For a real gas obeying van der waal's equation , graph is plotted between `PV_m` (y- axis) and P (x - axis) where `V_m` is molar volume . Y - intercept the graph is

Options

A. RT
B. `(P+a/V^2)`
C. `(RT)/(V-b)`
D. Cannot be determined

Answer

To find the y-intercept of the graph plotted between \( PV_m \) (y-axis) and \( P \) (x-axis) for a real gas obeying van der Waals equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the van der Waals Equation**:
The van der Waals equation for one mole of a real gas is given by:
\[ \left( P + \frac{a}{V_m^2} \right)(V_m - b) = RT \]
Where:
- \( P \) = pressure
- \( V_m \) = molar volume
- \( R \) = universal gas constant
- \( T \) = temperature
- \( a \) and \( b \) are van der Waals constants.

2. **Rearranging the Equation**:
For one mole, we can rearrange the van der Waals equation to express \( PV_m \):
\[ P V_m = RT - P b - \frac{a}{V_m} \]

3. **Graphing \( PV_m \) vs. \( P \)**:
We need to express \( PV_m \) in terms of \( P \):
\[ PV_m = RT - Pb - \frac{a}{V_m} \]
This implies that \( PV_m \) is a function of \( P \).

4. **Finding the y-intercept**:
To find the y-intercept of the graph, we need to consider the case when \( P = 0 \):
\[ PV_m = RT - 0 \cdot b - \frac{a}{V_m} \quad \text{(as \( P \) approaches 0)} \]
Therefore, the y-intercept (when \( P = 0 \)) is:
\[ PV_m = RT \]

5. **Conclusion**:
Thus, the y-intercept of the graph of \( PV_m \) vs. \( P \) is:
\[ \text{Y-intercept} = RT \]

### Final Answer:
The y-intercept of the graph is \( RT \).