If volume of the gas is very large, then the second virial coefficient B in virial equation is

Options

A. `(b+(a)/(RT))`
B. `(b-(a)/(RT))`
C. `(b+(a)/(RTV))`
D. `(b-(a)/(RTV))`

Explanation

To determine the behavior of the second virial coefficient \( B \) when the volume of the gas is very large, we can analyze the virial equation step by step.

### Step-by-Step Solution:

1. **Understanding the Virial Equation**:
The virial equation can be expressed as:
\[ P = \frac{RT}{V - B} - \frac{A}{V^2} \]
where \( P \) is the pressure, \( R \) is the universal gas constant, \( T \) is the temperature, \( A \) and \( B \) are constants related to the interactions between gas molecules.

2. **Considering Large Volume**:
When the volume \( V \) of the gas is very large, the term \( B \) (which represents the volume excluded due to the finite size of gas molecules) becomes negligible compared to \( V \). Thus, we can simplify the equation.

3. **Simplifying the Equation**:
As \( V \) approaches infinity, we can approximate:
\[ V - B \approx V \]
Therefore, the virial equation simplifies to:
\[ P \approx \frac{RT}{V} \]

4. **Analyzing the Second Virial Coefficient \( B \)**:
The second virial coefficient \( B \) is defined in the context of the virial expansion. For very large volumes, the contributions from molecular interactions become less significant, and thus:
\[ B \to 0 \]
This indicates that as the volume increases, the second virial coefficient approaches zero.

5. **Conclusion**:
Therefore, we conclude that if the volume of the gas is very large, the second virial coefficient \( B \) approaches zero:
\[ B \approx 0 \]