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-one^th law of thermodynamics.

This includes Newton’s third law (which is tantamount to conservation of momentum) and Newton’s second law, with the associated ideas of force, mass, acceleration, et cetera. Note that the concept of pseudowork, which shows up in some thermodynamic discussions, is more closely related to the momentum and kinetic energy than it is to the total energy.

In particular, this includes the notion of conservation of energy, which is a well-established part of nonthermal classical mechanics. From this we conclude that the first law of thermodynamics is redundant and should, logically, be left unsaid (although it remains true and important).

If you are going to apply thermodynamics to a chemical system, you need to import the fundamental notions of chemistry. This includes the notion that atoms exist and are unchanged by ordinary chemical reactions (which merely defines what we mean by a “chemical” as opposed to “nuclear” reaction). This implies about a hundred additional approximate¹ conservation laws, one for each type of atom. The familiar practice of “balancing the reaction equation” is nothing more than an application of these atom-conservation laws.

If you are going to apply thermodynamics to an electrical or magnetic system, you need to import the laws of electromagnetism, i.e. the Maxwell equations.

The Maxwell equations imply conservation of charge. This is essential to chemistry, in the context of redox reactions. It means you have to balance the reaction equation with respect to charge. This is in addition to the requirement to balance the reaction equation with respect to atoms.

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.

Subject to the approximation that nuclear reactions can be neglected.

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