Question

A constant volume gas thermometer shows pressure readings at $50cm$ and $90cm$ of mercury at $0^{\circ }C$ and ${100}^{\circ }C$ respectively. What is the temperature on gas scale when pressure reading is $60cm$ of mercury?

• A. ${20}^{\circ }C$
• B. ${30}^{\circ }C$
• C. ${25}^{\circ }C$
• D. ${40}^{\circ }C$

Answer 1

The correct option is C ${25}^{\circ }C$

We know, when V is constant, P is proportional to T.

$P=AT+B$

When $T=0,P=50cm$ of mercury

$50=0+B$

$B=50$

When$T=100,P=90cm$ of mercury

$90=100A+50$

$A=0.4$

Now, when $P=60cm$ of mercury

$P=AT+B$

$60=\left(0.4\right)\left(T\right)+50$

$T=\frac{10}{0.4}={25}^{\circ }C$