Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contain 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

\frac{(v_{1} + v_{2})}{2}

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(v_{1} v_{2})^{\frac{1}{2}}

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v_{2}

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\sqrt{\frac{3 k T}{M}}

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Solution

The correct option is C $v_{2}$
As we know, $V_{a v g} = \sqrt{\frac{8 R T}{Π m}}$

All the kinetic energy of gas depends upon the temp. of the vessel that is same for all vessels

$∴ V_{a v g} o f N_{2} i n v e s s e l B = V_{a v g} o f N_{2} i n v e s s e l C = V_{2}$

So, the correct option is $C$

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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)

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