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

[Herbert Schulz <herbs@wideopenwest.com>]

> On Mar 3, 2015, at 5:19 PM, Bernard Cleyet <bernard@cleyet.org> wrote:
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> On 2015, Mar 03, , at 13:44, Bill Nettles <bnettles@uu.edu> wrote:
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> > However!! Following this result they state: "If it were possible to use the heat rejected in the process [2-3, the isochoric decompression] to be added to the cycle during process [4-1, the isochoric compression] in a reversible fashion (this is called regeneration), the resulting efficiency would be ... 1-T_l/T_h. Note that this efficiency is equal to that of a Carnot engine."
> >
> > So my guess is that Carl's analysis is irreversible at some juncture, namely, the heat rejected to the cold reservoir in the isochoric decompression.
>
>
> JD has disabused me. I, until now, thought the Carnot was the most efficient.  To determine if a “modern” text implied the previous I skimmed Eisberg and Lerner, in which I found: [p. 877]  “All reversible engines have the same efficiency as a Carnot engine operating between the same heat reservoirs.”  (E&L’s italics).  Further, from my skimming, it appears that the authors "proved" this algebraically.  
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> bc relieved.  And needs to read the next post (HS’s).

Howdy,

Why is an isochoric process necessarily irreversible? During an isochoric process any heat transfer goes into internal energy. In the complete cycle the gas ends up at the same temperature as it starts so the net change in internal energy already is zero. The definition of efficiency of any given engine is simply W(out)/Q(in) over one cycle and doesn't care when heat enters or leaves the engine.

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)