The correct order of temperature for a real gas is
`{:("Boyle temp.","Critical temp.","Inversion temp.",),((I),(II),(III),):}`

Options

A. `III gt I gt II`
B. `I gt II gt III`
C. `II gt I gt III`
D. `I gt III gt II`

Explanation

To determine the correct order of temperature for a real gas among Boyle temperature (Tb), Critical temperature (Tc), and Inversion temperature (Ti), we can use the formulas provided in the video transcript.

### Step-by-Step Solution:

1. **Identify the Formulas**:
- Boyle Temperature (Tb):
\[ T_b = \frac{A}{R_b} \]
- Critical Temperature (Tc):
\[ T_c = \frac{8A}{27R_b} \]
- Inversion Temperature (Ti):
\[ T_i = \frac{2A}{R_b} \]

2. **Analyze the Relationships**:
- From the formulas, we can see that all three temperatures depend on the constants A and Rb.
- To compare them, we can express them in terms of A and Rb.

3. **Express the Temperatures**:
- For Boyle Temperature (Tb):
\[ T_b = \frac{A}{R_b} \]
- For Critical Temperature (Tc):
\[ T_c = \frac{8A}{27R_b} \]
- For Inversion Temperature (Ti):
\[ T_i = \frac{2A}{R_b} \]

4. **Compare the Values**:
- To compare these temperatures, we can look at the coefficients of A and Rb:
- \( T_b = \frac{A}{R_b} \)
- \( T_i = \frac{2A}{R_b} \)
- \( T_c = \frac{8A}{27R_b} \)

5. **Determine the Order**:
- Since \( \frac{8}{27} < 1 \), we can conclude that:
\[ T_c < T_b < T_i \]
- Therefore, the order from least to greatest temperature is:
\[ T_c < T_b < T_i \]

6. **Final Answer**:
- The correct order of temperatures is:
\[ \text{Critical Temperature (Tc)} < \text{Boyle Temperature (Tb)} < \text{Inversion Temperature (Ti)} \]