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)

$4^{1/3}{W}_1$

Here, volume of bubble,

$V=\frac{4}{3}\pi R^3$ or $R={\left(\frac{3V}{4\pi }\right)}^{1/3}$

Work done, $W=Surfaceenergy=S\times 8\pi R^2=S\times 8\pi {\left(\frac{3V}{4\pi }\right)}^{2/3}$

or $W\propto V^{2/3}$

$\therefore \frac{W_2}{W_1}={\left(\frac{V_2}{V_1}\right)}^{2/3}={\left(\frac{2V}{V}\right)}^{2/3}=2^{2/3}$

$\therefore W_2=4^{1/3}{W}_1$