Final answer:
The change in internal energy, ΔU, is independent of the path taken between two states and is a state function. The difference in work done between reversible and irreversible paths is due to the opposing external pressure. In an adiabatic irreversible expansion process, the work done is still given by -Pext ΔV, but the change in internal energy will not be equal to Cv dT.
Step-by-step explanation:
The student is missing the fact that the change in internal energy, ΔU, is independent of the path taken between two states and is a state function. This means that if there are reversible and irreversible paths between the same two states, the change in internal energy will be the same for both paths. The difference in work done between the reversible and irreversible paths is due to the opposing external pressure.
During an adiabatic reversible expansion process, the change in internal energy, dU, can be determined using the equation dU = Cv dT, where Cv is the heat capacity at constant volume and dT is the change in temperature. The work done during this process is given by Wrev = -Pext ΔV, where Pext is the external pressure and ΔV is the change in volume.
In an adiabatic irreversible expansion process, the work done is still given by Wirrev = -Pext ΔV, but the change in internal energy, dU, will not be equal to Cv dT. The reason for this is that in an irreversible process, there are additional sources of energy dissipation, such as friction or turbulence, that result in a loss of energy as heat. Therefore, the work done during the irreversible process will be less than the work done during the reversible process, but the change in internal energy will still be the same for both paths.