Question

Suppose a cold front blows into your locale and drops the temperature by 40.0 Fahrenheit degrees. How many degrees Celsius does the temperature decrease when there is a 40.0ºF decrease in temperature?

a) (22.2ºC)
b) (44.0ºC)
c) (55.6ºC)
d) (77.8ºC)

Answer 1

When the temperature drops by 40.0 Fahrenheit degrees, it decreases by 22.2 Celsius degrees. The correct conversion factor is nine-fifths or 5/9 when converting changes in temperature between Fahrenheit and Celsius, specifically for changes not initial temperatures.

Step-by-step explanation:

To determine how many degrees Celsius the temperature decreases when there is a 40.0°F decrease, we use the relationship between Fahrenheit and Celsius changes in temperature, which states that any change in temperature in Fahrenheit degrees is nine-fifths of the change in Celsius degrees. The formula for converting a change in Fahrenheit to a change in Celsius is:

Change in °C = (Change in °F - 32) ÷ 1.8

To convert a change of 40.0°F:

Change in °C = (40.0 °F - 32) ÷ 1.8

However, since we are only interested in the change in temperature, not the temperature itself, the 32 does not come into the calculation. Therefore:

Change in °C = 40.0 °F ÷ (5/9)

Change in °C = 22.2°C

So, when the temperature drops by 40.0 Fahrenheit degrees, it decreases by 22.2 Celsius degrees. Thus, answer choice (a) (22.2°C) is correct.