Which of the following plots are correct ?

Options

A.
B.
C.
D.

Explanation

To determine which plots are correct based on the relationships between volume (V), pressure (P), and temperature (T) in gases, we can analyze each graph step by step.

### Step-by-Step Solution:

1. **Analyze the First Graph (V vs. P at Constant T)**:
- The relationship between volume (V) and pressure (P) at constant temperature (T) is given by Boyle's Law, which states that \( PV = k \) (where k is a constant).
- Rearranging this gives \( V = \frac{k}{P} \).
- This equation represents a hyperbolic relationship, indicating that as pressure increases, volume decreases.
- **Conclusion**: The first graph is incorrect if it does not show a hyperbolic curve.

2. **Analyze the Second Graph (V vs. T at Constant P)**:
- The relationship between volume (V) and temperature (T) at constant pressure (P) is given by Charles's Law, which states that \( V = kT \).
- This indicates a direct linear relationship between volume and temperature.
- **Conclusion**: The second graph is correct if it shows a straight line.

3. **Analyze the Third Graph (P vs. T at Constant V)**:
- The relationship between pressure (P) and temperature (T) at constant volume (V) is given by Gay-Lussac's Law, which states that \( P = kT \).
- This also indicates a direct linear relationship between pressure and temperature.
- **Conclusion**: The third graph is correct if it shows a straight line.

4. **Analyze the Fourth Graph (P vs. V vs. T)**:
- The combined gas law states that \( PV = nRT \), where n and R are constants.
- If we consider \( PV \) as one variable and T as another, we can rearrange it to show that \( PV \) is directly proportional to T.
- This implies a linear relationship when plotted.
- **Conclusion**: The fourth graph is correct if it shows a straight line.

### Final Conclusion:
- Based on the analysis:
- The first graph is incorrect.
- The second graph is correct.
- The third graph is correct.
- The fourth graph is correct.

Thus, the correct options are **B, C, and D**.