Select the correct alternative.

Options

A. `T_(i) gt T_(B)`
B. `T_(B) gt T_(i)`
C. `T_(C) gt T_(i)`
D. `T_(C) = T_(i)`

Explanation

To solve the question regarding the relationships between the inversion temperature (Ti), boiling temperature (Tb), and critical temperature (Tc), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Inversion Temperature (Ti)**: Given by the formula \( Ti = \frac{2a}{Rb} \)
- **Boiling Temperature (Tb)**: Given by the formula \( Tb = \frac{a}{Rb} \)
- **Critical Temperature (Tc)**: Given by the formula \( Tc = \frac{8a}{27Rb} \)

2. **Identify the Common Terms**:
- All three temperatures involve the term \( \frac{a}{Rb} \). We can denote this common term as \( x \) for simplification:
- \( Ti = 2x \)
- \( Tb = x \)
- \( Tc = \frac{8}{27}x \)

3. **Compare the Values**:
- From the expressions:
- \( Ti = 2x \)
- \( Tb = x \)
- \( Tc = \frac{8}{27}x \)
- We can see that:
- \( Ti > Tb \) since \( 2x > x \)
- \( Tb > Tc \) since \( x > \frac{8}{27}x \)

4. **Order the Temperatures**:
- Therefore, we can conclude the order of the temperatures:
- \( Ti > Tb > Tc \)

5. **Evaluate the Options**:
- The question asks to select the correct alternative.
- Option A states \( Ti > Tb \) which is correct.
- Option B states \( Tb > Ti \) which is incorrect.
- Option C states \( Tc > Ti \) which is also incorrect.

6. **Conclusion**:
- The only correct option is A: \( Ti > Tb \).