Question

The resistance Ro, of a substance at temperature t°c, which is measured by a mercury thermometer is
Rt=Ro/1+ alpha t^2
Where Ro is the resistance of the substance at 0°c and alpha= 5 ×10^-5.Calculate the resistance of the substance at 80°c and 100°c.If the resistance of the substance is used as a thermometer, what will the resistance thermometer read when a mercury thermometer read 80°c and 100°c

Answer 1

$$R(80)=\frac{R_0}{1+(5 \cdot10^{-5})(80)^2}=0.7576R_0$$

$$R(100)=\frac{R_0}{1+(5 \cdot10^{-5})(100)^2}=0.6667R_0$$

When a mercury thermometer reads 100°c

$$T=\frac{R(100)-R_0}{R(100)-R_0}100=100\degree C$$

When a mercury thermometer reads 80°c

$$T=\frac{R(80)-R_0}{R(100)-R_0}100=\frac{0.7576-1}{0.6667-1}100=72.7\degree C$$