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?

Answer

To solve the problem step by step, we need to understand the concept of internal energy and how it behaves during reversible and irreversible processes.

### Step 1: Identify the initial and final states
The system changes from state X to state Y, and then returns from state Y to state X.

**Hint:** Always identify the states involved in the process.

### Step 2: Understand the change in internal energy
The change in internal energy (ΔU) from state X to state Y is given as +25 kJ/mol. This means that the internal energy of the system increases by 25 kJ/mol when moving from X to Y.

**Hint:** Remember that a positive ΔU indicates an increase in internal energy.

### Step 3: Analyze the return path
The system returns from state Y to state X via an irreversible path. However, it is important to note that the internal energy of a system is a state function, which means it depends only on the initial and final states, not on the path taken.

**Hint:** Internal energy is a state function; it does not depend on how the change occurs.

### Step 4: Calculate the net change in internal energy
Since the system returns to its original state (state X), the net change in internal energy for the entire process (from X to Y and back to X) can be calculated as follows:
- Change from X to Y: +25 kJ/mol
- Change from Y back to X: -25 kJ/mol (since it returns to the original state)

Thus, the total change in internal energy is:
ΔU_total = ΔU(X to Y) + ΔU(Y to X) = +25 kJ/mol - 25 kJ/mol = 0 kJ/mol.

**Hint:** When calculating total changes in state functions, sum the changes and consider the sign.

### Conclusion
The net change in internal energy for the entire process is **0 kJ/mol**.

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