Question

The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature on a centigrade mercury scale when this thermometer reads 32°?

Answer 1

Given:
Ice point of a mercury thermometer, T₀ = 20° C
Steam point of a mercury thermometer, T₁₀₀ = 80° C
Temperature on thermometer that is to be calculated in centigrade scale, T₁ = 32° C​
Temperature on a centigrade mercury scale, T, is given as:
$$\begin{gathered} T\mathit{=}\frac{T_{\mathit{1}}\mathit{-}{T}_{\mathit{0}}}{T_{\mathit{100}}\mathit{-}{T}_{\mathit{0}}}\times 100 \\ \Rightarrow T=\frac{32-20}{80-20}\times 100 \\ \Rightarrow T=\frac{12}{60}\times 100 \\ \Rightarrow T=\frac{120}{6} \\ \Rightarrow T=20°\mathrm{C} \end{gathered}$$
Therefore, the temperature on a centigrade mercury scale will be 20^o C.