Why the Carnot Cycle? | Understanding Efficiency in Heat Engines

[Amin2014]

1-Is the efficiency of heat engines working in cycles other than Carnot independent of the nature of substance used? Can we still claim that maximum efficiency in converting heat to work is attained during reversible processes for such cycles? For which engines/cycles can we do this?

2- Why is the Carnot cycle used to prove ∫dq_rev/T = 0 in a cycle? Why not use some other cycle? We use the ideal gas as our working substance because it's easier to calculate dq/T for ideal gas along the path of the cycle, but why does the cycle have to be Carnot? Or does it?

Of course the integral will be zero for any substance in ANY reversible cycle, but can you actually PROVE this general result to be true using some cycle other than Carnot?

In other words, in his quest to prove ∫dq_rev/T =0 solely from the second law, how was man motivated to pick the Carnot cycle (among other cycles) as his cycle of choice for the proof?

 

[Astronuc]

The Carnot cycle provides the maximum theoretical efficiency, so any other cycle should be less efficient.

 

[Amin2014]

The Carnot cycle provides the maximum theoretical efficiency, so any other cycle should be less efficient.

A Carnot cycle is defined to be a reversible cycle between two constant temperature reservoirs. If we have two constant temperature reservoirs, it can be shown that the greatest efficieny belongs to an engine which goes through a reversible cycle between these two constant temperature reservoirs. The carnot cycle is just another name for a reversible cycle operating between two constant temperature reservoirs, so yes it has the greatest efficiency of all cycles between two constant temperature reservoirs.

But why are we considering constant temperature reservoirs in the first place? Our goal is to prove ∫dq_rev/T =0 for all cycles, so why not start with a rectangular cycle ( a cycle with rectangular P-V diagram)?