Work `W` is required to form a bubble of volume `V` from a given solution. What amount of work is required to be done to form a bubble of volume `2V` ?

Options

A. W
B. 2 W
C. ` 2 ^(1//3 ) barW`
D. ` 4^(1//2) bar W `

Answer

D

Explanation

` V= (4)/(3) pi R^ 3 and 2 V = (4)/(3) pi (R' ) ^ 3 rArr 2 (4)/(3) pi R ^ 3 = (4)/(3) pi ( R' ) ^ 3 rArr R' 2 ^(1//3 ) ` R
` rArr W = (2 xx 4pi [ 2 ^(1//3) R ] ^2 sigma ) = 2^(2//3) xx 2 xx 4 pi R ^ 2 sigma = 4 ^(1//3 )W `