The Fahrenheit temperature scale is defined so that ice melts at 32°F and water boils at 212°F.

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

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

Problem 1P

Solution 1P

Step 1 :

In this question, we need to derive formulas to convert from Fahrenheit to Celsius and back

In the second part, we need to find absolute zero on Fahrenheit scale

Step 2 :

It is given

Melting point in Fahrenheit scale is

Melting point Celsius scale is

Boiling point in Fahrenheit scale is

Boiling point in Celsius scale is

Considering both Fahrenheit and Celsius scale, we have linear relation as

Case 1 :

For melting point, we have

Substituting values we get

Thus we have

Case 2 :

For boiling point, we have

Substituting values we get

Thus we have