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I understand that the work a system can do is greatest in a reversible process. For example, if you look at a PV diagram you can see that the area under a curve is greatest for a reversible process. However, I am having trouble understanding it from more of a mathematical viewpoint. Can someone please explain why this is so in a more quantitative way? Thanks.
In a TA review session he explained that when you have a rev process you are extracting the max work bc you are making such small changes that you can appoximate P-internal = P-external at every instant. PV=nRT. P=nRT/v. substitute w=-nRT/V and integrate w respect to V. this is where you get w = -nRTln(Vf/Vi).
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