The Critical temperature , Boyle's temperature and inversion temperature respectively are given as

Options

A. `1/(Rb) , (8a)/(27 Rb),(2a)/(Rb)`
B. `(8a)/(27 Rb),(a)/(Rb),(2a)/(Rb)`
C. `(8a)/(Rb),(a)/(Rb),(2a)/(Rb)`
D. `(a)/(Rb),(a)/(27Rb),(2a)/(Rb)`

Answer

To solve the question regarding the critical temperature, Boyle's temperature, and inversion temperature, we need to identify the formulas for each of these temperatures based on the information provided.

### Step-by-Step Solution:

1. **Identify the Critical Temperature:**
- The critical temperature (Tc) is given as:
\[ T_c = \frac{8A}{27B_r} \]

2. **Identify Boyle's Temperature:**
- The formula for Boyle's temperature (Tb) is given as:
\[ T_b = \frac{A}{R_b} \]

3. **Identify Inversion Temperature:**
- The formula for inversion temperature (Ti) is given as:
\[ T_i = \frac{2A}{R_b} \]

4. **Match the Values:**
- Now we can summarize the values:
- Critical Temperature (Tc) = \(\frac{8A}{27B_r}\)
- Boyle's Temperature (Tb) = \(\frac{A}{R_b}\)
- Inversion Temperature (Ti) = \(\frac{2A}{R_b}\)

5. **Choose the Correct Option:**
- According to the provided options, we need to match:
- Option 2 states:
- First value: \(\frac{8A}{27B_r}\)
- Second value: \(\frac{8A}{R_b}\)
- Third value: \(\frac{2A}{R_b}\)
- The correct match is:
- First value: \(\frac{8A}{27B_r}\) (Critical Temperature)
- Second value: \(\frac{A}{R_b}\) (Boyle's Temperature)
- Third value: \(\frac{2A}{R_b}\) (Inversion Temperature)

6. **Conclusion:**
- Therefore, the answer is Option 2.