Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only ${O_2},\,B$ only ${N_2}$ and $C$ a mixture of equal quantities of ${O_2}$ and ${N_2}$. If the average speed of the ${O_2}$ molecules in vessel A is ${V_1}$, that of the ${N_2}$ molecules in vessel B is ${V_2}$, the average speed of the ${O_2}$ molecules in vessel $C$ is

Q: Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only ${O_2},\,B$ only ${N_2}$ and $C$ a mixture of equal quantities of ${O_2}$ and ${N_2}$. If the average speed of the ${O_2}$ molecules in vessel A is ${V_1}$, that of the ${N_2}$ molecules in vessel B is ${V_2}$, the average speed of the ${O_2}$ molecules in vessel $C$ is

b Both $O _{2}$ and $N _{2}$ gases in vessel $C$ will behave independently since, $V _{ av }=$ $\sqrt{\frac{8 RT }{\pi M }}$ depends only on the temperature and mass of the gas molecule, there is no difference between the $V _{\text {av }}$ of $O _{2}$ in vessel $A$ and $C$ is $V _{1}$

Question

A$({V_1} + {V_2})/2$
B${V_1}$
C${({V_1}{V_2})^{1/2}}$
D$\sqrt {3kT/M} $

IIT 1992, Medium

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