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 the `O_(2)` molecules in vessel (A) is `v_(1)` that of `N_(2)` molecules in vessel (B) is `v_(2)`. then 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)`