Question

Let W be the work done when a bubble of volume V is formed from a given solution. Work is required to form a bubble of volume 2V is:

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

Answer 1

The correct option is D $4^{1/3}W$

$WorkdoneW=8\pi R^{2}T$
Let r be radius of bubble of volume V
$\Rightarrow \frac{4}{3}\pi r^3=V$
$\frac{4}{3}\pi (r^{{}^{\prime }}{)}^3=2V$
$\Rightarrow =r^{{}^{\prime }}=2^{1/3}r$
$\therefore workdone{W}^{{}^{\prime }}=8\pi 2^{2/3}{r}^{2}T$
$=2^{2/3}W$
$=4^{1/3}W$