Can anyone please explain how Carnot's theorem which states that "working between two same temperature limits,a reversible engine has maximum efficiency " and the second law of thermodynamics ? By second law , I mean here Clausius and Kelvin-Planck statement. Or is there any other way of interpreting the second law in the light of Carnot's theorem ?

Thank you.

  • $\begingroup$ I have not seen Carnot's theorem stated that way. Can you cite a reference? $\endgroup$
    – Bob D
    Feb 23, 2019 at 0:21
  • $\begingroup$ 'Thermal physics' by AB Gupta and HP Roy. The actual statement guven in the book is "working between same two temperature limits, no engine can be more efficient than a reversible one". $\endgroup$
    – Jabeen
    Feb 23, 2019 at 13:17

1 Answer 1


The equivalence of the three formulations of the second law that concern themselves with heat engines and heat pumps is usually established by a series of demonstrations that if you violate one of them you can violate the others.

Do all the combinations and you have established that each is necessary and sufficient for the others.

Example. Assume I have a machine that violates the Clausius statement. If I combine it with an ordinary heat engine, I can move the waste heat of the engine back to the hot reservoir, so that the combined machine is converting all of it's net heat drawn from the hot reservoir to work: a violation of the Kelvin-Plank statement.

Working through all the combinations is tedious but not hugely difficult.

  • 1
    $\begingroup$ As an aside there are at least two other basis for constructing statements of the second law (statistic and entropy). Basically the second law of thermodynamics is a master of disguise and shows up all over the place. $\endgroup$ Feb 21, 2019 at 22:21

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