Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas ? (P and V stand for pressure and volume of the gas respectively)
Show Hint
For an ideal gas, any plot of \( PV \) against \( P \) or \( V \) at constant temperature will always be a horizontal straight line. Deviations from this line indicate non-ideal (real) gas behavior.
Step 1: Understanding the Concept:
Boyle's Law states that for a fixed mass of an ideal gas at a constant temperature, the pressure of the gas is inversely proportional to its volume.
This means the product of pressure and volume remains constant. Step 2: Key Formula or Approach:
From the ideal gas equation:
\[ PV = nRT \]
At constant temperature (\( T \)) and constant amount of gas (\( n \)), the term \( nRT \) is a constant.
Therefore, \( PV = \text{constant} \). Step 3: Detailed Explanation:
Since \( PV \) is a constant, its value does not change regardless of the pressure \( P \) applied to the gas.
If we plot \( PV \) on the y-axis and \( P \) on the x-axis, the graph will be a straight line with a slope of zero.
This results in a horizontal line parallel to the pressure axis.
The other graphs represent different relationships:
- Graph A shows \( PV \) directly proportional to \( P \), which is incorrect.
- Graph B shows \( PV \) inversely proportional to \( P \), which is incorrect.
- Graph C shows a hyperbolic relationship, which usually describes \( P \) vs \( V \), not \( PV \) vs \( P \). Step 4: Final Answer:
The correct plot is a horizontal line, as shown in option (D).
