202010220700 Problem 1, Chapter 1.1

The Fahrenheit temperature scale is defined so that ice melts at $32^\circ \textrm{F}$ and water boils at $212^\circ \textrm{F}$ .

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

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

Solution.

Given that the melting point is $32^\circ\textrm{F}$ and the boiling point $212^\circ \textrm{F}$ .

Therefore $1\,\textrm{C}^\circ =\displaystyle{\frac{212-32}{100}}\textrm{F}^\circ = 1.8\,\textrm{F}^\circ$ .

Then $F=32+1.8C$ and $C=\displaystyle{\frac{F-32}{1.8}}$ .

Absolute zero on Fahrenheit scale is $F=32+1.8(-273)=-459.4^\circ\textrm{F}$ .