The inversion temperature for vander Waal's gas is

Options

A. `T_(i)=2a//Rb`
B. `T_(i)=a//Rb`
C. `T_(i)=a//Rb`
D. `T_(i)=0.5T` Boyle

Answer

To find the inversion temperature for a van der Waals gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Inversion Temperature**:
- The inversion temperature (T_i) is defined as the critical temperature below which a non-ideal gas can be expanded at constant enthalpy while experiencing a decrease in temperature.

2. **Identify the Expression for Inversion Temperature**:
- For van der Waals gases, the inversion temperature can be expressed using the formula:
\[ T_i = \frac{2A}{R \cdot B} \]
where:
- \( A \) is the van der Waals constant related to the attraction between particles,
- \( R \) is the universal gas constant,
- \( B \) is the van der Waals constant related to the volume occupied by the gas particles.

3. **Select the Correct Option**:
- From the options provided, we need to find the one that matches our derived formula for \( T_i \).
- The correct option is:
\[ T_i = \frac{2A}{R \cdot B} \]
- This matches with option A.

4. **Conclusion**:
- Therefore, the inversion temperature for a van der Waals gas is given by the expression:
\[ T_i = \frac{2A}{R \cdot B} \]