Question

The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50 and 6.50 $\Omega$ respectively. Find the boiling point (${}^{o}C$) of sulphur on the platinum scale. The ice point and the steam point measure $0^{\circ }C$ and ${100}^{\circ }C$ respectively.

Answer 1

Given : $R_T=6.50\Omega$ $R_{{100}^{o}C}=3.50\Omega$ $R_{0^{o}C}=2.50\Omega$
Resistance of platinum resistance thermometer $R^{\prime }=R[1+\alpha \Delta T]$

Boiling point : $R_T=R_{0^{o}C}[1+\alpha (T-0\left)\right]$

$\therefore$ $6.5=2.5[1+\alpha T]$ $⟹\alpha T=1.6$ ........(1)

Steam point : $R_{{100}^{o}C}=R_{0^{o}C}[1+\alpha (100-0\left)\right]$

$\therefore$ $3.5=2.5[1+\alpha (100\left)\right]$ $⟹\alpha \left(100\right)=0.4$ ........(2)

Dividing (1) and (2) we get $\frac{T}{100}=\frac{1.6}{0.4}$

$⟹$ $T={400}^{o}C$