Calculate at the temperature `t = 16 ^@C` :
(a) the root mean square velocity and the mean kinetic energy of an oxygen molecule in the process of translational motion ,
(b) the root mean square velocity of the molecules `eta = 1.50` times ?

Explanation

(a) From the equipartition theorem
`overline epsilon = (3)/(2) k T = 6 xx 10^-21 J` , and `v_(rms) = sqrt((3 k T)/(m)) = sqrt((3 RT)/(M)) = 0.47 km//s`
(b) In equilibrium the mean kinetic energy of the droplet will be equal to that of a molecule.
`(1)/(2) (pi)/(6) d^3 rho v_(rms)^2 = (3)/(2) kT` or `v_(rms) = 3 sqrt((2 kT)/(pi d^3 rho)) = 0.15 m//s`.