Consider figure 7.12 in section 7.4 on page 156 ... including the un-numbered equation
E = K + U + E_s + E_th
and the words that go along with it. Overall, this figure express seriously incorrect physics.
In addition to the issues raised in item #35 and item #36, here is another way of seeing why it cannot possibly be correct.
The figure says explicitly elastic energy is counted as part of U.
Meanwhile, it is clear that 100% of the energy of an ideal gas is considered thermal energy, i.e. E_th; this is particularly clear if we skip ahead to chapter 20, especially section 20.5 on page 547.
Let's pursue these two ideas.
Suppose we have a black box containing some ideal gas. If you move the walls inward, the energy goes up.
Right beside it we have a black box containing a steel spring connected to the walls. If you move the walls inward, the energy goes up.
Operationally, at this level of detail, it's hard to distinguish the two. In the real world, some trucks ride on steel springs, while others ride on air springs.
At the level of fundamental physics, the close correspondence continues. If you have a single particle in a box and move the walls inward, the energy goes up. The story is essentially the same if you have an enormous number of particles in the box; if you move the walls inward, the energy goes up.
In the case of an ideal gas, the resistance to compression comes from the gas molecules.
In the case of a chunk of metal, the resistance to compression comes from the electron gas.
The temperature-dependence of the pressure is different in the two cases, because the electron gas is degenerate ... but I consider this to be a detail, irrelevant to the principle of the thing, irrelevant to the fundamental concept of pressure.
Here's another way of saying almost the same thing: According to figure 7.12, the E_th term is characterized as «incoherent» while the U term (including elasticity) is characterized as «coherent». However,
The volume we attribute to a sample of idea gas (under constant-pressure conditions) comes from the thermal agitation of the gas molecules.
The size we attribute to atoms comes from the zero-point agitation of the electrons within the atom.
So, unless you think quantum fluctuations are somehow less «incoherent» than thermal fluctuations, both the gas and the metal are entirely dependent on incoherent processes when they resist compression. (The positive ion cores in the metal keep the electrons from expanding too much, but obviously they cannot prevent the electron gas from contracting; indeed, the more the Fermi gas contracts the happier the ion cores are.)
The entropy of the Fermi gas is less than the entropy of the ideal gas, but that's irrelevant if we compress both boxes adiabatically. (I mean adiabatic in both senses of the word: thermally isolated and isentropic.) Classical physics is sensitive only to differences in entropy, and there aren't any in this scenario.
Tangential remark: The thing we are calling elastic potential energy, as part of U, comes mainly from the kinetic energy of the atomic electrons. That's not the main point I want to emphasize, but it counts as one more reason why the categories set forth in figure 7.12 cannot withstand scrutiny.
Suggestion:
This whole section should just go away. It's wrong in principle and wrong in practice. It's wrong operationally, pedagogically, and in every other way. If the index is to be believed, source energy is introduced on pages 156-158 and then never used again. I find that it is mentioned on page 547, but in that case it is immediately set to zero, so E_s seems quite expendable. Similarly, E_th is used, as far as I can tell, only in situations where it is equal to the total energy, so E_th also seems quite expendable.
Generally speaking, the laws of physics depend on the overall undivided energy. The more ways you divide up the energy, the more likely you are to make a mistake.
Minor additional suggestion:
The energy-category equation (or whatever replaces it, if it survives at all) needs to be made more prominent. Moving it or copying it into the main text would be an improvement.
The equation needs to be numbered. There are places in the book that implicitly refer to it (notably page 547, which is relevant to item #36), and it would help to make these references more explicit. Even if the book didn't refer to it, students (and reviewers) need to refer to it.
Most of the equations in the book are already numbered, so it seems ironic that one of the equations that most needs a number doesn't have one.
Consider figure 7.12 in section 7.4 on page 156 ... including the un-numbered equation
and the words that go along with it. Overall, this figure express seriously incorrect physics.
In addition to the issues raised in item #35 and item #36, here is another way of seeing why it cannot possibly be correct.
Let's pursue these two ideas.
Operationally, at this level of detail, it's hard to distinguish the two. In the real world, some trucks ride on steel springs, while others ride on air springs.
At the level of fundamental physics, the close correspondence continues. If you have a single particle in a box and move the walls inward, the energy goes up. The story is essentially the same if you have an enormous number of particles in the box; if you move the walls inward, the energy goes up.
The temperature-dependence of the pressure is different in the two cases, because the electron gas is degenerate ... but I consider this to be a detail, irrelevant to the principle of the thing, irrelevant to the fundamental concept of pressure.
Here's another way of saying almost the same thing: According to figure 7.12, the E_th term is characterized as «incoherent» while the U term (including elasticity) is characterized as «coherent». However,
So, unless you think quantum fluctuations are somehow less «incoherent» than thermal fluctuations, both the gas and the metal are entirely dependent on incoherent processes when they resist compression. (The positive ion cores in the metal keep the electrons from expanding too much, but obviously they cannot prevent the electron gas from contracting; indeed, the more the Fermi gas contracts the happier the ion cores are.)
The entropy of the Fermi gas is less than the entropy of the ideal gas, but that's irrelevant if we compress both boxes adiabatically. (I mean adiabatic in both senses of the word: thermally isolated and isentropic.) Classical physics is sensitive only to differences in entropy, and there aren't any in this scenario.
Tangential remark: The thing we are calling elastic potential energy, as part of U, comes mainly from the kinetic energy of the atomic electrons. That's not the main point I want to emphasize, but it counts as one more reason why the categories set forth in figure 7.12 cannot withstand scrutiny.
Suggestion:
This whole section should just go away. It's wrong in principle and wrong in practice. It's wrong operationally, pedagogically, and in every other way. If the index is to be believed, source energy is introduced on pages 156-158 and then never used again. I find that it is mentioned on page 547, but in that case it is immediately set to zero, so E_s seems quite expendable. Similarly, E_th is used, as far as I can tell, only in situations where it is equal to the total energy, so E_th also seems quite expendable.
Generally speaking, the laws of physics depend on the overall undivided energy. The more ways you divide up the energy, the more likely you are to make a mistake.
Minor additional suggestion:
Most of the equations in the book are already numbered, so it seems ironic that one of the equations that most needs a number doesn't have one.