A : Work done by a gas in isothermal expension is more than the work done by the gas in the same expasion adiabatically.
R : Temperature remains constant in isothermal expansion and not in adiabatic expansion.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion
C. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements

Answer

To solve the problem, we need to analyze the assertion and reason provided in the question regarding the work done by a gas during isothermal and adiabatic expansions.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the work done by a gas in isothermal expansion is greater than the work done by the gas in the same expansion adiabatically.

2. **Understanding the Reason**:
The reason given is that the temperature remains constant in isothermal expansion and not in adiabatic expansion.

3. **Analyzing Isothermal Expansion**:
- In an isothermal process, the temperature (T) of the gas remains constant.
- The work done (W) by the gas during isothermal expansion can be calculated using the formula:
\[ W = nRT \ln\left(\frac{V_f}{V_i}\right) \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, \( V_f \) is the final volume, and \( V_i \) is the initial volume.

4. **Analyzing Adiabatic Expansion**:
- In an adiabatic process, there is no heat exchange with the surroundings (\( Q = 0 \)), and the temperature of the gas changes as it expands.
- The work done in an adiabatic process can be expressed as:
\[ W = \frac{P_f V_f - P_i V_i}{\gamma - 1} \]
where \( \gamma \) is the heat capacity ratio \( C_p/C_v \).

5. **Comparing Work Done**:
- When comparing the two processes for the same change in volume, the area under the PV curve for the isothermal process is greater than that for the adiabatic process.
- This is because, in the isothermal process, the gas does work while maintaining constant temperature, allowing it to absorb heat from the surroundings, which contributes to more work done.

6. **Conclusion**:
- Therefore, the assertion is correct: the work done in isothermal expansion is indeed greater than in adiabatic expansion.
- However, the reason provided does not adequately explain why the assertion is true. The reason focuses on temperature constancy but does not address the relationship between work done and the areas under the respective curves.

7. **Final Answer**:
- Both the assertion and reason are true, but the reason is not the correct explanation for the assertion.