• # question_answer Air is filled at $60{}^\circ C$ in a vessel of open mouth. The vessel is heated to a temperature T so that 1/4th 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) $171{}^\circ C$

For open mouth vessel, pressure is constant. Volume is also given constant. Hence from $pV=\mu RT$                                 $=\left( \frac{m}{M} \right)RT$ $\Rightarrow$                               $T\propto \frac{1}{m}$ $\Rightarrow$                               $\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}$ $\because$ $\frac{1}{4}th$ part escapes, so remaining mass in the  vessel ${{m}_{2}}=\frac{3}{4}{{m}_{1}}$ $\Rightarrow$               $\frac{(273+60)}{T}=\frac{3/4{{m}_{1}}}{{{m}_{1}}}$ $\Rightarrow$               $T=444K={{171}^{o}}C$