Answer :
Final answer:
The Fahrenheit and Celsius scales have the same numerical value at -40 degrees. The change in temperature in Fahrenheit degrees is nine-fifths of the change in Celsius degrees. For example, a 40.0°F drop equates to a 22.2°C decrease.
Explanation:
There is indeed one temperature point where the Fahrenheit and Celsius scales read the same numerical value, which is -40 degrees. Below is how you can see that both scales match:
Using the formula to convert Fahrenheit to Celsius which is C = 5/9 × (F − 32), setting C equal to F and solving for the temperature gives us:
- 9/5 × C + 32 = C
- 9/5 × C - C = -32
- 4/5 × C = -32
- C = -40
Therefore, -40°C equals -40°F. For the second part of the question, the Fahrenheit and Kelvin scales never match numerically as they start from different zero points and have different size degrees.
The relationship between a change in Fahrenheit and Celsius is also straightforward. A change in temperature in Fahrenheit degrees is always nine-fifths of the change in Celsius degrees. This can be shown by the basic conversion formula:
- ∆F = 9/5 × ∆C
If a cold front drops the temperature by 40.0°F, the corresponding decrease in Celsius would be:
- ∆C = 5/9 × ∆F = 5/9 × 40 = 22.2°C