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)

$(V_{1} + V_{2}) / 2$

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$V_{1}$

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$(V_{1} V_{2})^{1 / 2}$

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$\sqrt{\frac{k T}{M}}$

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Solution

The correct option is B
$V_{1}$

Average speed of gas molecules, $v_{a v} = \sqrt{\frac{8 k T}{π m}}$ . 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 $V_{1}$

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Similar questions

Q. Three closed vessels, A, B and C 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

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)