For a given mass of a gas, what is the shape of (pV) versus (T) graph on isothermal process ?

Explanation

To determine the shape of the (pV) versus (T) graph during an isothermal process for a given mass of gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Isothermal Process**:
- In an isothermal process, the temperature (T) of the gas remains constant. This means that during the entire process, the temperature does not change.

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

3. **Consider the Fixed Mass of Gas**:
- Since the mass of the gas is fixed, the number of moles \(n\) is constant. Therefore, \(nR\) is also a constant value.

4. **Analyze the Equation for Isothermal Conditions**:
- For an isothermal process, since \(T\) is constant, the product \(PV\) must also remain constant. This can be expressed as:
\[ PV = \text{constant} \]
- This implies that for any change in pressure or volume, the product \(PV\) will not change as long as the temperature remains constant.

5. **Graphing \(PV\) versus \(T\)**:
- Now, we need to plot \(PV\) on the y-axis and \(T\) on the x-axis. Since \(PV\) is constant and does not change with temperature in an isothermal process, the graph will be a horizontal line.
- This means that regardless of the value of \(T\), the value of \(PV\) remains the same.

6. **Conclusion**:
- Therefore, the shape of the (pV) versus (T) graph during an isothermal process is a horizontal line, indicating that \(PV\) is constant for a fixed mass of gas at a constant temperature.

### Final Answer:
The shape of the (pV) versus (T) graph on an isothermal process is a horizontal line.