Question

The pressure of a gas filled in the bulb of a constant volume gas thermometer at $0^o$C and ${100}^o$C are $28.6cm$ and $36.6cm$ of mercury respectively. The temperature of bulb at which pressure will be $35.0cm$ of mercury will be

• A. ${80}^o$C
• B. ${70}^o$C
• C. ${55}^o$C
• D. ${40}^o$C

Answer 1

The correct option is A ${80}^o$C

In a constant volume gas thermometer, the pressure of the gas varies in proportion to the temperature of the gas. The temperature varies linearly wrt to the pressure and vice versa.

So the formula is: $T=\frac{(P-P_0)}{(P_{100}-P_0)}\times {100}^{\circ }C$

Where $T$ is the temperature at pressure $P$.

$P_0$ is pressure at $T_0=0^{\circ }C$

and $P_{100}$ is pressure at $T_{100}=100⁰C$

$T=\frac{(35.0-28.6)}{(36.6-28.6)}\times {100}^{\circ }C$

$={80}^{\circ }C$