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

[Herbert Schulz <herbs@wideopenwest.com>]

> On Mar 4, 2015, at 11:58 AM, John Denker <jsd@av8n.com> wrote:
>
> On 03/04/2015 10:15 AM, Carl Mungan wrote:
> > Please explain in detail how you will accomplish a reversible 
> > isochoric process ...
>
> OK, now we understand what the real question is.  It's a 
> big-league question.  This is what makes Stirling engines 
> infamously hard to analyze.
>
> Executive summary:
>  1) There has to be a regenerator.
>  2) If the regenerator is done right, it has no effect
>   on the overall efficiency, because it doesn't transfer
>   any energy or entropy to/from the Th or Tc reservoirs.
>
>
> > Please explain in detail how you will accomplish a reversible
> > isochoric process without a sequence of infinitesimally different
> > temperature reservoirs.
>
> Let's be careful with what we mean by terms like "bath",
> "reservoir", "source", and "sink".  Note the contrast:
>
> *) We speak of the Tc heat-bath and the Th heat-bath.
>  Th is a source for energy and entropy.
>  Tc is a sink for energy and entropy.
>  Th and Tc could be called reservoirs.  They are
>   assumed to be infinite reservoirs, so that we
>   can run the engine for a long time without
>   depleting them.
>
>  *) In contrast:  The regenerator needs to have some
>   /finite/ heat capacity.  However, it is not a source
>   or a sink.  Whatever energy and entropy are removed
>   from it on one leg of the cycle are restored to it
>   half a cycle later.  I do not think of it as a
>   heat "bath", certainly not an infinite one.  You
>   can call it a "reservoir" if you want, but this
>   may be misleading, because it is not the same
>   category as the Th and Tc reservoirs.
>
> Let's be clear:  For an ideal regenerator, it contributes
> nothing to the energy budget and entropy budget when summed
> over a cycle.  Whatever it takes it gives back over the
> course of a cycle.
>
>  If there are nonidealities, at some point we must 
>  take those into account, but that wasn't the question
>  that was asked.
>
> As a separate matter, you don't necessarily need an infinite 
> sequence of regenerators;  one will do, if you're clever
> about it.  The regenerator gradually heats itself up in the 
> process of being used (on one leg) and gradually cools down 
> (on the opposite leg), so it's always at about the right
> temperature.  Designing such a thing will make you tear
> your hair out, but it's possible in principle.

Howdy,

And I always thought a Stirling Engine was one that ran using the Stirling Cycle. Now you're including a device (how do you design such a thing? isn't it yet another Heat Engine? if it can't be drawn as a cycle of some sort isn't it irreversible and therefore the efficiency still must be lower than a Carnot Engine anyway?) as part of the Stirling Engine. 

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)