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Maxwell's Speed of Distribution Law

A closed vess...

Question

A closed vessel of volume $V_{0}$ contains oxygen at a pressure $P_{0}$ and temperature $T_{0}$ . Another closed vessel of the same volume $V_{0}$ contains helium at a pressure $P_{0}$ and temperature $\frac{T_{0}}{2}$ . Find the ratio of the masses of oxygen to the helium.

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Solution

$w = \frac{P V M}{R T}$
$\frac{w_{O_{2}}}{w_{H e}} = \frac{P_{O_{2}} V_{O_{2}} M_{O_{2}}}{R T_{O_{2}}} \times \frac{R T_{H e}}{P_{H e} V_{H e} M_{H e}}$

$\frac{w_{O_{2}}}{w_{H e}} = \frac{P_{0} V_{0} \times 32}{T_{0}} \times \frac{\frac{T_{0}}{2}}{P_{0} V_{0} \times 4} = \frac{4}{1}$

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