A system changes from state X to Y with a change in internal energy measuring to `"25 kJ mol"^(-1)`, by a reversible path and returns from Y to X by an irreversible path. What will be the net change in internal energy?

Options

A. 25 kJ
B. > 25 kJ
C. < 25 kJ
D. zero

Explanation

To solve the problem, we need to analyze the change in internal energy as the system transitions between two states, X and Y.

### Step-by-Step Solution:

1. **Identify the Change in Internal Energy from X to Y**:
- The problem states that the change in internal energy (ΔU) when the system moves from state X to state Y is +25 kJ/mol. This means that the internal energy increases by 25 kJ/mol when going from X to Y.

2. **Understand the Return from Y to X**:
- The system then returns from state Y to state X. However, this return occurs via an irreversible path. Despite the path being irreversible, we need to remember that internal energy is a state function.

3. **Recognize Internal Energy as a State Function**:
- Since internal energy is a state function, the change in internal energy depends only on the initial and final states, not on the path taken between them. Therefore, when the system returns to state X from state Y, the change in internal energy (ΔU) will be the negative of the change when going from X to Y.

4. **Calculate the Change in Internal Energy from Y to X**:
- The change in internal energy when returning from Y to X is -25 kJ/mol (the negative sign indicates a decrease in internal energy).

5. **Determine the Net Change in Internal Energy**:
- To find the net change in internal energy for the entire process (X to Y and then Y to X), we sum the changes:
\[ \Delta U_{\text{net}} = \Delta U_{XY} + \Delta U_{YX} = (+25 \, \text{kJ/mol}) + (-25 \, \text{kJ/mol}) = 0 \, \text{kJ/mol} \]

6. **Conclusion**:
- The net change in internal energy after the complete cycle from X to Y and back to X is 0 kJ/mol.

### Final Answer:
The net change in internal energy is **0 kJ/mol**.