The variation of PV with V of fixed mass of an ideal gas at constant temperature is graphically represented by the curve

Options

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Answer

To solve the question regarding the variation of PV with V for a fixed mass of an ideal gas at constant temperature, 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 absolute temperature.

2. **Identify the Conditions**:
In this problem, we are dealing with a fixed mass of gas at constant temperature. This means that \( n \), \( R \), and \( T \) are constants.

3. **Rearranging the Equation**:
Since \( nRT \) is a constant when temperature is constant, we can denote it as \( C \):
\[ PV = C \]
This implies that the product \( PV \) remains constant as the volume \( V \) changes.

4. **Analyzing the Relationship**:
If we consider the relationship \( PV = C \), we can express pressure \( P \) in terms of volume \( V \):
\[ P = \frac{C}{V} \]
This indicates that as the volume \( V \) increases, the pressure \( P \) decreases, and vice versa.

5. **Graphical Representation**:
To graph \( PV \) against \( V \):
- The x-axis will represent volume \( V \).
- The y-axis will represent the product \( PV \).
- Since \( PV \) is constant, the graph will be a horizontal line at the value \( C \).

6. **Conclusion**:
Therefore, the variation of \( PV \) with \( V \) at constant temperature is represented by a horizontal line, indicating that \( PV \) does not change with varying volume.

### Final Answer:
The correct representation of the variation of \( PV \) with \( V \) for a fixed mass of an ideal gas at constant temperature is a horizontal line.