The work done in blowing a soap bubble of volume `V` is `W`. The work done in blowing a soap bubble of volume `2V` is

Options

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

Answer

D

Explanation

We know that surface tension is related to work as
`W = S xx Delta A`
Since, surface area of a sphere is `4pi R^(2)` and the there are two free surfaces, we have
`W = S xx 8pi R^(2)` …(i)
i.e., `V = (4)/(3)pi R^(3) rArr R = ((3V)/(4pi))^(1//3)` ...(ii)
From Eqs. (i) and (ii), we get
`W = S xx 8pi xx ((3V)/(4pi))^(2//3) rArr W prop V^(2//3)`
So, `(W_(2))/(W_(1)) = ((2V_(1))/(V_(1)))^(2//3) rArr W_(2) = 2^(2//3) W_(1) = 4^(1//3) W`