1. Tardigrade
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  4. A cubical box with porous walls containing an equal number of O2 and H2 molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature T. The ratio of root mean square speed of O2 molecules to that of the H2 molecules is

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Q. A cubical box with porous walls containing an equal number of $O_{2}$ and $H_{2}$ molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature $T.$ The ratio of root mean square speed of $O_{2}$ molecules to that of the $H_{2}$ molecules is

NTA AbhyasNTA Abhyas 2020

Solution:

$\because $ $V_{r m s}=\sqrt{\frac{\gamma R T}{M}}$
$\Rightarrow \frac{\left(V_{r m s}\right) O_{2}}{\left(V_{r m s}\right) H_{2}}=\sqrt{\frac{\left(M_{0}\right) H_{2}}{\left(M_{0}\right) O_{2}}}$
$=\sqrt{\frac{2}{32}}=\frac{1}{4}$