`-40^@F` on absolute scale is equal to

Options

A. 0 K
B. 233 K
C. 273 K
D. 313 K

Answer

To convert -40°F to the absolute scale (Kelvin), we can use the formula that relates Fahrenheit to Kelvin:

\[ T_F = \frac{9}{5} (T_K - 273) + 32 \]

Where:
- \( T_F \) is the temperature in Fahrenheit,
- \( T_K \) is the temperature in Kelvin.

### Step-by-Step Solution:

1. **Start with the given temperature in Fahrenheit:**
\[ T_F = -40°F \]

2. **Substitute the value of \( T_F \) into the formula:**
\[ -40 = \frac{9}{5} (T_K - 273) + 32 \]

3. **Isolate the term involving \( T_K \):**
- First, subtract 32 from both sides:
\[ -40 - 32 = \frac{9}{5} (T_K - 273) \]
\[ -72 = \frac{9}{5} (T_K - 273) \]

4. **Multiply both sides by \( \frac{5}{9} \) to eliminate the fraction:**
\[ -72 \cdot \frac{5}{9} = T_K - 273 \]
\[ -40 = T_K - 273 \]

5. **Solve for \( T_K \):**
- Add 273 to both sides:
\[ T_K = -40 + 273 \]
\[ T_K = 233 \]

6. **Conclusion:**
- Therefore, -40°F is equal to 233 Kelvin.

### Final Answer:
\[ -40°F = 233 \text{ K} \]