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 explantion of the assertion, then mark(1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided:

### Step 1: Understand the Assertion (A)
The assertion states that the work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion adiabatically.

**Hint:** Recall the definitions of isothermal and adiabatic processes.

### Step 2: Understand the Reason (R)
The reason states that temperature remains constant in isothermal expansion and not in adiabatic expansion.

**Hint:** Consider how temperature affects the internal energy and work done in both processes.

### Step 3: Analyze Isothermal Expansion
In an isothermal process, the temperature of the gas remains constant. According to the first law of thermodynamics, the work done by the gas can be calculated using the formula:
\[ W = nRT \ln\left(\frac{V_f}{V_i}\right) \]
where \( W \) is the work done, \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the absolute temperature, \( V_f \) is the final volume, and \( V_i \) is the initial volume.

**Hint:** Think about how the constant temperature influences the energy exchange.

### Step 4: Analyze Adiabatic Expansion
In an adiabatic process, there is no heat exchange with the surroundings. The work done in an adiabatic process can be expressed as:
\[ W = \frac{P_i V_i - P_f V_f}{\gamma - 1} \]
where \( \gamma \) is the heat capacity ratio (Cp/Cv).

**Hint:** Remember that in adiabatic processes, the internal energy change is equal to the work done.

### Step 5: Compare Work Done in Both Processes
In an isothermal expansion, since the temperature remains constant, the gas can do more work as it absorbs heat from the surroundings to maintain the temperature. In contrast, during adiabatic expansion, the gas does work but does not absorb heat, which results in a lower amount of work done.

**Hint:** Visualize the pressure-volume (P-V) diagrams for both processes to see the area under the curve representing work done.

### Step 6: Conclusion
Since the area under the curve (which represents work done) for the isothermal process is greater than that for the adiabatic process, we can conclude that the assertion (A) is true. The reason (R) is also true but does not fully explain the assertion, as it only states the condition of temperature without relating it to the work done.

**Final Answer:** Both assertion and reason are correct, but the reason is not a correct explanation of the assertion.