A temperature difference of 5K is equal to: a) a difference of 12 on the Celsius scale. b) a difference of 9 on the Fahrenheit scale. c) a difference of 2.8 on the Fahrenheit scale. d) a difference of 32.5 on the Fahrenheit scale.
The Correct Answer and Explanation is:
Correct Answer: b) a difference of 9 on the Fahrenheit scale.
Explanation:
To understand how temperature differences relate across various scales, it’s essential to remember that Kelvin (K) and Celsius (°C) use the same size unit. This means:
A difference of 1 K = a difference of 1 °C
So, a difference of 5 K = difference of 5 °C.
Now, to convert a temperature difference from Celsius to Fahrenheit, we do not use the normal temperature conversion formula, which includes addition or subtraction. Instead, we convert differences using only the scaling factor, which is 1.8 (or 9/5).
Formula for Converting Temperature Difference:
Δ°F=Δ°C×95\Delta°F = \Delta°C \times \frac{9}{5}Δ°F=Δ°C×59Δ°F=5°C×95=9°F\Delta°F = 5°C \times \frac{9}{5} = 9°FΔ°F=5°C×59=9°F
So, a temperature difference of 5 Kelvin is:
- A difference of 5°C, because Kelvin and Celsius scale differences are equivalent.
- A difference of 9°F, because 5×95=95 × \frac{9}{5} = 95×59=9.
Summary of Choices:
| Choice | Meaning | Correct? |
|---|---|---|
| a) 12°C | Incorrect (5 K = 5°C) | ❌ |
| b) 9°F | Correct (5°C × 9/5 = 9°F) | ✅ |
| c) 2.8°F | Incorrect (confused with conversion between °C and K values, not differences) | ❌ |
| d) 32.5°F | Incorrect (might be confused with freezing point diff, not scale difference) | ❌ |
Conclusion:
The correct answer is b) a difference of 9 on the Fahrenheit scale. This demonstrates the importance of knowing that while temperature values and temperature differences are related, they are converted differently across scales.
