The internal energy change when a system goes fromk state `A` to `B` is `40 kJ mol^(-1)`. If the system goes from `A` to `B` by a reversible path and returns to state `A` by an irreversible path, what would be the net change in internal energy?

Options

A. `lt 40 kJ`
B. Zero
C. `40 kJ`
D. `gt 40kJ`

Answer

To solve the problem, we need to analyze the change in internal energy as the system transitions between states A and B, and then back to A.

### Step-by-Step Solution:

1. **Identify the Change in Internal Energy from A to B**:
- The problem states that the internal energy change when the system goes from state A to state B is given as \( \Delta U_{A \to B} = 40 \, \text{kJ mol}^{-1} \).

2. **Understand the Nature of Internal Energy**:
- Internal energy (U) is a state function. This means that the change in internal energy depends only on the initial and final states of the system, not on the path taken to get there.

3. **Consider the Return Path from B to A**:
- The system returns from state B back to state A. The path taken for this return is irreversible. However, since internal energy is a state function, the change in internal energy for this part of the process is also determined solely by the initial and final states.

4. **Calculate the Change in Internal Energy for the Entire Process**:
- For a complete cycle (from A to B and then back to A), the overall change in internal energy can be expressed as:
\[ \Delta U_{\text{total}} = \Delta U_{A \to B} + \Delta U_{B \to A} \]
- Since the system returns to its initial state A, we have:
\[ \Delta U_{B \to A} = -\Delta U_{A \to B} = -40 \, \text{kJ mol}^{-1} \]
- Therefore, the total change in internal energy is:
\[ \Delta U_{\text{total}} = 40 \, \text{kJ mol}^{-1} + (-40 \, \text{kJ mol}^{-1}) = 0 \, \text{kJ mol}^{-1} \]

5. **Conclusion**:
- The net change in internal energy when the system returns to state A after going from A to B and back to A is \( 0 \, \text{kJ mol}^{-1} \).

### Final Answer:
The net change in internal energy is \( 0 \, \text{kJ mol}^{-1} \).

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