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

Options

A.
B.
C.
D.

Explanation

To determine which graph represents the behavior of an ideal gas, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ pV = nRT \]
where:
- \( p \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = universal gas constant
- \( T \) = temperature

### Step 2: Analyze the Relationships
From the ideal gas law, we can derive relationships between different variables:
1. If pressure (\( p \)) is held constant, then volume (\( V \)) is directly proportional to temperature (\( T \)):
\[ V \propto T \]
This means that if we plot a graph of volume (y-axis) versus temperature (x-axis), we should see a straight line that slopes upwards.

### Step 3: Evaluate the Given Graphs
Now, we need to evaluate the four graphs provided:
1. **Graph 1**: If this graph shows a straight line with volume on the y-axis and temperature on the x-axis, it represents the relationship \( V \propto T \) at constant pressure. This graph is correct.
2. **Graph 2**: If this graph suggests that \( pV \) is dependent on \( T \) directly, it is incorrect because \( pV \) is equal to \( nRT \) and not dependent on \( T \) alone.
3. **Graph 3**: If this graph shows a linear decrease between pressure and volume, it is incorrect. According to Boyle's Law, pressure is inversely proportional to volume at constant temperature, which should yield a hyperbolic curve.
4. **Graph 4**: If this graph indicates that \( pV \) is dependent on \( T \) in a linear fashion, it is also incorrect since \( pV \) is equal to \( nRT \) and does not vary linearly with \( T \).

### Step 4: Conclusion
After evaluating all the graphs, we conclude that **Graph 1** correctly represents the behavior of an ideal gas.

### Final Answer
The correct graph that represents the behavior of an ideal gas is **Graph 1**.

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