Question

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

• A. ${45}^{\circ }C$
• B. ${30}^{\circ }C$
• C. ${25}^{\circ }C$
• D. ${20}^{\circ }C$

Answer 1

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

Solution

$T_0=0^{\circ }C,T_1={100}^{\circ }C,h_0=50cm$

and $h_1=90cm$,

Rate of change in height wrt $T=\frac{h_1-h_0}{T_1-T_0}$

$\frac{\Delta h}{\Delta t}=\frac{40}{100}$

for height (h)= 60 cm, let the

corresponding temperature be T. Then

$\frac{h-h_0}{T-T_0}=\frac{\Delta h}{\Delta t}=\frac{40}{100}$

$\Rightarrow \frac{60-50}{T-0^{\circ }C}=\frac{4}{10}$

$\Rightarrow \frac{10\times 10}{4}=T\Rightarrow T={25}^{\circ }C$

Option - C is correct.