Statement -1: Entropy change in reversible adiabatic expansion of an ideal gas is zero.
Statement-2: The increase in entropy due to volume increase just compensates the decrease in entropy due to fall in temperature.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-6
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-6
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To analyze the given statements regarding the entropy change in a reversible adiabatic expansion of an ideal gas, we will break down the reasoning step by step.

### Step-by-Step Solution:

1. **Understanding Reversible Adiabatic Process**:
- In a reversible adiabatic process, there is no heat exchange with the surroundings. This means that the heat transfer \( dq \) is equal to zero.
- The first law of thermodynamics states that the change in internal energy \( dU \) is equal to the work done \( dW \) on the system since \( dq = 0 \).

2. **Entropy Change Calculation**:
- The change in entropy \( dS \) for a reversible process is given by the formula:
\[ dS = \frac{dq_{rev}}{T} \]
- Since \( dq_{rev} = 0 \) for an adiabatic process, we have:
\[ dS = \frac{0}{T} = 0 \]
- Therefore, the total change in entropy \( \Delta S \) for the entire process is also zero.

3. **Evaluating Statement 1**:
- Statement 1 claims that the entropy change in reversible adiabatic expansion of an ideal gas is zero. Based on our calculation, this statement is **correct**.

4. **Evaluating Statement 2**:
- Statement 2 suggests that the increase in entropy due to the volume increase compensates for the decrease in entropy due to the fall in temperature.
- In a reversible adiabatic expansion, while the volume increases, the temperature of the gas decreases. This means that although the volume increase tends to increase entropy, the decrease in temperature tends to decrease entropy.

5. **Understanding the Compensation**:
- However, the key point is that the total entropy change in a reversible adiabatic process is zero, meaning the increase in entropy due to volume increase does not actually compensate for the decrease in entropy due to the fall in temperature in a way that results in a net change. Instead, they balance out perfectly, leading to no change in entropy overall.

6. **Conclusion on Statement 2**:
- Therefore, Statement 2 is **incorrect** because it implies a net change in entropy when in fact, the total change is zero.

### Final Assessment:
- **Statement 1**: Correct
- **Statement 2**: Incorrect