Question

1. A student has designed his own thermometer with a temperature scale called S. Here 

he has marked the freezing point of water as 20 °S and the boiling point of water as 

150 °S. The S scale has 130 divisions.

(a) By drawing a suitable diagram, express the relation (mathematical equation) 

between 𝑇𝐶 (temperature in Celsius) and 𝑇𝑆

(temperature in S)

(b) What reading will be shown in S scale when he measures the temperature of an 

object at 60℃.

Answer 1

a) $150^\circ S - 20^\circ S = 130^\circ S = 100^\circ C$ , therefore $1^\circ C = \dfrac{130}{100}^\circ S = 1.3^\circ S.$

Let us assume $TC = \alpha TS + \beta.$

We know that $0^\circ C= \alpha\cdot 20^\circ S + \beta$ and $100^\circ C= \alpha\cdot 150^\circ S + \beta$, therefore we solve these equations simultaneously and get

$100^\circ C = \alpha \cdot (150^\circ S - 20^\circ S) \Rightarrow \alpha = \dfrac{100^\circ C}{130^\circ S} \approx 0.7692 (^\circ C/^\circ S).$

$\beta = 100^\circ C - 0.7692\cdot150^\circ S = -15.385^\circ C.$

So the dependence is

$TC = 0.7692 TS - 15.385.$

b) $60 = 0.7692 TS - 15.385 \Rightarrow TS =98^\circ S.$