Which of the following graphs represent the behaviour of an ideal gas ?

Options

A. 1.
B. 2.
C. 3.
D. 4.

Explanation

To determine which graph represents the behavior of an ideal gas, we can analyze the options based on the Ideal Gas Law, which is expressed as:

\[ PV = nRT \]

Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles of gas
- \( R \) = Ideal gas constant
- \( T \) = Temperature

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
- The equation \( PV = nRT \) shows the relationship between pressure, volume, and temperature for an ideal gas.

2. **Analyze Option 1**:
- The graph shows \( P \) vs \( T \) with \( V \) held constant.
- Rearranging the Ideal Gas Law for constant \( V \) gives \( P \propto T \).
- This indicates a linear relationship, which can be represented as \( P = kT \) (where \( k \) is a constant).
- This graph will be a straight line passing through the origin.
- **Conclusion**: This graph represents the behavior of an ideal gas.

3. **Analyze Option 2**:
- The graph shows \( PV \) vs \( T \).
- From the Ideal Gas Law, if \( n \) and \( R \) are constants, then \( PV = nRT \) implies \( PV \) is directly proportional to \( T \).
- However, if the graph does not pass through the origin, it does not represent a direct proportionality.
- **Conclusion**: This graph does not represent the behavior of an ideal gas.

4. **Analyze Option 3**:
- The graph shows \( P \) vs \( V \) with \( T \) held constant.
- From the Ideal Gas Law, if \( T \) is constant, then \( PV = \text{constant} \).
- This relationship describes a hyperbola, not a straight line.
- **Conclusion**: This graph does not represent the behavior of an ideal gas.

5. **Analyze Option 4**:
- The graph shows \( PV \) vs \( T \).
- As established, \( PV \) should be a straight line when plotted against \( T \) if \( n \) and \( R \) are constant.
- If the graph is curved, it does not represent a direct proportionality.
- **Conclusion**: This graph does not represent the behavior of an ideal gas.

### Final Answer:
- **Option 1** is the only correct option that represents the behavior of an ideal gas.