Question

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

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

Answer 1

Answer: (D)

From the definition of surface tension $(T)$, the surface tension of a liquid is equal to the work (W) required to increase the surface area $(A)$ of the liquid film by unity at constant temperature.
$\therefore W=T\times \Delta A$
Since, surface area of a 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
$\Rightarrow W\propto V^{2/3}$
$W=T\times 8\pi \times {\left(\frac{3V}{4\pi }\right)}^{2/3}$
$\therefore W_1\propto V_1^{2/3}$ and $W_2\propto V_2^{2/3}$
$\therefore \frac{W_2}{W_1}={\left(\frac{2V_1}{V_1}\right)}^{2/3}$
$\Rightarrow W_2=2^{2/3}{W}_1=4^{1/3}W$