Reversible Expansions

[Nicole Nikolov 1K]

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.

[704887365]

I’m not sure how to explain it quantitatively but work done reversibly does not lose as much heat energy (due to friction and other unwanted processes)

[Michael Downs 1L]

^

[melissa carey 1f]

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).