Select the incorrect statement

Options

A. For isothermal process of ideal gas, `DeltaU = 0`
B. For isochoric process, `W = 0`
C. For adiabatic process, `DeltaU = -DeltaW`
D. For cyclic process, `DeltaW = 0`

Answer

To solve the question of selecting the incorrect statement regarding thermodynamic processes, let's analyze each statement step by step.

### Step 1: Understand the Isothermal Process
- **Statement A**: For an isothermal process of an ideal gas, ΔU = 0.
- **Explanation**: In an isothermal process, the temperature remains constant. For an ideal gas, the change in internal energy (ΔU) is a function of temperature. Since the temperature does not change, ΔU is indeed zero.
- **Conclusion**: This statement is correct.

### Step 2: Understand the Isochoric Process
- **Statement B**: For an isochoric process, work is zero.
- **Explanation**: An isochoric process occurs at constant volume. The work done (W) is given by the formula W = PΔV. Since ΔV = 0 (volume does not change), the work done is zero.
- **Conclusion**: This statement is correct.

### Step 3: Understand the Adiabatic Process
- **Statement C**: For an adiabatic process, ΔU = -Q.
- **Explanation**: An adiabatic process is characterized by no heat exchange with the surroundings (Q = 0). According to the first law of thermodynamics, ΔU = Q + W. If Q = 0, then ΔU = W, not -Q. Therefore, this statement is incorrect.
- **Conclusion**: This statement is incorrect.

### Step 4: Understand the Cyclic Process
- **Statement D**: For a cyclic process, ΔW = 0.
- **Explanation**: In a cyclic process, the system returns to its initial state, which means the change in internal energy (ΔU) is zero. However, the work done (W) is not necessarily zero; it is equal to the area enclosed by the cycle on a PV diagram. Therefore, this statement is also incorrect.
- **Conclusion**: This statement is incorrect.

### Final Conclusion
After analyzing all statements:
- Statement A is correct.
- Statement B is correct.
- Statement C is incorrect (ΔU = W, not -Q).
- Statement D is incorrect (the work done in a cyclic process is not necessarily zero).

Thus, the incorrect statements are C and D, but since we need to select one, we can conclude that **Statement C is the most clearly incorrect** regarding the adiabatic process.