Copyright © 2012 jsd
This is the first step toward a review of:
|Serway and Faughn|
I could not bear to read the book cover to cover, so I just spot-checked it. Here are a few of the things I noticed.
«The sails of this boat billow out round and full. As the boat begins moving forward faster and faster, a ball on the deck rolls toward the stern.»
In the real world, long before the ball rolled toward the stern, it would have rolled to the leeward side of the boat. This should be obvious from the illustration.
I mention this because it really offends me when textbooks use fake data. Either the authors have no idea how real sailboats work, and they are making a bad guess based on what they think “should” happen, based on an oversimplified model ... or perhaps they do know, and are deliberately falsifying the data to make it conform to the oversimplified model. Either way, it is shameful.
In fact, the potential energy of the spring does not depend on the position of the spring, if we think of the spring as an object unto itself. Similarly, its potential energy does not depend on interactions with its environment.
In the definition of gravitational potential energy, it is not at all clear what it means for energy to be «associated» with an object. We can “associate” an energy GMm/r with the moon as it sits in the gravitational field of the earth, and we can equally well “associate” the exact same energy GMm/r with the earth as it sits in the gravitational field of the moon. If we do both, we overcount the energy by a factor of two. It might be better to associate the gravitational energy with the system as a whole, including the gravitational field as well as the two objects.
Similarly the book seems to be telling us that an electrical LC oscillator cannot be analyzed in terms of kinetic and potential energy, even though the profoundly similar mass-on-a-spring oscillator can. This is nuts.
Similarly the book seems to be telling us that thermal energy cannot be either kinetic or potential. This is inconsistent with what the book says in chapter 10; see item 30.
This may actually be the correct strategy. It is more important for students to have a feel for what energy does than to have a rote declarative statement of what energy is.
Still, it would be helpful to students and teachers and everybody else if the book were more explicit about the definition or non-definition, to save us from hunting for it and wondering whether we have overlooked something.
The problem is, mass per se is not equivalent to energy per se. The text actually does a decent job of explaining the modern (post-1908) point of view, namely that mass corresponds to the rest energy, and is only part of the overall energy.
Students are often taught to highlight the most important idea in a chapter. It is bad pedagogy for the text to very prominently highlight a statement that is not correct, and indeed embodies an all-too-widespread misconception.
First of all, there is a rule that says ideas are more important than terminology. That is, ideas should be explained before terminology is defined. Defining rotation in terms of spin places far too much emphasis on words, simply defining one word in terms of another word.
Secondly, there is a rule that says learning proceeds from the known to the unknown. It makes no sense to define rotation in terms of spin, because a student who doesn’t know what rotation is probably doesn’t know what spin is, either. It make just as much sense (i.e. no sense at all) to define spin in terms of rotation.
Thirdly, it’s even worse than that, because according to standard physics terminology, spin is not equivalent to rotation. Figure 7-2 on page 244 is the perfect illustration of this, since the people riding the Ferris wheel orbit around the center without spinning. People tend to identify with people, so students can be expected to identify with the riders, so figure 7-2 is almost the perfect example to falsify the claims the book is making.
It goes on to say «The phenomenon is correctly explained as follows ...» which is a sly way of suggesting, falsely, that the explanation in terms of centrifugal force is not correct.
The fact is, centrifugal force exists in a rotating reference frame and not otherwise. If the book chooses not to use rotating frames, that’s fine ... but that is a choice, not a law of nature, and should be presented as such.
This is important, because it is very common for students to have notions of centrifugal force that are deeply ingrained and highly useful but poorly understood. It is important for them to understand when such notions can be used and when they can’t.
The formula is boldly asserted. There is no attempt to derive the equation, even though it could be derived using one or two lines of elementary algebra. This means the student must learn it by rote, or not at all. There is no opportunity (let alone incentive) for the student to think about how the formula might be connected to other notions, such as kinetic energy and gravitational potential energy.
There is a one-sentence attempt to explain qualitatively the physical basis for the equation, but the explanation is wrong. At any altitude, if an object’s speed is just barely «greater than the speed required to keep it in orbit» it is nowhere near escape velocity.
Let’s not even get into the fact that real-world cat doors generally have magnetic latches and/or seals that greatly complicate the torque profile.
That’s not right. Hint: First-order phase transition, such as ice-water or boiling water.
That’s wrong twice over. Not all internal energy pertains to motion per se.
It would be closer to the truth to say that the motional part of the energy is proportional to temperature ... but even that is untrue in the low-temperature limit.
Passages like this cause students to develop deep-seated misconceptions that will have to be unlearned later, at great cost.
We complain when students engage in “equation hunting” and apply equations by rote, without any feel for what the equations mean. I say it is unfair to blame the students, given that the textbook does exactly the same thing.
That’s not entirely true, because in the real world, a pencil will bounce a few times when it hits the floor. The gravitational potential energy will go down, then up, then down, then up for several cycles.
What they say about the pencil is approximately true if you ignore conservation of energy and assume friction is dominant, i.e. Aristotelian mechanics. It is exceedingly weird and confusing to suddenly start assuming this, without warning, without explanation, since the entire book up to this point has assumed just the opposite. The overview in Chapter 1 said we are required to neglect friction; see item 3.
This violates the pedagogical principle that learning proceeds from the known to the unknown. We are being asked to understand heat flow in terms of something (namely pencil behavior) that cannot be understood in terms of anything that the book has touched on so far. It would make just as much sense (i.e. no sense at all) to explain the irreversibility of the pencil behavior in terms of the observed irreversibility of heat flow.
|Let’s defer to item 35 any discussion of whether heat is or is not analogous to pencils. The alleged analogy is imperfect, but that’s not the point. All analogies are imperfect to some degree.||The problem has to do with the non-explanation of the pencil behavior.|
|Learning a new idea properly requires mulling it over, looking for connections to previously-known ideas, and (!) checking for inconsistencies.||Here there is not any attempt to connect the pencil behavior to previously-known ideas, nor any attempt to explain why the assumptions in this chapter are inconsistent with all previous assumptions.|
|Physics is supposed to be logical and consistent. There is supposed to be a logical explanation that covers all of the evidence.||Physics stands in contrast to lawyering and axe-grinding, where it is considered OK to select facts that support the point you are trying to make, while ignoring inconvenient facts.|
Observing two things and remarking that they are in some sense similar does not mean that you have explained either one of them.
The analogy between heat flow and the gravitational potential energy of a pencil is nothing more than a Just-So Story (without the Kiplingesque humor). You could just as well say that similar to the way a growing baby gets bigger not smaller, heat always flows in one direction, from hot things to cold things. It’s an analogy, and it’s not entirely wrong ... but it is not rooted in physics.
In particular, throughout chapter 10 there is an effort to connect kinetic energy to temperature. So perhaps we should look at the pencil’s KE instead of PE. When you drop a pencil, its KE increases to a maximum, then bounces around a bit before settling back to zero. There is no reason why the macroscopic KE should be any worse than the macroscopic PE as a model for the microscopic thermal energy flow, so we must conclude that neither one of them tells us anything about the real physics.
You could fix this by talking about the total energy (rather than KE or PE), subject to a number of restrictions, but the book makes no attempt to do this.
I cannot understand what is being said. I cannot imagine how students could possibly understand it. The thrust of the argument seems to be that “at equilibrium, everything is evenly distributed”. However, that leaves us with more questions than we started with. Consider, for example, a tall column of air in a gravitational field. At equilibrium, why should the kinetic energy be evenly distributed, as opposed to the total energy? That is, high in the column, where the molecules have a higher PE, why should they not have a correspondingly lower KE?
As it turns out, it actually is possible to understand temperature and heat-flow and equilibrium in microscopic terms, and if this were a book for college juniors rather than high-school juniors it would be appropriate to delve into it. The problem is, the verbiage on page 366 of this book bears not even the slightest resemblance to the actual physical explanation.
Even if it were understandable, it wouldn’t be a legitimate explanation.
My gripe is not with the terminology, but with the concept itself. The concept of “heat” that is being put forth here is fundamentally unsound and will have to be unlearned later.
That’s just not true. Hint: First-order phase transition.
This error is to some extent corrected on page 376. However, it is bad pedagogy to ask students to learn a wrong idea and then unlearn it later. What’s worse, on page 411 the book returns to the idea that if the parcel’s temperature is constant, no heat has been transfered to or from it.
That is wildly oversimplified. The thermal energy transfer depends partly on temperature differenc and partly on a host of other considerations ... and not all energy transfers are thermal.
That’s wrong twice over. For starters, we need to distinguish the amount of energy transferred from the rate of energy transfer. The amount depends on rate times time. The maximum amount that can be transferred depends very much on the size of the objects.
Also it is simply not true that the rate of transfer is proportional to temperature, or even a monotonic function of temperature. Hint: Leidenfrost.
|ΔPE + ΔKE + ΔU = 0 (1)|
This is just amazingly bad. For one thing: The equation would make sense if the kinetic energy, potential energy, and internal energy were defined to be mutually exclusive, but they most certainly are not; compare for example table 10-1.
As another way of saying more-or-less the same thing, this chapter does not give a useful sufficiently-detailed explanation of the difference between “internal” and non-internal energy. For example, is the energy of a pressurized gas inside a black box internal or not? Is the energy of a tightly-compressed spring inside a black box internal or not? Is the energy of a flywheel spinning inside a black box internal or not?
Secondly: There is a super-important distinction between conservation and constancy. They are the same for a closed system, but not otherwise. You can’t even argue that a closed system is “implied” because heat is defined in terms of transfer across a boundary, so a notion of open system and a clear distinction between conservation and constancy is absolutely needed here.
Conservation of energy is one of the most fundamental and most useful ideas in all of physics. You would think somebody would take care to state it correctly in the textbooks.
This notation is unwise and highly nonstandard. It interferes with conceptual understanding of what temperature is, or indeed what any measured quantity is. The correct concept is that temperature is temperature, no matter what units are used to measure it. In an equation of the form T = 123 C or T = 456 K, the units of measurement belong on the RHS, not the LHS.
Note that listing three different kinds of temperature (using three different scales of measurement) is inconsistent with listing only one kind of specific heat capacity and one kind of latent heat (using SI units only).
That’s not just some minor mumble; it is a subsection heading. Also, it is not restricted to ideal gases; the cited example is a complex mechanical device, namely a car. Are you seriously trying to tell me that no work can be done by or on a car, so long as it maintains constant volume? Really?
It says that emphatically, in a subsection title. The only problem is, it’s not true. It can’t possibly be true. Disorder, to the extent that you can define it at all, is a property of the microstate. Entropy is, by definition, a property of the macrostate. The entropy of any specified microstate is zero, whether the microstate looks “disorderly” or not.
In fact there is only one kind of electric charge. This has been understood since the mid-1700s. See reference 7.
First of all, that’s not an explanation. Paraphrase is not explanation.
This is a big deal, because one of the goals of the course should be to promote critical thinking. That includes knowing what the word “because” means, and knowing what constitutes a meaningful explanation and what doesn’t.
Secondly, the physics is wrong. In the two-sphere apparatus being discussed, the capacitance from one sphere to the earth might or might not be larger than the capacitance from one sphere to the other.
That’s just ridiculous.
This flatly contradicts what was said earlier in the book; see item 16.
Alas, this is not reliably true ... especially in the context of electricity and magnetism. See reference 8
Connections are important for effective learning.
This is not an example of wrong physics, just bad pedagogy.
The problem is particularly flagrant on page 815 in connection with transformers, which absolutely depend on the voltage not being a potential. Note that when Faraday’s law of induction was introduced on page 798, it was expressed in terms of «emf», but when it was applied to transformers it was expressed in terms of potential difference.
The terminology is wrong, but more importantly the underlying concept is wrong.
It is, alas, an archaic and confusing term. Modern good practice is to call it the open-circuit voltage. This makes contact with the Thévenin-Norton theorem.
However, this must still be considered bad pedagogy, because it is very unlikely that this passage will convey the correct idea to students. There is a very widespread misconception that states of definite energy are the only allowed states, and this passage tends to reinforce that misconception. Certainly it does nothing to dispell the misconception.
The correct physics is discussed in reference 9.
That is nonsense. That would violate conservation of energy.
We all agree that the energy eigenstates of a particular mode of the electromagnetic field are equally spaced in energy, and that the energy-spacing is ΔE = ℏω. We also agree that the photoelectric experiment is a good way to measure this energy-spacing.
However, this does not mean that energy states are the only states. It does not mean that «all electromagnetic waves are quantized». See reference 9.
Students ask: If the valence band is responsible for conduction, what is the conduction band responsible for?
A good textbook would teach students to have a feel for the physics. I don’t see that here. Instead, to an alarming degree, this book teaches students to apply equations outside their domain of applicability. See e.g. item 33 and item 44.
I am reminded of the title (if not the contents) of the book All I Really Need to Know I Learned in Kindergarten. Specifically, I am thinking of the dictum, “Check Your Work”. The need to check your work gets emphasized in kindergarten and in every grade thereafter. I mention it because so many of the statements in this book do not withstand even a moment’s scrutiny. See e.g. item 44.
Overall, I reckon this book is better than Hewitt (reference 10) on the grounds that Hewitt is written at a lower level and covers less material, yet has all the same faults.
This book is better than the deplorable reference 1 ... but that is exceedingly faint praise.
Copyright © 2012 jsd