JEE Main & Advanced Physics Kinetic Theory of Gases Sample Paper Topic Test - Kinetic Theory of Gases

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 \[{{O}_{2}}\] 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) \[\sqrt{3kT/M}\]

Correct Answer: B

Solution :

[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 \[{{V}_{1}}\].