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21  Thermodynamics, Restricted or Not

There are various ways of restricting the applicability of thermodynamics, including

Indeed, there are some people who seem to think that thermodynamics applies only to microcanonical reversible processes in a fully-equilibrated ideal gas.

To make progress, we need to carefully distinguish two ideas:

  a) Simplifying assumptions made in the context of a particular scenario. Depending on details, these may be entirely appropriate. Sometimes the gases involved are ideal, to an excellent approximation … but not always. Sometimes a process is reversible, to an excellent approximation … but not always.
  b) Restrictions applied to the foundations of thermodynamics. We must be very careful with this. There must not be too many restrictions, nor too few. Some restrictions are necessary, while other restrictions are worse than useless.

Some thermodynamic concepts and/or formulas necessarily have restricted validity.

In contrast, very importantly, the law of conservation of energy applies without restriction. Similarly, the law of paraconservation of entropy applies without restriction. You must not think of E and/or S as being undefined in regions where “non-ideal” processes are occurring. Otherwise, it would be possible for some energy and/or entropy to flow into the “non-ideal” region, become undefined, and never come out again, thereby undermining the entire notion of conservation.

The ideas in the previous paragraph should not be overstated, because an approximate conservation law is not necessarily useless. For example, ordinary chemistry is based on the assumption that each of the chemical elements is separately conserved. But we know that’s only approximately true; if we wait long enough uranium will decay into thorium. Still, on the timescale of ordinary chemical reactions, we can say that uranium is conserved, to an excellent approximation.

When a law has small exceptions, you shouldn’t give up on the law entirely. You shouldn’t think that just because a process is slightly non-ideal, it becomes a free-for-all, where all the important quantities are undefined and none of the laws apply.

If you want to make simplifying assumptions in the context of a specific scenario, go ahead … but don’t confuse that with restrictions on the fundamental laws.

Also, in an elementary course, it might be necessary, for pedagogical reasons, to use simplified versions of the fundamental laws … but you need to be careful with this, lest it create misconceptions.

Finally, it must be emphasized that one should not ask whether thermodynamics “is” or “is not” applicable to a particular situation, as if it were an all-or-nothing proposition. Some concepts (such as energy and entropy) are always valid, while other concepts (such as equilibrium and temperature) might or might not be valid, depending on the situation.


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