Which of the following diagrams, Fig. depicts ideal gas behaviour ?

Options

A.
B.
C.
D.

Explanation

To determine which diagrams depict ideal gas behavior, we will analyze each option based on the relationships defined by the ideal gas law, \( PV = nRT \).

### Step-by-Step Solution:

1. **Analyze Diagram A:**
- Diagram A shows the relationship between volume (V) and temperature (T) at constant pressure (P).
- According to the ideal gas law, \( V \propto T \) when pressure is constant.
- Therefore, as temperature increases, volume also increases, which is consistent with ideal gas behavior.
- **Conclusion:** Diagram A depicts ideal gas behavior.

2. **Analyze Diagram B:**
- Diagram B shows the relationship between pressure (P) and volume (V) at constant temperature (T).
- According to the ideal gas law, \( PV = \text{constant} \) when temperature is constant, which implies \( P \propto \frac{1}{V} \).
- The graph should be a hyperbola, indicating that as volume increases, pressure decreases.
- **Conclusion:** Diagram B does not depict ideal gas behavior as it does not show the expected hyperbolic relationship.

3. **Analyze Diagram C:**
- Diagram C shows the relationship between pressure (P) and temperature (T) at constant volume (V).
- According to the ideal gas law, \( P \propto T \) when volume is constant.
- Therefore, as temperature increases, pressure also increases, which is consistent with ideal gas behavior.
- **Conclusion:** Diagram C depicts ideal gas behavior.

4. **Analyze Diagram D:**
- Diagram D shows the relationship between the product of pressure and volume (PV) and temperature (T).
- According to the ideal gas law, \( PV = nRT \), which implies that \( PV \propto T \).
- The graph should be a straight line passing through the origin, indicating a direct proportionality.
- However, if the graph does not appear linear, it suggests a deviation from ideal gas behavior.
- **Conclusion:** Diagram D does not depict ideal gas behavior.

### Final Answer:
- The diagrams that depict ideal gas behavior are **Diagram A** and **Diagram C**.

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