Why does the energy difference of a reversible process not equal that of an irreversible process in an adiabatic expansion?
I think the premise of the question itself is false: if you start with a given state (P1, V1) and undergo a reversible, adiabatic (hence isentropic) expansion, you can get to state P2, V2. But if you don't have the requirement of reversibility, I don't think it is possible to gain the same second state - there will be either internal heating/cooling, causing the expected final volume (or pressure, depending on the mechanism of expansion) to not be P2 or V2.