Assertion: In the process pT=constant, if temperature of gas is increased work done by the gas is positive.
Reason: For the given process, `VpropT`.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that in the process where \( P \cdot T = \text{constant} \), if the temperature of the gas is increased, the work done by the gas is positive.

2. **Ideal Gas Law**:
Recall the ideal gas law, which states:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

3. **Analyzing the Process**:
Given that \( P \cdot T = \text{constant} \), we can express pressure \( P \) in terms of volume \( V \) and temperature \( T \):
\[ P = \frac{nRT}{V} \]
Substituting this into the equation \( P \cdot T = \text{constant} \), we get:
\[ \frac{nRT \cdot T}{V} = \text{constant} \]
Simplifying this gives:
\[ \frac{nR T^2}{V} = \text{constant} \]
This implies:
\[ V \propto T^2 \]

4. **Implications of Increasing Temperature**:
If the temperature \( T \) increases, then according to the relationship \( V \propto T^2 \), the volume \( V \) must also increase. This indicates that the gas is expanding.

5. **Work Done by the Gas**:
Work done by the gas during expansion is given by:
\[ W = P \Delta V \]
Since the volume \( V \) is increasing (i.e., \( \Delta V > 0 \)), and assuming pressure \( P \) remains positive, the work done \( W \) will also be positive.

6. **Conclusion on Assertion**:
Therefore, the assertion is correct: if the temperature of the gas increases, the work done by the gas is indeed positive.

7. **Analyzing the Reason**:
The reason states that for the given process, \( V \) is directly proportional to \( T \). However, we found that \( V \) is actually proportional to \( T^2 \), not \( T \). Therefore, the reason is incorrect.

8. **Final Evaluation**:
The assertion is true, but the reason is false.

### Final Answer:
- Assertion: True
- Reason: False