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 `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 (where `M` is the mass of an oxygen molecules)

Options

A. `sqrt(v_(1)v_(2))`
B. `sqrt((3KT)/M)`
C. `1/2(v_(1)+v_(2))`
D. `v_(1)`

Answer

D

Explanation

For a given mass (M) of a gas `vpropsqrtT`. All the three vessels are at the same temperature. The average speed of `O_(2)` molecules in `A=v_(1)`.
`therefore` The average speed of `O_(2)` molecules in `C=v_(1)`
Similarly the average speeds of `N_(2)` molecules is B and C are equal i.e. `v_(2)`.