# Is Carnot's theorem equivalent to the Second Law of Thermodynamics?

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

• 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. – dmckee Jan 20 '17 at 21:35
• @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. – Javier Jan 20 '17 at 22:56
• 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. – dmckee Jan 20 '17 at 22:58