# Efficiency of heat engines

I have been taught that the an engine running on the Carnot's cycle has the maximum energy among the maximum efficiency, however I never found a convincing proof for it. Wherever I have put this question up, everyone just said pit it up against any engine and it will come out with a higher efficiency.

I would like to know if there is any way to prove mathematically that the Carnot's cycle has the maximum efficiency among any cycle?

Also, I have the belief that the second law of thermodynamics is a consequence of the fact that the Carnot's cycle has the maximum efficiency among any cycle. Because the Carnot's cycle has come before the second law of thermodynamics, I suppose that the former points to the latter. Is it actually true that the second law of thermodynamics comes from Carnot's theorem, and is it possible to prove that a Carnot's cycle would have the maximum efficiency for a particular amount of heat given in?

• What do you mean by maximum energy. – Bob D Nov 24 '19 at 14:16
• Sorry it's efficiency – Sandeep Kumar Dash Nov 24 '19 at 15:58
• OK, then see my answer – Bob D Nov 24 '19 at 16:08
• It if I remember the definition of entropy comes from the fact that Carnot's cycle has the highest entropy. – Sandeep Kumar Dash Nov 24 '19 at 16:19
• The Carnot cycle is a reversible cycle in which zero entropy is generated. Not sure where you got the idea of it having the "highest entropy". – Bob D Nov 24 '19 at 16:34