Question

The change is energy when a big drop is split in small $n$ droplets is.

• A. $4R^2(n^{2/3}-1)T$
• B. $4\pi R^2(n^{1/3}-1)T$
• C. $4\pi R^2(n^{-1/3}-1)T$
• D. $4\pi R^2[n^{-2/3}-1]T$

Answer 1

The correct option is B $4\pi R^2(n^{1/3}-1)T$

When a drop of radius R split into $n$ smaller drops (each of radius $r$), then surface area of liquid increases. Hence, the work is to be done against surface tension. Since, the volume of liquid remains constant.
$\therefore \frac{4}{3}\pi R^3=n\frac{4}{3}\pi r^3$
$\therefore R^3=n{r}^3$
Work done $=T\times \Delta A$
$=T[n4\pi r^2-4\pi R^2]$
$=4\pi R^{2}T(n^{1/3}-1)$