First slide

Temperature and heat-thermal properties of matter

Question

Air is filled at $60^{0} C$ in a vessel of open mouth. The vessel is heated to a temperature ‘T’ so that $1 / 4^{t h}$ mass of air escapes from the vessel. Assuming the volume of vessel remaining constant, the value of ‘T’ is

Moderate

A

$80^{0} C$
B

$444^{0} C$
C

$333^{0} C$
D

$171^{0} C$

Solution

$\begin{array}{l} PV = \frac{m}{M} RT \\ ⟹ T \propto \frac{1}{M} \\ T_{1} = 607 - 273 = 333 K \\ \begin{array}{l} \frac{T_{1}}{T_{2}} = \frac{m_{2}}{m_{1}} \\ \frac{333}{T_{2}} = \frac{m (\frac{3}{4})}{m} \\ T_{2} = 444 K \\ Value of T_{2} is 444 Kelvin or 171^{\circ} C \end{array} \end{array}$

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