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)

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} $