(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to find the final temperature of a carnot engine with two finite thermal reservoirs. We're told that the heat capacities for both reservoirs are constant (and equal) and to regard the change in each reservoir's temperature during any 1 cycle as negligible.

2. Relevant equations

W=PdV for isothermal expansions/compressions and dE=0 for those portions so the work done by (or on) the gas is equal to the energy supplied by (or to) the reservoir.

P=NKT/V where T will be the temperature of either reservoir depending one whether we're compressing or expanding.

3. The attempt at a solution

If each cycle's effect on the reservoir's temperature is neglible, then you might say its dT, so the dq = CdT, but the energy supplied by heating (or cooling is definitely finite, so its more like q=CdT). Also, while I suspect there's an integral somewhere here, I'm not sure of what the other integration variable is, there are going to be a lot of cycles, we might even model it as an infinite number of them, but how would that parameter come into play? I've thought about viewing this as a volume in P-T-V land, so some double integral over the T-V plane, after all, an integral under one isotherm gives the work from that that isotherm. I know that the isotherms are going to approach each other (and the volumes will drift) so that eventually the engine stalls. This sweeps out a surface over the T-V plane with height P(T,V) at a given point.

I suspect that I'm working way too hard at this, since everything changes by a little bit after each cycle. I don't expect, or want much help, just a tiny nudge to get me going.

Thanks ahead of time.

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# Homework Help: Carnot engine with finite reservoirs

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