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°?.Comment on answer

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

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

When a mercury thermometer reads 80°c

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

The readings of two types of thermometer are the same for 100°c because 100°c is upper fixed point of the Celsius scale. All thermometers agreed at the fixed points.

The reading of the resistance thermometer, 72.7°C, differs from that of the mercury thermometer, 80°C, because the resistance of the substance and the expansion of mercury do not vary linearly or in the same manner with increasee in temperature.