Final answer:
A 40.0 Fahrenheit degree temperature decrease is equivalent to a 22.2 Celsius degree decrease. Temperature in Fahrenheit is nine-fifths of the temperature in Celsius minus 32 for a direct conversion but just nine-fifths of the Celsius temperature for a change in temperature. Temperature is a scalar quantity with magnitude but no direction
Step-by-step explanation:
The student is asking about the decrease in temperature when it drops by 40.0 Fahrenheit degrees, how this relates to Celsius, and other comparisons between temperature scales and conditions.
To convert a change in temperature from Fahrenheit to Celsius, we use the formula C = (F - 32) × (5/9), where F is the temperature in Fahrenheit and C is the temperature in Celsius.
However, for a change in temperature, we only use the 5/9 factor since the 32-degree offset for freezing points does not apply.
Therefore, a change of 40.0 Fahrenheit degrees corresponds to a change of 40 × (5/9) = 22.2 Celsius degrees.
To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, we can derive a simple relationship. When converting from Celsius to Fahrenheit, the formula is F = C × (9/5) + 32.
For a change in temperature, we do not add the 32, thus the change in Fahrenheit is indeed nine-fifths of the change in Celsius. Additionally, at -40 degrees, both Fahrenheit and Celsius scales read the same numerical value.
The concept of temperature as a scalar or vector quantity is also discussed. Temperature is a scalar quantity since it has magnitude but no specific direction in space. Physical quantities like velocity, which have both magnitude and direction, are vector quantities.