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5  The Rest of Physics, Chemistry, etc.

The previous sections have set forth the conventional laws of thermodynamics, cleaned up and modernized as much as possible.

At this point you may be asking, why do these laws call attention to conservation of energy, but not the other great conservation laws (momentum, electrical charge, lepton number, et cetera)? And for that matter, what about all the other physical laws, the ones that aren’t expressed as conservation laws? Well, you’re right, there are some quite silly inconsistencies here.

The fact of the matter is that in order to do thermo, you need to import a great deal of classical mechanics. You can think of this as the minus-oneth law of thermodynamics.

Sometimes the process of importing a classical idea into the world of thermodynamics is trivial, and sometimes not. For example:

The law of conservation of momentum would be automatically valid if we applied it by breaking a complex object into its elementary components, applying the law to each component separately, and summing the various contributions. That’s fine, but nobody wants to do it that way. In the spirit of thermodynamics, we would prefer a macroscopic law. That is, we would like to be able to measure the overall mass of the object (M), measure its average velocity (V), and from that compute a macroscopic momentum (MV) obeying the law of conservation of momentum. In fact this macroscopic approach works fine, and can fairly easily be proven to be consistent with the microscopic approach. No problem.   The notion of kinetic energy causes trouble when we try to import it. Sometimes you want a microscopic accounting of kinetic energy, and sometimes you want to include only the macroscopic kinetic energy. There is nontrivial ambiguity here, as discussed in section 18.4 and reference 18.


1
Subject to the approximation that nuclear reactions can be neglected.

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