-moving train (as shown by the red arrow) and the same process imparts leftward momentum to the ambient air (as shown by the blue arrow). It would be nice to have a work/KE theorem that included this drag force, but Teaching Introductory Physics leaves us without one.

Figure 2: Skin Friction Drag

The book’s approach is a travesty of science and logic. It is akin to the ad-hoc arguments attributed to Faust in section 4.23.

This also makes a mockery of the so-called historical approach, since the relationship between work and frictional heating has been known since 1798, and should have been taken into account when Q and W were first introduced. Actually the book recognized this problem in the opening sentences on page III-iii (item 38). But the problem, having been recognized, is never solved.

There are ways in which this problem could have been solved, but they are not hinted at in the book. In a small sense the work/KE theorems can be rescued as discussed in reference 12. In a much larger sense thermodynamics can be rescued by giving up on work (W) and heat (Q) and instead talking about energy and entropy, as in reference 7.

As far as I can tell, the word “entropy” does not appear in the book. It is definitely not in the index or the table of contents. Does it appear in the body of the text? If so, it is very inconspicuous. That is really quite astonishing.

You can’t do thermodynamics without entropy.

58.    (+) On page III-147:  The quote from Percy Bridgman explains that the law of conservation of energy is falsifiable, i.e. not merely a convention or assumption.

4  The Twistorical Approach

In many places, this book follows the “historical approach” as a way to motivate and to organize an introductory-level course. This is not good.

An introductory course should keep things simple and straightforward. Real history is neither simple nor straightforward. The real history of science is a tale of confusion, with much backtracking out of blind alleys. Nobody would be so foolish as to inflict the real history on introductory-level students.

Examples of what can go wrong include item 30 and especially item 45. One might argue that item 30 (i.e. explicitly uncritical acceptance of Faraday’s field hypothesis) is OK, according to the maxim “no harm no foul”, since we know in hindsight that Faraday’s speculations turned out to be correct. However, there are at least two reasons why we should consider it a problem:

While item 30 is bad enough, when it comes to item 45 things get much worse. The book spends many pages retracing the path to a theory that turned out to be wrong, namely the conservation of heat. Students who follow this path will learn the wrong theory, and will have a hard time unlearning it. The wrong theory is all the more pernicious because it is plausible.

There is no law that says pedagogy must recapitulate phylogeny. In introductory classes we should use the best available evidence, not the most ancient evidence. For more on this, see reference 16.

I have the greatest respect for real history and real historians. If someone really wants to study the history of science, that’s commendable. The history of science is advanced topic, suitable for those who already have a good grasp of science and a good grasp of historical methods. Please do not confuse introductory physics with the history of physics.

5  References

John Denker,
“Principles of Teaching and Learning”
John Denker,
“Weight, Gravitational Force, et cetera”
John Denker,
“Multi-Dimensional Rotations, Including Boosts”
John Denker,
“Introduction to Vectors”
John Denker,
“Twice-A-Day and Once-A-Day Tides”
Benjamin Thompson,
“Heat is a Form of Motion: An Experiment in Boring Cannon”
Philosophical Transactions 88 (1798)
John Denker,
“The Laws of Thermodynamics”
John Denker,
“One Kind of Charge”
John Denker, “The Geometry and Trigonometry of Spacetime”.
John Denker,
“Odometers and Clocks in Introductory Relativity”.
John Denker,
“Measurements and Uncertainties”
John Denker,
“ Kinetic Energy, Work, Momentum, Force times Time, and Force dot Distance”
John Denker,
“Thermodynamics and Differential Forms”
John Denker,
“Visualizing Non-Conservative Fields and Ungrady One-Forms”.
Thomas Kuhn,
The Structure of Scientific Revolutions
John Denker,
“Students Need the Best Evidence, Not the Most Ancient Evidence”

The book’s frontispiece gives 1997 as the date of copyright, but provides a CIP card giving 1996 as the date of publication.
Copyright © 2007 jsd