Question

Air is filled at $60^{\circ} C$ in a vessel of open mouth. The vessel is heated to a temperature $T$ so that $1/4^\text{th}$ part of air escapes. Assuming the volume of the vessel remaining constant, the value of $T$ is

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

Answer 1

Answer: (D)

For open mouth vessel, pressure is constant. Volume is also given constant.
Hence from $p V=\mu R T=\left(\frac{m}{M}\right) R T$
$\Rightarrow T \propto \frac{1}{m} $
$\Rightarrow \frac{T_{1}}{T_{2}}=\frac{m_{2}}{m_{1}}$
$\because \frac{1}{4} t h$ part escapes,
so remaining mass in the vessel
$m_{2}=\frac{3}{4} m_{1} $
$\Rightarrow \frac{(273+60)}{T}=\frac{3 / 4 m_{1}}{m_{1}}$
$\Rightarrow T=444 K=171^{\circ} C$