Question

Work done in making a soap bubble of volume V is W. Find the work done to make its volume into 2V.

Answer 1

As volume of bubble $v=\frac{4}{3}\pi R^3$

Then $R^2\propto v^{2/3}$

$w=8\pi R^{2}T$

$w\propto R^2\propto v^{2/3}$

$\frac{w_2}{w_1}={\left(\frac{v_2}{v_1}\right)}^{2/3}={\left(\frac{2v}{v}\right)}^{2/3}=(2{)}^{2/3}=4^{1/3}$

$\Rightarrow w_2=3\sqrt{4w}$