Assertion: Straight line on (p - T) graph for an ideal gas represents isochoric process.
Reason: If `p prop T, V = constant`.

Options

A. If both Assertion and Reason are true and the reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

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

### Step 1: Understand the Assertion
The assertion states that a straight line on a (p - T) graph for an ideal gas represents an isochoric process. An isochoric process is one where the volume remains constant.

### Step 2: Analyze the (p - T) Graph
In a (p - T) graph:
- Pressure (p) is plotted on the y-axis.
- Temperature (T) is plotted on the x-axis.

For an ideal gas, the relationship between pressure, volume, and temperature is given by the ideal gas law:
\[ PV = nRT \]
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles of gas
- \( R \) = Universal gas constant
- \( T \) = Temperature

### Step 3: Determine the Nature of the Line
If we consider the case where volume (V) is constant (as in an isochoric process), we can rearrange the ideal gas law to express pressure in terms of temperature:
\[ P = \frac{nR}{V} T \]
This equation shows that pressure is directly proportional to temperature when volume is constant. Therefore, if we plot this relationship, we will get a straight line that passes through the origin.

### Step 4: Evaluate the Assertion
The assertion claims that any straight line on the (p - T) graph represents an isochoric process. However, this is not entirely accurate. A straight line on the (p - T) graph indicates a linear relationship between pressure and temperature, but it does not necessarily indicate that the volume is constant unless it specifically passes through the origin. Thus, the assertion is **false**.

### Step 5: Evaluate the Reason
The reason states that if \( p \propto T \), then \( V \) must be constant. This is true because, from the ideal gas law, if pressure is directly proportional to temperature, the volume must remain constant for a specific amount of gas. Therefore, the reason is **true**.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, and the reason is true.

### Final Answer
The assertion is false, and the reason is true.

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