Two bulbs `A` and `B` of equal capacity are filled with `He` and `SO_(2)`, respectively, at the same temperature.
(a) If the pressures in the two bulbs are same, what will be the ratio of the velocities of the molecules of the two gases?
(b)At what temperature will the velocity of `SO_(2)` molecules become half of the velocity of `He` molecules at `27^(@)C`?
(c) How will the velocities be affected if the volume of `B` becomes four times that of `A`?
(d) How will the velocities be affected if half of the molecules of `SO_(2)` are removed from `B`?

Explanation

Let the velocities of `He` and `SO_(2)` be `u_(1)` and `u_(2)`.
(`a`) `u_(1)=sqrt((3RT)/(M_(He))), u_(2)=sqrt((3RT)/(M_(SO_(2))))`
`(u_(1))/(u_(2))=sqrt(M_(SO_(2))/(M_(He)))=sqrt((64)/(4))=4`
(`b`) Let the velocity of `He` be `u_(1)`
Velcotiy of `SO_(2)=(u_(1))/(2)`
`u_(1)=sqrt((3RT_(1))/(M_(He))), (u_(1))/(2)=sqrt((3RT_(2))/(M_(SO_(2)))`
`sqrt((3RT_(1))/(M_(He)))=2xxsqrt((3RT_(2))/(M_(SO_(2)))`
`sqrt((T_(1))/M_(He))=2xxsqrt((T_(2))/(M_(SO_(2))))`
`(T_(1))/M_(He)=4xxs(T_(2))/(M_(SO_(2)))`
`T_(2)=(300xx64)/(4xx4)=1200 K`
Temperature `=1200-273=927^(@)C`
(`c`) Velocity given by the realtion `u=sqrt((3PV)/(M))`. When volume increases by four times, pressure becomes `1//4` and `PV` remains constant. So there will be no change in the velocities.
(`d`) Since volume do not depend on the number of molecules, there will be no change in velocities.