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)

Options

A.
B.
C.
D.

Answer

To solve the question regarding the correct PV vs P plot at constant temperature for an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**: The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

2. **Identify Constants**: In this scenario, we are told that the temperature is constant and the amount of gas (number of moles) is also constant. Therefore, \( n \), \( R \), and \( T \) are constants.

3. **Determine the Implication of Constants**: Since \( n \), \( R \), and \( T \) are constant, the product \( PV \) must also be constant. This means that as the pressure \( P \) changes, the volume \( V \) must change in such a way that the product \( PV \) remains the same.

4. **Graphical Representation**: When plotting \( PV \) against \( P \) (or \( V \)), we need to recognize that if \( PV \) is constant, the graph will reflect a hyperbolic relationship. Specifically, if we plot \( PV \) on the y-axis and \( P \) on the x-axis, the graph will be a horizontal line at the value of the constant \( PV \).

5. **Conclusion**: The correct graph for \( PV \) vs \( P \) at constant temperature for an ideal gas will be a horizontal line, indicating that \( PV \) does not change with varying pressure \( P \).

### Final Answer:
The correct plot of \( PV \) vs \( P \) at constant temperature for an ideal gas is a horizontal line.

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