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Sat this problem in an exam recently and it's got me wondering. First off, you have a reservoir at a lower temperature T1. You also have a mass of water at a higher temperature T2 (in this case it was 10C and 100C, I can't remember the mass but let's say it was 1, and Cv 4.2).

First we were asked how much work can be extracted taking the water to the revervoirs temperature, which can be solved by setting up the appropriate integral

Cv * int (1 - T1 / T2) dT2

The next part of the question was more tricky. Instead of a revervoir at the lower temperature, we had another body of water, which also changes temperature. Now what is the maximum work we can extract?

I have in the past solved a similar question by looking at the entropy of each body of water and considering energetics, but can anyone think of a cunning integral that could be used to solve this problem?

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# Homework Help: Carnot Engines

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