Three closed vessels A, B, and C are at the same temperature T and contain gases which obey the Maxwell distribution of speed. 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 $O_{2}$ molecules in vessel A is $V_{1}$ , that of the $N_{2}$ molecules in vessel is $V_{2}$ then the average speed of the $O_{2}$ molecules in vessel C will be

(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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\frac{V_{1}}{2}

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Solution

The correct option is B $V_{1}$
According to Maxwell distribution the average speed of the molecule of a gas is $V = \sqrt{\frac{8 K T}{π M}}$
Thus the average speed depends on temperature and the mass of a molecule.
Therefore the average speed of the $O_{2}$ molecule in the mixture will remain $V_{1}$ , as the temperature is unchanged.
Hence, the answer is $V_{1} .$

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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 contain gases which obey Maxwell distribution law of velocities. Vessel A contains $O_{2}$ , B only $N_{2}$ and C mixture of equal quantities of $O_{2}$ and $N_{2}$ . If the average speed of $O_{2}$ molecules in vessel A is $V_{1}$ and that of $N_{1}$ molecules in vessel B is $V_{2}$ , then 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)