Question

A Centigrade thermometer has its lower and upper fixed points marked $-{0.5}^{\circ }C$ and ${100.5}^{\circ }$. What is the true temperature when this thermometer reads ${30}^{\circ }$? The bore of the thermometer is uniform.

Answer 1

Ideally a Thermometer should be divided into 100 equal parts, the upper fixed point should be ${100}^o$, and the lower should be $0^o$

$100.5-(-0.5)=101$

This means that the given thermometer is divided into 101 equal parts.

The lower fixed point is $-{0.5}^o$. This means that the given thermometer is half step behind the ideal one.

Also note that any one step on this thermometer means $\frac{100}{101}$ step of the ideal thermometer.

Hence if it shows the reading as ${30}^o$ then it should mean $\left(\frac{30\times 100}{101}\right)+\left(\frac{0.5\times 100}{101}\right)=30.198$

Answer:- 30.198${}^o$C