Question

A platinum resistance thermometer reads 0° when its resistance is 80 Ω and 100° when its resistance is 90 Ω.
Find the temperature at the platinum scale at which the resistance is 86 Ω.

Answer 1

Given:
Resistance at 0^oC, R₀ = 80 $\mathrm{\Omega }$
Resistance at 100^oC, R₁₀₀ = 90 $\mathrm{\Omega }$
Let t be the temperature at which the resistance (R_t) is 86 $\mathrm{\Omega }$.
$$\begin{gathered} t=\frac{R_t-R_0}{R_{100}-R_0}\times 100 \\ \Rightarrow t=\frac{86-80}{90-80}\times 100 \\ \Rightarrow t=\frac{6}{10}\times 100 \\ \Rightarrow t=60° \end{gathered}$$
Therefore, the resistance is 86 $\mathrm{\Omega }$ at 60^oC.