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

[John Denker <jsd@av8n.com>]

On 03/03/2015 09:56 AM, Carl Mungan wrote:
> I'm a bit confused about efficiency. For a Carnot cycle, we have two
> isothermal steps and two adiabatic steps. The efficiency is then found to
> be 1 - Tcold/Thot.
>
> Okay but what about a non-Carnot but still reversible cycle

The efficiency of any reversible heat engine is
the same:  1 - Tcold/Thot.                  [1]

If it's reversible, entropy is conserved, and
that's all you need to prove equation [1].

The "Carnot cycle" is an easy-to-analyze example,
but not the only example, not by a long shot.

Note that any cycle can be approximated as closely
as you wish by a sum over Carnot cycles.  Think 
of tiling the area on the indicator diagram (PV
diagram).

>  Would you still call
> that the "Carnot" efficiency? 

Sure, why not?

> I'm a bit surprised intro textbooks don't discuss ideal efficiencies for
> non-Carnot cycles. Have I missed something?

Omitting a generalization is not wrong, it's
just lazy.  So on the scale of things, compared
to all the outright wrong stuff in those books,
this is the least of your problems.