Question

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 (where $M$ is the mass of an oxygen molecule)

• A. $\left(V_1+V_2\right)/2$
• B. $V_1$
• C. ${\left(V_1{V}_2\right)}^{1/2}$
• D. $\sqrt{3kT/M}$

Answer 1

Answer: (B)

Average speed of gas molecule $v_{av}=\sqrt{\frac{8kT}{\pi m}}.$
It depends on temperature and molecular mass.
So the average speed of oxygen will be same in vessel $A$ and vessel $C$ and that is equal to $V_1$.