Question

The Fahrenheit temperature scale is defined so that ice melts at 32⁰ F and water boils at 212⁰ F.

(a) Derive the formula for converting from Fahrenheit to Celsius and back

(b) What is absolute zero on the Fahrenheit scale?

Short answer

(a)$\frac{9}{5}°C+32=°F$

(b) -459.67$°F$

Step-by-step solution

Part (a) Step 1 : Fahrenheit scales values of freezing point and boiling point.

Fahrenheit freezing point of water = 32$°F$

Fahrenheit boiling point of water = 212$°F$

212 - 32 = 180$°F$ between the freezing point and boiling point of water.

Part (a) Step 2 :  Celsius scales values of freezing and boiling point.

Celsius freezing point of water = 0$°C$

Celsius boiling point of water = 100$°C$

100 - 0 = 100$°C$ between the freezing point and boiling point of water.

Part (a) Step 3 : Ratio for Celsius to Fahrenheit scale values. 

The ratio for Celsius to Fahrenheit of $\frac{100}{180}=\frac{5}{9}$and the ratio of Fahrenheit to Celsius of $\frac{180}{100}=\frac{9}{5}$

then 32$°F$= 0$°C$

Hence the formula for degree Celsius to Fahrenheit is localid="1649151785065" ${}^{}\frac{9}{5}°C+32=°F$

Part (b) Step 1: Absolute zero in celsius

Absolute zero = 0K

K - 273.15 = $°C$

$°C$ = 0 - 273.15 = -273.15$°C$

Part (b) Step 2: Absolute zero in Fahrenheit

we know that $°F=\frac{9}{5}°C+32$

$°F=\frac{9}{5}(-273.15)+32$

$°F=-459.67°F$