StatementI: Work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion adaibatically.
Statement II: Temperature remains constant in isothermal ecpansion but not in adiabatic expansion.

Options

A. Statement I: is true, Statement II is true and Statement II is the correct explanation for Statement I.
B. Statement I: is true, Statement II is true and Statement II is NOT the correct explanation for Statement I.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.

Explanation

To solve the question, we need to analyze both statements provided:

**Statement I**: Work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion adiabatically.

**Statement II**: Temperature remains constant in isothermal expansion but not in adiabatic expansion.

### Step-by-Step Solution:

1. **Understanding Isothermal Expansion**:
- In an isothermal process, the temperature of the gas remains constant. According to the ideal gas law, the relationship between pressure (P), volume (V), and temperature (T) is given by \(PV = nRT\). Since T is constant, if the volume increases, the pressure must decrease accordingly.
- The work done (W) during an isothermal expansion can be calculated using the formula:
\[ W = nRT \ln\left(\frac{V_f}{V_i}\right) \]
- Here, \(V_f\) is the final volume and \(V_i\) is the initial volume.

2. **Understanding Adiabatic Expansion**:
- In an adiabatic process, there is no heat exchange with the surroundings. The temperature of the gas changes as it expands. The relationship for an adiabatic process is given by \(PV^\gamma = \text{constant}\), where \(\gamma\) is the heat capacity ratio (C_p/C_v).
- The work done during an adiabatic expansion can be calculated using the formula:
\[ W = \frac{P_i V_i - P_f V_f}{\gamma - 1} \]
- Here, \(P_i\) and \(P_f\) are the initial and final pressures, respectively.

3. **Comparing Work Done**:
- In an isothermal expansion, the area under the PV curve (which represents work done) is larger than that in an adiabatic expansion for the same change in volume.
- Therefore, **Statement I is true**: The work done in isothermal expansion is indeed greater than that in adiabatic expansion.

4. **Analyzing Statement II**:
- By definition, in an isothermal process, the temperature remains constant throughout the expansion. In contrast, during an adiabatic expansion, the gas cools down as it does work on the surroundings, leading to a decrease in temperature.
- Thus, **Statement II is also true**: Temperature remains constant in isothermal expansion but not in adiabatic expansion.

5. **Conclusion**:
- Both statements are true, and Statement II correctly explains Statement I. Therefore, the correct option is that both statements are true and Statement II explains Statement I.

### Final Answer:
Both Statement I and Statement II are true, and Statement II correctly explains Statement I.

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