A student forgot to add the reaction mixture to the round bottomed flask at $27^{\circ} C$ but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was $477^{\circ} C$ . What fraction of air would have been expelled out?

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Solution

Let the volume of the round bottomed flask be V.
Then, the volume of air inside the flask at $27^{\circ} C$ is V.
Now,
$V_{1} = V$
$T_{1} = 27^{\circ} C = 300 K, V_{2} = ?$
$T_{2} = 477^{\circ} C = 750 K$
According to Charles's law,
$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$
$\Rightarrow V_{2} = \frac{V_{1} T_{2}}{T_{2}}$
$= \frac{750 V}{300}$
$= 2.5 V$
Therefore, volume of air expelled out = $2.5 V - V = 1.5 V$
Hence, fraction of air expelled out $= \frac{1.5 V}{2.5 V} = \frac{3}{5}$

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