[Higgs]

Hey guys, I was assigned a problem and am having a problem with the last part of the problem, i will type it in bold.


            Explain why more work is always done by a reversible isothermal expansion of a gas than by a spontaneous one. Support your explanation by showing the amount of work done as a shaded area on a pV-Isotherm and describing why a shaded region corresponding to the work is always less for a spontaneous expansion even a very slow one. Explain why all this is still true whether the gas is ideal or real.

Let it be known that I plan on submitting my own work.

[jusy1]

Hello Higgs,

I think we can think like this: There's no mathematical equation that describes the real gas exactly, so we can't write the gas pressure as a function of its volume and do the integral (for the reversible process). However we know 3 things that must happen when a reversible expansion occurs (whether real or ideal gas): The initial pressure inside the container must be higher than the external pressure (if it wasn't there would be no expansion), the final pressure will be equal to the external pressure (it might not be but we assume it is so we can compare it to the irreversible process) and the gas pressure must vary continuously (if it didn't the process wouldn't be irreversible and the integral couldn't even be calculated).

Having this in consideration and you can do a graphic plotting the intial and final state points I think we prove that the sentence is still true whether the gas is ideal or real.