Question

If the work done in blowing a soap bubble of volume $V$ is $W$ , then the work done in blowing a soap bubble of volume $2\,V$ under the same conditions will be

• A. $W$
• B. $2W$
• C. $\sqrt{2}W$
• D. $4^{1 / 3}\,W$

Answer 1

Answer: (D)

The work done will be against surface tension and we know that surface tension is related to work as $W = T \times \Delta A$
Since, the surface area of sphere is $4 \pi R^{2}$ and there are two free surfaces, we have
$W = T \times 8 \pi R ^{2} \ldots( i )$
and volume of sphere $V=\frac{4}{3} \pi R^{3}$
$\Rightarrow R =\frac{3 V }{4 \pi}^{1 / 3} \ldots \text { (ii) }$
From Eqs. (i) and (ii), we get
$W = T \times 8 \pi \times{\frac{3 V ^{2 / 3}}{4 \pi}}^{2}$
$\Rightarrow W \propto V ^{2 / 3}$
$\therefore W _{1} \propto V _{1}^{2 / 3}$
and, $W _{2} \propto V _{2}^{2 / 3}$
$\frac{ w _{2}}{ w _{1}}={\frac{2 v _{1}}{ v _{1}}}^{2 / 3}$
$\Rightarrow W _{2}=2^{2 / 3} W _{1}=4^{1 / 3} W$