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Understanding Internal Energy Change
The question revolves around the concept of internal energy in thermodynamics. Internal energy is a state function, which means its value depends only on the state of the system and not on the path taken to reach that state.
Internal Energy Change from A to B
When the system goes from state A to state B, the internal energy change is given as 40 kJ/mole. This means that the internal energy of the system increases by 40 kJ/mole when it transitions from state A to state B.
Returning from B to A
Next, the system returns from state B to state A through an irreversible path. However, since internal energy is a state function, the change in internal energy for the entire process (from A to B and back to A) depends only on the initial and final states, not on the path taken.
Net Change in Internal Energy
Since the system returns to its original state A, the net change in internal energy for the complete cycle (A to B and back to A) is:
\[
\Delta U = U_A - U_A = 0
\]
Thus, the net change in internal energy is zero.
Conclusion
Therefore, the correct answer to the question is that the net change in internal energy is zero, regardless of the path taken during the return from B to A.
