If the temperature rises by 18 degrees Fahrenheit, what is the equivalent rise on the Celsius scale?
The Correct Answer and Explanation is:
To convert the temperature rise from Fahrenheit to Celsius, we use the formula that relates the temperature difference in Fahrenheit to the temperature difference in Celsius:
[
\Delta C = \frac{\Delta F – 32}{1.8}
]
However, because we are dealing with a temperature change (not an absolute temperature), we do not need to subtract 32 as we would for an absolute conversion. Instead, we use the simplified version of the formula for temperature change:
[
\Delta C = \frac{\Delta F}{1.8}
]
Where:
- (\Delta C) is the temperature change in Celsius
- (\Delta F) is the temperature change in Fahrenheit
In this case, (\Delta F = 18) degrees Fahrenheit.
Now, we apply the formula:
[
\Delta C = \frac{18}{1.8}
]
[
\Delta C = 10 \text{ degrees Celsius}
]
Explanation:
- Understanding the Formula: The formula (\Delta C = \frac{\Delta F}{1.8}) works by recognizing that 1 degree Celsius is equivalent to a change of 1.8 degrees Fahrenheit. The reason for this is that the size of a degree on the Celsius scale is smaller than on the Fahrenheit scale. Specifically, the Celsius scale divides the range between the freezing and boiling points of water (0°C to 100°C) into 100 equal parts, while the Fahrenheit scale divides the same range into 180 parts. Hence, the ratio between the changes is 1.8.
- Application: For a temperature increase of 18 degrees Fahrenheit, we divide this value by 1.8 to find the equivalent change in Celsius. The result is 10 degrees Celsius, meaning that a rise of 18°F is equivalent to a 10°C rise.
In summary, a temperature rise of 18°F is equivalent to a 10°C rise. This relationship allows us to easily convert temperature changes between the two scales, ensuring accurate comparisons and calculations in both everyday and scientific contexts.