Staetement -1: The magniyude of the work involed in an isothermal expansion is greater than that involved in an adiabatic expansion.
Statement -2: P-v cure (pon y -axas and V on X-axas) decrease more repidly for reversible asiabatic expansion compared to reversible isothermal expansion starting from same initial state.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-5
B. If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-5
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 statements provided in the question, we need to evaluate the concepts of isothermal and adiabatic expansions in thermodynamics.

### Step-by-Step Solution:

1. **Understanding Isothermal Expansion**:
- In an isothermal process, the temperature of the system remains constant. For an ideal gas, this means that the internal energy does not change, and the work done by the gas can be calculated using the formula:
\[ W = nRT \ln\left(\frac{V_f}{V_i}\right) \]
- Here, \(W\) is the work done, \(n\) is the number of moles, \(R\) is the gas constant, \(T\) is the absolute temperature, \(V_f\) 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 work done in an adiabatic expansion can be expressed as:
\[ W = \frac{P_i V_i - P_f V_f}{\gamma - 1} \]
- Here, \(\gamma\) is the heat capacity ratio (\(C_p/C_v\)), and \(P_i\) and \(P_f\) are the initial and final pressures, respectively.

3. **Comparing Work Done**:
- When comparing the work done in isothermal and adiabatic expansions, it is observed that:
- The area under the P-V curve for isothermal expansion is larger than that for adiabatic expansion when both processes start from the same initial state. This is because the isothermal process allows for more expansion work due to the constant temperature, which sustains higher pressure for a longer volume change compared to the adiabatic process.

4. **Evaluating Statement 1**:
- Statement 1 claims that the magnitude of work involved in an isothermal expansion is greater than that involved in an adiabatic expansion. This is **true** based on the analysis above.

5. **Understanding the P-V Curve**:
- In a P-V diagram, the slope of the curve during an adiabatic process is steeper than that of an isothermal process. This means that for a given change in volume, the pressure drops more rapidly in an adiabatic process than in an isothermal process.

6. **Evaluating Statement 2**:
- Statement 2 states that the P-V curve decreases more rapidly for reversible adiabatic expansion compared to reversible isothermal expansion starting from the same initial state. This is also **true** as explained by the steeper slope of the adiabatic curve.

7. **Conclusion**:
- Both statements are correct. Statement 2 correctly explains why statement 1 is true, as the nature of the curves directly relates to the work done in each process.

### Final Answer:
- **Statement 1** is true: The magnitude of the work involved in an isothermal expansion is greater than that involved in an adiabatic expansion.
- **Statement 2** is true: The P-V curve decreases more rapidly for reversible adiabatic expansion compared to reversible isothermal expansion starting from the same initial state.