What's special about the Carnot Cycle?

[Opus_723]

Why do we always talk about the Carnot cycle as being the most efficient, ideal engine? Doesn't the same equation hold for any reversible heat engine operating between two thermal reservoirs? Couldn't you prove e = 1-T$_{L}$/T$_{H}$ for any reversible cycle? And then you can apply the usual "no perfect refrigerator" argument to show that this must be the maximum efficiency for a reversible heat engine. What's so special about the Carnot cycle? Is it simply easier to get the above equation from a Carnot cycle, or is it actually the only reversible cycle that reaches this efficiency? Does it have other interesting properties besides being used to prove the above equation in textbooks?

 

[kuruman]

Why do we always talk about the Carnot cycle as being the most efficient, ideal engine?

Because it is. The idea is to get the maximum amount of mechanical work and the minimum amount of heat added. During the isothermal expansion, whatever heat goes in the gas is converted into mechanical work and nothing is retained as internal energy; during the adiabatic expansion, you get even more work out at the expense of the internal energy without any heat being added. Of course, you need to complete the cycle and return to the point where you started with the minimum amount of rejected heat. The isothermal compression ensures that whatever heat is rejected goes into reducing the volume to a point where an adiabatic compression that rejects no heat returns you to where you started. So the expansion part of the Carnot cycle maximizes the work out and the compression part minimizes the rejected heat.