I don't think there should be an "energy law" such as equation 9.1. That introduces a concept and gives it a name, when in fact we don't need either the concept or the name! (See item #183 for a catalog of needless names.) It would be better to stick to the principle of the thing. The principle is _conservation of energy_ pure and simple. Equation 9.1 can be characterized as a corollary of the general law, applicable to a certain special case. Ditto for equation 20.1.
These are significant applications of conservation of energy, and should be indexed as such, both under C for conservation and under E for energy. (See #181 for a catalog of index-related issues.)
Minor suggestions:
In section 9.5 on page 213, equation 9.1 should be marked as a special case. It will be generalized later.
Equation 9.1 should be accompanied by a reference to the more general expression.
In section 20.1 on page 532 there are some words that describe the relationship between energy, work, and thermal transfer. This relationship should also be written in mathematical form, with symbols, with an actual equal sign: ΔE = W + Q
This should be indexed, under both C for conservation and E for energy.
This equation should be given an equation number, because it is referred to elsewhere in the book, notably on page 547, as mentioned in item #36.
This new equation is inconsistent with the "energy law" on page 213. I assume it is intended as a generalization, rather than a flat contradiction. The relationship is eventually explained in connection with equation 20.1 in section 20.5 on page 547 ... but it should be more explicitly elucidated, on page 532 as well as page 213. BTW this is the original and best meaning of what a "gloss" is ... an explanatory note.
I don't recommend it, but if we are going to have an "energy law" at all, it should be indexed as such, so readers can find it when needed.
Main suggestions:
Minor suggestions: