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https://www.youtube.com/watch?v=LUoUb4hGMH8

I was looking at the reason as to why a Carnot Engine and watched this video on KhanAcademy. He used a very clever method of proving this by using the method of contradiction.

First he took the new Better Engine and added to an up scaled reversed carnot engine to show that the new device formed will not obey the Second Law of Thermodynamics.

However instead if we use the Carnot Engine itself instead of the better engine and a very low efficieny engine instead of the carnot, then wouldn't it prove that carnot's engine is the worse one.

This arguement can also be used to prove that no engine is more efficient than another.

Where am I getting it wrong?

I looked at other similar questions but none of it gives the answer.

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Your flaw is in assuming that you can run an arbitrary engine backwards. In order to reverse the operation of a heat engine the heat engine must be reversible, which the Carnot engine is. The proof shows that all reversible engines must have the same efficiency and that no irreversible engine can be more efficient than a reversible one, but does not apply to engines more generally.

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  • $\begingroup$ So no engine other than the carnot engine run in a backward direction? $\endgroup$ – harshit54 Sep 29 '18 at 12:25
  • $\begingroup$ The proof actually shows that reversible engines operating between two fixed reservoirs are equally efficient. But for this to be the case you need two isotherms in your cycle. I think the end result is that practically you do need a Carnot cycle. $\endgroup$ – jacob1729 Sep 29 '18 at 12:25
  • $\begingroup$ Can you explain how it shows that reversible engines operating between two fixed reservoirs are equally efficient? $\endgroup$ – harshit54 Sep 29 '18 at 12:28
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    $\begingroup$ By exactly the argument in your question. If I have 2 reversible engines I can use either of them to run the other one backwards, so neither can be more efficient than the other, so they must have the same efficiency $\endgroup$ – By Symmetry Sep 29 '18 at 12:32

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