Three closed vessels A, B and C are at the same temperature T and contain gasses which obey the Maxwellian distribution of velocities. Vessel A contain only `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 us `v_2,` the average speed of the `O_2` molecules in vessel C is

Options

A. `((v_1+v_2))/(2)`
B. `v_1`
C. `(v_1v_2)^(1//2)`
D. `sqrt(3kT//M)`

Answer

B

Explanation

The average speed of molecules of an ideal gas is given by
`lt v gt =sqrt((8RT)/(piM))`
i.e., `lt v gt prop sqrt(T)` for same gas.
Since temperature of `A` and `C` are same, average speed of `O_(2)` molecules will be equal in `A` and `C` , i.e., `v_(1)`