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In thermodynamics we have Carnot's Theorem which states that the efficency of any heat engine wich works with only two temperature's source is less or equal to Carnot's engine which works between the same two temperatures. This statement follows from the second principle of thermodynamics. Can we say indeed that this statement is equivalent to that principle ? If yes i would like to get a proof or otherwise a controexample.

Or More precisely: how can I see that if does not exist heat engine which works with only two sources that has efficiency more of the Carnot' s one, than •does not exist any heat machine with efficiency equal to 1 Or
•we can't make a transform having as unique effect to transfer heat form a cold body to an hot body Or
•we can't transfor with a cycle all heat absorbed into work Or •deltaS>=0

Thank you

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  • $\begingroup$ Try this: assume you can violate Carnot's statement and see if you can design a machine for violating one of the other statements of the second law by using your super-carnot engine. $\endgroup$
    – dmckee --- ex-moderator kitten
    Jan 20, 2017 at 21:35
  • $\begingroup$ @dmckee: Isn't that also a proof of Second Law $\implies$ Carnot? Contrapositive and all that. You would have to either assume the second law is false and contradict Carnot, or assume that Carnot is true and derive the second law. $\endgroup$
    – Javier
    Jan 20, 2017 at 22:56
  • $\begingroup$ Sure. And you can construct those kinds of if-and-only-if proofs between all the varied ways of stating the second law. Kelvin's version $\iff$ Plank's version, and so on. $\endgroup$
    – dmckee --- ex-moderator kitten
    Jan 20, 2017 at 22:58

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Carnot's theorem IS the second law of thermodynamics - the Kelvin-Planck version can be derived from it. "Entropy always increases" is just camouflage - the statement is not even wrong. I have discussed this many times in StackExchange.

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  • $\begingroup$ maybe you did not understand my questions which is: how can I see that if does not exist heat engine which works with only two sources that has efficiency more of the Carnot' s one, than •does not exist _any heat machine with efficiency equal to 1 Or •we can't make a transform having as unique effect to transfer heat form a cold body to an hot body Or •we can't transfor with a cycle all heat absorbed into work Or •deltaS>=0 Hope this time the question is more clear $\endgroup$
    – Sergio Piccione
    Jan 21, 2017 at 14:47
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    $\begingroup$ We've been around this before. Just because you prefer to found a particular discipline on one set of axioms does not make that set privileged with respect to other equivalent sets. Frankly I suspect that if you ask most physicist how they prefer to set up thermal physics they'll chose a statistical basis rather than something from the historical development. $\endgroup$
    – dmckee --- ex-moderator kitten
    Jan 21, 2017 at 20:44

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