Question

If $W_{1}$ be the work to be done to form a bubble of volume $V$ from a given solution. The work required to be done to form a bubble of volume $2 V$ is

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

Answer 1

Answer: (B)

$4^{1/3} \, W_{1}$

Answer 2

Here, volume of bubble, $V=\frac{4}{3}\pi R^{3}$ or $R=\left(\frac{3V}{4\pi}\right)^{1 /3}$ Work done, $W=S\times8\pi R^{2}=S\times8\pi\left(\frac{3V}{4\pi}\right)^{2 /3}$ or $W \propto V^{2/ 3}$ $\therefore \frac{W_{2}}{W_{1}}=\left(\frac{V_{2}}{V_{1}}\right)^{2/ 3}$ $=\left(\frac{2V}{V}\right)^{2 /3}=2^{2/ 3}$ $\therefore W_{2}=4^{1 /3} W_{1}$