Question

Derive a relation between the Celsius and Fahrenheit Scales of temperature using the fixed points in the two different scales.

Answer 1

1. We know that the freezing point of water on the Celsius scale is $0°c$ and on the Fahrenheit scale it is $32°F$.
2. Also, the boiling point of water is $100°C$on the celsius scale and $212°F$ on the Fahrenheit scale.
3. Thus for any fixed value of temperature, the factor

$$\begin{gathered} \frac{(scalereading-freezingpoint)}{boilingpoint-freezingpoint}=cons\tan t \\ \therefore \frac{C-0}{100-0}=\frac{F-32}{212-32} \end{gathered}$$

4. On simplifying we get,

$\frac{C}{100}=\frac{F-32}{180}$

$$\begin{gathered} \Rightarrow \frac{C}{5}=\frac{F-32}{9} \\ \Rightarrow \frac{9}{5}C=F-32 \\ \Rightarrow \frac{9}{5}C+32=F \end{gathered}$$

The above relation is the required relation.