Which of the following gives straight line plot, keeping the third parameter correct ?

Options

A. P versus V
B. P versus `1//V`
C. V ersus T
D. P versus T.

Explanation

To solve the question regarding which of the following relationships gives a straight line plot while keeping a third parameter constant, we will analyze each option based on the gas laws.

### Step-by-Step Solution:

1. **Understanding the Options**:
- Option A: Pressure vs. Volume (P vs. V)
- Option B: Pressure vs. 1/Volume (P vs. 1/V)
- Option C: Volume vs. Temperature (V vs. T)
- Option D: Pressure vs. Temperature (P vs. T)

2. **Analyzing Option A (P vs. V)**:
- According to Boyle's Law, pressure (P) is inversely proportional to volume (V) when temperature is constant:
\[ P \propto \frac{1}{V} \]
- This means that the graph of P vs. V will be a hyperbola, not a straight line.
- **Conclusion**: This does not give a straight line plot.

3. **Analyzing Option B (P vs. 1/V)**:
- From Boyle's Law, if we rearrange the equation:
\[ P = k \cdot \frac{1}{V} \]
- This indicates that if we plot pressure (P) against the inverse of volume (1/V), we will get a straight line with a slope of k.
- **Conclusion**: This gives a straight line plot.

4. **Analyzing Option C (V vs. T)**:
- According to Charles' Law, volume (V) is directly proportional to temperature (T) when pressure is constant:
\[ V \propto T \]
- Therefore, if we plot volume against temperature, we will get a straight line.
- **Conclusion**: This gives a straight line plot.

5. **Analyzing Option D (P vs. T)**:
- According to Gay-Lussac's Law, pressure (P) is directly proportional to temperature (T) when volume is constant:
\[ P \propto T \]
- Thus, if we plot pressure against temperature, we will also get a straight line.
- **Conclusion**: This gives a straight line plot.

6. **Final Conclusion**:
- The options that give a straight line plot while keeping the third parameter constant are:
- Option B (P vs. 1/V)
- Option C (V vs. T)
- Option D (P vs. T)

### Answer:
The correct options that give straight line plots are **B, C, and D**.

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