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. `4^(2//3) W_(1)`
B. `4^(1//3) W_(1)`
C. `2^(1//2) W_(1)`
D. `2^(3//2) W_(1)`

Answer

B

Explanation

Here, volume of bubble,
`V=(4)/(3)piR^(3)` or `R=((3V)/(4pi))^(1//3)`
Work done, `W=S xx 8piR^(2)=Sxx 8pi((3V)/(4pi))^(2//3)`
or `W prop V^(2//3)`
`therefore (W_(2))/(W_(1))=((V_(2))/(V_(1)))^(2//3)=((2V)/(V))^(2//3)=2^(2//3)`
`therefore W_(2)=4^(1//3)W_(1)`