To determine for which process the change in internal energy (ΔE or ΔU) is zero, we will analyze the four types of thermodynamic processes: cyclic, isothermal, isochoric, and adiabatic.
### Step-by-Step Solution:
1. **Understanding ΔU**:
- ΔU represents the change in internal energy of a system. It is a state function, meaning it depends only on the initial and final states of the system, not on the path taken.
2. **Cyclic Process**:
- In a cyclic process, the system returns to its initial state after completing a cycle. Therefore, the initial and final states are the same.
- Since ΔU depends only on these states, for a cyclic process, ΔU = U_final - U_initial = 0.
- **Conclusion**: ΔU = 0 for cyclic processes.
3. **Isothermal Process**:
- In an isothermal process, the temperature remains constant (ΔT = 0).
- The change in internal energy for an ideal gas is given by ΔU = Cv * ΔT, where Cv is the heat capacity at constant volume.
- Since ΔT = 0, it follows that ΔU = Cv * 0 = 0.
- **Conclusion**: ΔU = 0 for isothermal processes.
4. **Isochoric Process**:
- In an isochoric process, the volume remains constant (ΔV = 0).
- The work done (W) is given by W = -PΔV, which equals 0 since ΔV = 0.
- According to the first law of thermodynamics, ΔU = Q + W. Since W = 0, ΔU = Q, which is not necessarily zero (it depends on the heat added or removed).
- **Conclusion**: ΔU ≠ 0 for isochoric processes.
5. **Adiabatic Process**:
- In an adiabatic process, there is no heat exchange with the surroundings (Q = 0).
- Using the first law of thermodynamics, ΔU = Q + W = 0 + W = W. Thus, ΔU is equal to the work done, which is not necessarily zero.
- **Conclusion**: ΔU ≠ 0 for adiabatic processes.
### Final Answer:
The change in internal energy (ΔU) is zero for:
- **Cyclic Process** (Option 1)
- **Isothermal Process** (Option 2)
