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I understand how Carnot's theorem implies that irreversible heat engines must be no more efficient than reversible one's, but it is less clear why they need to be less efficient, as I have seen stated in some places.

If they could be equally efficient then an irreversible engine engine could be used to drive a reversible engine operating between the same heat reservoirs, without any net energy transfer between the reservoirs. It would then be unclear what is irreversible about the irreversible engine. Does that constitute an actual contradiction though? If so can the argument be stated more tightly? It feels a little sloppy as is.

It could also be a question of how an irreversible engine is defined in Carnot's theorem. I understood it to mean one that cannot be run in reverse as a heat pump, which could presumably include a Carnot engine with a one way ratchet attached. If it really means an engine whose thermodynamic effects can not be undone, the implication would be trivial.

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I understand how Carnot's theorem implies that irreversible heat engines must be no more efficient than reversible one's, but it is less clear why they need to be less efficient, as I have seen stated in some places.

The answer is that it is always possible to construct an incredibly inefficient engine, which is to say, it is always possible to obtain a lower efficiency than the reversible engine. This, coupled with the fact that it is very difficult to construct a truly reversible engine, places real engines at efficiencies below that of the Carnot limit.

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  • $\begingroup$ This does not seem to answer the question. They are asking why an irreversible engine must be less efficient than a reversible one. Just because it's possible to have a lower efficiency than a reversible engine doesn't explain why an irreversible one must be less efficient. $\endgroup$ – JMac Dec 5 '18 at 12:32
  • $\begingroup$ I don't understand your objection. If an engine has the Carnot efficiency, it is reversible. By definition then, irreversible engine means lower efficiency than Carnot. Are you asking why it is not possible to construct a truly reversible engine? $\endgroup$ – Themis Dec 5 '18 at 18:58

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