Final answer:
The net change in internal energy after the system goes from state A to state B by a reversible path and returns to state A by an irreversible path is 0 kJ/mol, as internal energy is a state function and doesn't depend on the path taken.
Step-by-step explanation:
The internal energy change when a system goes from state A to state B is 40 kJ/mol. If the system goes from A to B by a reversible path and returns to state A by an irreversible path, the net change in internal energy is based on the first law of thermodynamics, which states that the internal energy of an isolated system is constant.
On the reversible path from A to B, the system absorbs 40 kJ/mol of energy. When the system goes from B back to A on an irreversible path, the first law of thermodynamics implies that if no energy is exchanged with the surroundings during the return to state A, the system's internal energy will return to its initial value. Internal energy is a state function, so it does not depend on the path taken. Therefore, the net change in internal energy after completing the cycle back to state A is 0 kJ/mol.