A soap bubble has surface tension 'T' and its radius 'p'. The mean square velocity of air molecules inside`v_1` and outside `v_2`. Given that `v_1 - v_2 = ((a T)/(r rho))`, where `'rho'` and 'a' is a constant, then the value of ’a’= ____

Answer

A, B

Explanation

For soap bubble the excess pressure inside is, `DeltaP = (4T)/r`
From kinetic theory of gases,
`P = 1/3 rho c^2`
`therefore (c^2)_("in") = - (c^2)_("out") = 3/rho (P_("in") - P_("owt"))`
`= 3/(rho) DeltaP`
` = 3/(rho) ((4T)/(r))`
`therefore ((a T)/(r rho)) - (12 T)/(r p)`
`therefore a = 12`