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)

$171^{\circ} C$

Answer 2

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 $m_{2}=\frac{3}{4} m_{1}$ $\Rightarrow \frac{(273+60)}{T}=\frac{3 / 4 m_{1}}{m_{1}}$ $\Rightarrow T=444 K=171^{\circ} C$