Statement-1: Two gases at same pressure, volume & temperature are compressed to same volume. The first isothermally and second adiabatically, greater work is done on the gas for an adiabatic process.
Statement-2: Final temperature for gas going under isothermal process is more than gas going under adiabatic process.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for 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 problem, we need to analyze the two statements regarding the work done during isothermal and adiabatic processes and the final temperatures of the gases involved.

### Step 1: Analyze Statement 1
**Statement 1:** Two gases at the same pressure, volume, and temperature are compressed to the same volume; the first isothermally and the second adiabatically. Greater work is done on the gas for an adiabatic process.

1. **Understanding Isothermal Process:**
- In an isothermal process, the temperature remains constant. The relationship between pressure and volume is given by:
\[ P_i V_i = P_f V_f \]
- Thus, the final pressure after compression can be expressed as:
\[ P_f = \frac{P_i V_i}{V_f} \]

2. **Understanding Adiabatic Process:**
- In an adiabatic process, there is no heat exchange with the surroundings, and the relationship is given by:
\[ P_i V_i^\gamma = P_f V_f^\gamma \]
- Therefore, the final pressure can be expressed as:
\[ P_f = \frac{P_i V_i^\gamma}{V_f^\gamma} \]

3. **Comparing Final Pressures:**
- Since \(\gamma > 1\), we can see that:
\[ P_f \text{ (adiabatic)} > P_f \text{ (isothermal)} \]
- This indicates that the final pressure in the adiabatic process is greater than that in the isothermal process.

4. **Work Done Comparison:**
- The work done on the gas during an isothermal process is given by:
\[ W_{iso} = nRT \ln\left(\frac{V_i}{V_f}\right) \]
- For the adiabatic process, the work done is generally greater because the pressure is higher at the same volume:
\[ W_{adi} = \text{(depends on specific heat capacities and temperature change)} \]
- Therefore, we conclude that:
\[ W_{adi} > W_{iso} \]
- **Conclusion for Statement 1:** True.

### Step 2: Analyze Statement 2
**Statement 2:** The final temperature for gas going under isothermal process is more than gas going under adiabatic process.

1. **Final Temperature in Isothermal Process:**
- Since the temperature remains constant in an isothermal process, we have:
\[ T_f = T_i \]

2. **Final Temperature in Adiabatic Process:**
- For an adiabatic process, the final temperature can be derived from the first law of thermodynamics and is generally lower than the initial temperature due to work done on the gas:
\[ T_f \text{ (adiabatic)} < T_i \]

3. **Comparison of Final Temperatures:**
- Since \(T_f \text{ (isothermal)} = T_i\) and \(T_f \text{ (adiabatic)} < T_i\), we can conclude:
\[ T_f \text{ (isothermal)} > T_f \text{ (adiabatic)} \]
- **Conclusion for Statement 2:** False.

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