Question

W is the work done, when a bubble of volume V is formed from a solution. How much work is required to be done to form a bubble of volume 2V?

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

Answer 1

The correct option is D $2^{2/3}W$

Let the radius of the bubble with volume $V$ be $r$.

Then the radius of the bubble with volume $2V$ is $2^{1/3}r$.

Work is only because of change in surface energy.

Ratio of work done = Ratio of surface energy =Rratio of surface area

$\frac{W_1}{W}=\frac{4\pi (2^{1/3}r{)}^2}{4\pi r^2}⟹W_1=2^{2/3}W$