This has to do with the passage on page 547 in section 20.5. This started out as a comment attached to item #36, but I'm promoting it to an item unto itself, because it addresses a different issue, not «thermal energy» strictly speaking.
As in item #36, the point here is that it is not possible to read this passage correctly.
Students are notorious for taking an equation that is valid in one context and applying it in some other context. This sort of over-generalization is sophomoric. It's not wise, but it's what sophomores do.
The book makes an effort to combat this by means of parenthetical restrictions attached to the equations. For example, equation 20.2 in section 2.05 on page 547 is marked (ideal gas). The general idea is correct, but this particular marking is not correct, insofar as the words immediately above the equation impose tremendous additional restrictions, including ΔK=ΔU=ΔE_s=0. So really we are talking about a highly restricted subset of ideal gasses. (Actually it's even worse than that, because there is evidently an unstated assumption that advection is absent ... but let's not worry about that just now. Similarly there seems to be an unstated assumption that the system is in thermal equilibrium.)
Alas, a few lines later, in equation 20.5, the parenthetical restriction has gone away. The sentence before the equation repeats the words "ideal gas", but the restriction to ΔK=ΔU=ΔE_s=0 has mysteriously vanished. I suppose you could argue that the astute reader will have figured out that the relevant restrictions go without saying ... but that's a disaster, because the very next equation, i.e. the un-numbered equation above equation 20.7, does not inherit these restrictions; instead it depends on some different, unexplained set of restrictions. In particular, the un-numbered equation applies just fine to non-ideal gases. It applies to liquids and solids. It applies in situations where ΔK is nonzero. It does however have some restrictions. Alas the restrictions are not explained here or in connection with the original equation 9.22. In particular, there appears to be a serious inconsistency in situations where ΔU is nonzero, for reasons discussed in item #186.
On page VII the book promises a "deductive" approach. I'm not sure a strictly deductive presentation is desirable, or even possible, for reasons discussed at https://www.av8n.com/physics/meaning.htm I would happily settle for a more modest goal, namely knowing what the equations mean, what they are good for, and what not.
I don't think page 547 meets this goal. Some of the equations are more broadly applicable than they seem, while others are more restricted than they seem.
This has to do with the passage on page 547 in section 20.5. This started out as a comment attached to item #36, but I'm promoting it to an item unto itself, because it addresses a different issue, not «thermal energy» strictly speaking.
As in item #36, the point here is that it is not possible to read this passage correctly.
Students are notorious for taking an equation that is valid in one context and applying it in some other context. This sort of over-generalization is sophomoric. It's not wise, but it's what sophomores do.
The book makes an effort to combat this by means of parenthetical restrictions attached to the equations. For example, equation 20.2 in section 2.05 on page 547 is marked (ideal gas). The general idea is correct, but this particular marking is not correct, insofar as the words immediately above the equation impose tremendous additional restrictions, including ΔK=ΔU=ΔE_s=0. So really we are talking about a highly restricted subset of ideal gasses. (Actually it's even worse than that, because there is evidently an unstated assumption that advection is absent ... but let's not worry about that just now. Similarly there seems to be an unstated assumption that the system is in thermal equilibrium.)
Alas, a few lines later, in equation 20.5, the parenthetical restriction has gone away. The sentence before the equation repeats the words "ideal gas", but the restriction to ΔK=ΔU=ΔE_s=0 has mysteriously vanished. I suppose you could argue that the astute reader will have figured out that the relevant restrictions go without saying ... but that's a disaster, because the very next equation, i.e. the un-numbered equation above equation 20.7, does not inherit these restrictions; instead it depends on some different, unexplained set of restrictions. In particular, the un-numbered equation applies just fine to non-ideal gases. It applies to liquids and solids. It applies in situations where ΔK is nonzero. It does however have some restrictions. Alas the restrictions are not explained here or in connection with the original equation 9.22. In particular, there appears to be a serious inconsistency in situations where ΔU is nonzero, for reasons discussed in item #186.
On page VII the book promises a "deductive" approach. I'm not sure a strictly deductive presentation is desirable, or even possible, for reasons discussed at https://www.av8n.com/physics/meaning.htm I would happily settle for a more modest goal, namely knowing what the equations mean, what they are good for, and what not.
I don't think page 547 meets this goal. Some of the equations are more broadly applicable than they seem, while others are more restricted than they seem.