Question

work done to blow a bubble of volume V is W the work done in blowing a bubble of volume 2V is

( 4^1/3 ) W

Answer 1

workdone to blow a bubble of radius r is given by, $W=4\pi r^2\sigma$.....(1)

where $\sigma$ is surface tension.

we know, volume of bubble = volume of sphere, V = 4/3 πr³

or, r³ = 3V/4π

or, r = (3V/4π)⅓ .......(2)

from equation (1) and (2),

$W=4\pi\left[\sqrt[3]{\frac{3V}{4\pi}}\right]^2\sigma$

here it is clear that $W\propto V^{2/3}$

so, $\frac{W_1}{W_2}=\frac{V_1^{2/3}}{V_2^{2/3}}$

$W_1=W,V_1=V,V_2=2V$

so, $\frac{W}{W_2}=\frac{V^{2/3}}{(2V)^{2/3}}=\frac{1}{4^{1/3}}$

or, $W_2=4^{1/3}W$

hence, workdone to blow a bubble of volume 2V is 4⅓W.