Re: [Phys-L] Carnot (?) efficiency of non-Carnot cycles

[John Denker <jsd@av8n.com>]

On 03/03/2015 01:28 PM, Herbert Schulz wrote:
> You can easily use the method you mentioned (breaking up an
> non-Carnot engine in differentially small Carnot engines) to prove
> that the efficiency of that engine MUST be lower than a Carnot engine
> acting between the same T(cold) and T(hot).

I beg to differ.

The efficiency of any *reversible* heat engine operating
between a given Tc and Th *must* be the same as the
efficiency of any other reversible heat engine operating
between the same two temperatures.

One-line proof:  Otherwise you could hook the two of
them in tandem and have a perpetual motion machine.

This concept is spelled out in more detail in Feynman
and probably a hundred other places.  See figure 44-7,
and maybe 44-8 also.
  http://www.feynmanlectures.caltech.edu/I_44.html

Secondly, we know that this efficiency has to be.

Carnot's epochal book used both of these arguments:
He proved that if you know the efficiency of one
reversible heat engine you know them all ... and
then he used a particularly convenient cycle to
calculate what this efficiency has to be.

The Stirling cycle is infamously inconvenient to
calculate, but it can be done, and sure enough the
efficiency is the same as any other reversible heat
engine.  The Stirling cycle is conspicuously different
from the Carnot cycle, but the efficiency is the same.