Statement-1.During isothermal expansion of an ideal gas, there is no change in the internal energy.
Statement -2.During isothermal expansion of an ideal gas , as temperature remains constant, no heat enters or leaves the system.

Options

A. Statement -1 is True, Statement-2 is True, Statement-2 is a correct explanation of Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement -1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True

Answer

To solve the question, we need to analyze both statements regarding the isothermal expansion of an ideal gas.

### Step-by-Step Solution:

1. **Understanding Isothermal Expansion**:
- Isothermal expansion refers to the process in which an ideal gas expands at a constant temperature (T). During this process, the internal energy (U) of an ideal gas, which depends only on temperature, remains constant.

2. **Evaluating Statement 1**:
- **Statement 1**: "During isothermal expansion of an ideal gas, there is no change in the internal energy."
- Since the temperature does not change during isothermal processes, the change in internal energy (ΔU) can be expressed as:
\[ \Delta U = nC_v \Delta T \]
where \(C_v\) is the molar heat capacity at constant volume. Because \(\Delta T = 0\), we find that:
\[ \Delta U = nC_v \cdot 0 = 0 \]
- Therefore, Statement 1 is **true**.

3. **Evaluating Statement 2**:
- **Statement 2**: "During isothermal expansion of an ideal gas, as temperature remains constant, no heat enters or leaves the system."
- In reality, during isothermal expansion, while the temperature remains constant, the gas does perform work (W) on the surroundings. According to the first law of thermodynamics:
\[ \Delta U = Q + W \]
Since \(\Delta U = 0\) (as established in Statement 1), we have:
\[ 0 = Q + W \implies Q = -W \]
- This indicates that heat (Q) must flow into or out of the system to compensate for the work done by the gas. Therefore, Statement 2 is **false**.

4. **Conclusion**:
- Based on the evaluations, we conclude that:
- Statement 1 is true.
- Statement 2 is false.
- Thus, the correct answer is that Statement 1 is true, and Statement 2 is false.

### Final Answer:
- Statement 1 is true, and Statement 2 is false.