Assertion: In isobaric process, (V - T) graph is a straight line passing through origin. Slope of this line is directly proportional to mass of the gas. (V) is taken on (y - axis).
Reason: `V = ((n R)/p) T`
`:.` Slope`prop n`
or `"slope" prop m`.

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.

Answer

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

### Step 1: Understand the Assertion
The assertion states that in an isobaric process, the graph of Volume (V) versus Temperature (T) is a straight line that passes through the origin.

### Step 2: Analyze the Isobaric Process
In an isobaric process, the pressure (P) remains constant. According to the ideal gas law, we have:
\[ PV = nRT \]
Since P is constant, we can rearrange this equation to express volume (V) in terms of temperature (T):
\[ V = \frac{nR}{P} T \]

### Step 3: Identify the Form of the Equation
The equation \( V = \frac{nR}{P} T \) is in the form of \( y = mx \), where:
- \( y \) is \( V \)
- \( x \) is \( T \)
- \( m \) (the slope) is \( \frac{nR}{P} \)

This confirms that the graph of V versus T is indeed a straight line passing through the origin.

### Step 4: Determine the Slope
The slope of the line is given by:
\[ \text{slope} = \frac{nR}{P} \]
Since \( n \) (the number of moles) is directly proportional to the mass (m) of the gas (where \( n = \frac{m}{M} \), with M being the molar mass), we can say:
\[ \text{slope} \propto n \propto m \]
Thus, the slope is directly proportional to the mass of the gas.

### Step 5: Analyze the Reason
The reason provided states that \( V = \frac{nR}{P} T \) and concludes that the slope is proportional to \( n \) or mass \( m \). This is consistent with our analysis in Step 4.

### Conclusion
Both the assertion and the reason are true. The reason correctly explains the assertion.

### Final Answer
Both assertion and reason are true, and the reason is the correct explanation of the assertion.

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