Question

Three closed vessels A, B and C are at the same temperature $T$ and contains 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 $V_2$, then the average speed of the $O_2$ molecules in vessel C is (where $M$ is the mass of an oxygen molecule)

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

Answer 1

The correct option is B

$V_1$

Average speed of gas molecules, $v_{av}=\sqrt{\frac{8kT}{\pi m}}$. 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 $V_1$