Which of the following graphs is inconsistent with ideal gas behaviour ? (Assume n = constant)

Options

A.
B.
C.
D.

Answer

To determine which graph is inconsistent with ideal gas behavior, we can analyze the relationships between pressure (P), volume (V), and temperature (T) based on the ideal gas law, which states:

\[ PV = nRT \]

Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles (constant)
- \( R \) = ideal gas constant
- \( T \) = temperature

### Step-by-Step Solution:

1. **Identify the Relationships**:
- From the ideal gas law, we can derive several relationships:
- \( P \propto \frac{1}{V} \) (at constant T)
- \( V \propto T \) (at constant P)
- \( P \propto T \) (at constant V)

2. **Analyze Each Graph**:
- **Graph A**: Pressure vs. \( \frac{1}{V} \)
- Since \( P \) is directly proportional to \( \frac{1}{V} \), this graph should show a linear relationship. If temperature increases, the slope will increase. This is consistent with ideal gas behavior.

- **Graph B**: Volume vs. Temperature
- Since \( V \) is directly proportional to \( T \) at constant pressure, this graph should also show a linear relationship. If pressure increases, the graph will shift upwards. This is consistent with ideal gas behavior.

- **Graph C**: Pressure vs. Volume
- Here, \( P \) is inversely proportional to \( V \) (Boyle's Law). If temperature increases, the graph should show that for a given temperature, as volume increases, pressure decreases. If T2 is greater than T1, the graph should shift upwards. This is consistent with ideal gas behavior.

- **Graph D**: \( \frac{V}{T} \) vs. Temperature
- This graph should show a linear relationship since \( V \) is directly proportional to \( T \). If pressure is constant, this graph is also consistent with ideal gas behavior.

3. **Conclusion**:
- After analyzing all the graphs, we find that Graph C (Pressure vs. Volume) is inconsistent with ideal gas behavior when considering the relationships derived from the ideal gas law. This graph should not show a linear relationship under varying temperatures.

### Final Answer:
The graph that is inconsistent with ideal gas behavior is **Graph C** (Pressure vs. Volume).