While solving problems, I have seen that the work done in reversible process comes out to be greater than that in irreversible process.
How can it be explained theoretically?
Please answer my doubt.
Assuming u started from the same pt. on the PV graph and ended at the same pt. too one would conclude that the work done during a reversible process is greater than that done during an irreversible process.
I assume that u know that the work done is the area under the P-V graph.
By definition and for practical reasons a reversible process is initiated and carried out in numerous small steps. On the other hand an irreversible process would occur in a few large steps.
Since the pressure volume equilibrium would take time to establish the width of the steps making up the process would be large during an irreversible process while it would be infinitely small during a reversible process.
Hence a larger area will be covered during a reversible process.
The argument is similar to integration where on one hand u have a significant delta x (irreversible process) while on the other hand it would involve an infinitestimally small dx where dx would tend to 0 (reversible process). Hence the area would be better covered and the valu approximated to a good extent.
for a much brilliant explanation refer to Feynman lectures Vol 1
the chapter on thermodynamics and reversible engines
the explanation may not be exactly to this question but is worth reading!!!!
I agree that Feynman lectures has got a good proof. But why not refer to Resnik and Halliday, or H.C.Verma or N.C.E.R.T. for the same proof. Infact, even a Mathematics book dealing with elementary integration or introduction to Calculas can be used to get the crux of the concept. All i have tried is to prove there exists a parallel.