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) W`
D. `4^(1//3) W`

Answer

D

Explanation

Let R and R' be the raius of bubble of volume V and 2V respectively. Then
`(4)/(3)pi R^(3)=V` and `(4)/(3)pi R'^(3) =2V`
So, `(R'^(3))/(R^(3))=2` or `R'=(2)^(1//3)R`
As, `W=Sxx(4 pi R^(2))2`
and `W'=Sxx(4pi R^(2))xx2`
`:. (W')/(W)=(R'^(2))/(R^(2))=(2)^(2//3) =(4)^(1//3)`
or `W'=(4)^(1//3) W`