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 $2V$ 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
$W=T\times 8\pi R^2$ ... $(i)$
and volume of sphere $=\frac{4}{3}\pi R^3$
i.e. $V=\frac{4}{3}\pi R^3$
$\Rightarrow R={\left(\frac{3V}{4\pi }\right)}^{1/3}$ ... $(ii)$
From Eqs. $(i)$ and $(ii)$ , we get
$W=T\times 8\pi \times {\left(\frac{3V}{4\pi }\right)}^{2/3}$
$\Rightarrow W\propto V^{2/3}$
$\therefore W_1\propto V_1^{2/3}$
and, $W_2\propto V_2^{2/3}$
$\frac{W_2}{W_1}={\left(\frac{2V_1}{V_1}\right)}^{2/3}$
$\Rightarrow W_2=2^{2/3}{W}_1=4^{1/3}W$