A closed vessel contains a mixture of two diatomic gases `A` and `B`. Molar mass of `A` is 16 times that of `B` and mass of gas `A` contained in the vessel is 2 times that of `B`. Which of the following statements are correct ?

Options

A. Average kinetic energy per molecule of A is equal to that of B
B. Root mean square value of translational velocity of B is four times that of A
C. Pressure exerted by B is eight times that exerted by A.
D. Number of molecule of B, in the cylinder, is eight times that of A.

Answer

A, B, C, D

Explanation

Since both the gases are contained in the same vessel, temperatrue of both the gases is same. Average KE per molecule of a diatomic gas is `5//2` KT. Hence, average KE per molecule of both the gases is same. Therefore 'a' is correct
`v_(rms)=sqrt((3RT)/(M))`, Hence, `((v_(rms))_(2))/((v_(rms))_(1))=`
`sqrt((M_(1))/(M_(2)))=sqrt(16)=4`, Hence 'b' is correct.
`mu_(1)=(2m)/(16m)` and `mu_(2)=(m)/(M)`
Hence, `(mu_(1))/(mu_(2))=(1)/(8)` , Hence, 'd' is correct
Partial pressure exerted by a gas is
`P=(muRT)/(V) (because mu prop N)`
Hence, `(P_(2))/(P_(1))=(N_(2))/(N_(1))=8`
Therefore, 'c' is also correct.