Question

Air is filled at ${60}^{\circ }C$ in a vessel of open mouth. The vessel is heated to a temperature $T$ so that $\frac{1}{4}th$ part of air escapes. The value of $T$ is :

• A. ${80}^{o}C$
• B. ${444}^{o}C$
• C. ${333}^{o}C$
• D. ${171}^{o}C$

Answer 1

The correct option is B ${444}^{o}C$

$PV=nRT$

No. of mass$=n=\frac{m}{M}=\frac{givenmass}{molarmass}$

Air is filled at $60°C$ in a vessel of open mouth.

Open mouth means constant pressure.

Given, the volume is constant.

$PV=\frac{m}{M}RT$

$⟹T\propto \frac{1}{M}$

$T_1=607-273=333$

After heating, $\frac{1}{4^{th}}$ of air escapes.

$m_1=m;$ then $m_2=\frac{3}{4}m$

$\frac{T_1}{T_2}=\frac{m_2}{m_1}$

$\frac{333}{T_2}=\frac{m\left(\frac{3}{4}\right)}{m}{T}_2=444$

Value of $T_2$ is $444$ Kelvin or $171°C$

Therefore, the correct option is B.