Air is filled at 60^oC in a vessel with an op | vedclass

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(D) For an open-mouthed vessel,the pressure $P$ remains constant as it is equal to the atmospheric pressure.The volume $V$ of the vessel is also const

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$171$

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(D) For an open-mouthed vessel,the pressure $P$ remains constant as it is equal to the atmospheric pressure.The volume $V$ of the vessel is also constant.From the ideal gas equation $PV = \mu RT = \left( \frac{m}{M} ight) RT$,where $m$ is the mass of the gas and $M$ is the molar mass,we have $m \propto \frac{1}{T}$ at constant $P$ and $V$.Therefore,$m_1 T_1 = m_2 T_2$,which implies $\frac{T_2}{T_1} = \frac{m_1}{m_2}$.Initial temperature $T_1 = 60 + 273 = 333 \ K$.Since $1/4^{th}$ of the air escapes,the remaining mass $m_2 = m_1 - \frac{1}{4}m_1 = \frac{3}{4}m_1$.Substituting the values: $\frac{T_2}{333} = \frac{m_1}{(3/4)m_1} = \frac{4}{3}$.$T_2 = 333 	imes \frac{4}{3} = 444 \ K$.Converting to Celsius: $T = 444 - 273 = 171^oC$.

Air is filled at $60^oC$ in a vessel with an open mouth. The vessel is heated to a temperature $T$ so that $1/4^{th}$ of the air escapes. Assuming the volume of the vessel remains constant,the value of $T$ is ....... $^oC$.

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