Assertion: For an ideal gas in a cyclic process and in an isothermal process change in internal energy is zero.
Reason: In both processes there is no change in temperature.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Answer

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion:** For an ideal gas in a cyclic process and in an isothermal process, the change in internal energy is zero.
**Reason:** In both processes, there is no change in temperature.

### Step-by-Step Solution:

1. **Understanding Internal Energy:**
- The internal energy (U) of an ideal gas depends only on its temperature. For an ideal gas, the change in internal energy (ΔU) can be expressed as:
\[ \Delta U = nC_v \Delta T \]
where \( n \) is the number of moles, \( C_v \) is the specific heat capacity at constant volume, and \( \Delta T \) is the change in temperature.

2. **Analyzing the Isothermal Process:**
- In an isothermal process, the temperature remains constant (ΔT = 0). Therefore, the change in internal energy is:
\[ \Delta U = nC_v \cdot 0 = 0 \]
- This confirms that for an ideal gas undergoing an isothermal process, the change in internal energy is zero.

3. **Analyzing the Cyclic Process:**
- In a cyclic process, the system returns to its initial state after completing a cycle. This means that the initial and final states of the system are the same, which implies that the temperature at the beginning and end of the cycle is also the same (ΔT = 0).
- Thus, for a cyclic process, the change in internal energy is also:
\[ \Delta U = nC_v \cdot 0 = 0 \]
- Therefore, the change in internal energy for an ideal gas in a cyclic process is also zero.

4. **Conclusion:**
- Both the assertion and the reason are correct. The assertion states that the change in internal energy is zero for both processes, and the reason correctly explains that this is due to the fact that there is no change in temperature in both cases.

### Final Answer:
- The assertion is true, and the reason is also true. The reason is the correct explanation for the assertion.