Question

If three gas molecules have velocity 0.5, 1 and `2 km//s` respectively, find the ratio of their root mean square speed and average speed.

Answer 1

Here, `C_(1) = 0.5 km//s, C_(2) = 1 km//s`
`C_(3) = 2 km//s`
rms speed, `C= sqrt((C_(1)^(2)+C_(2)^(2)+C_(3)^(2))/(2))`
`=sqrt(((0.5)^(2) + 1^(2)+2^(2))/(3)) = sqrt(1.75) = 1.323 km//s`
`C_(av) = (C_(1)+C_(2)+C_(3))/(3) = (0.5 +1 +2)/(3) = 1.167 km//s`
`(C)/(C_(av)) = (1.323)/(1.167) = 1.13`.