Question

A big drop is formed by coalescing 1000 small droplets of water. What will be the change in surface energy What will be the ratio between the total surface energy of the droplets and the surface energy of the big drop?

Answer 1

The correct answer is : $\frac{10}{1}$
By conservation of volume $\frac{4}{3}\pi R^3=1000\times\frac{4}{3}\pi r^3\implies r=\frac{R}{10}$
Surface energy of 1000 droplets = $1000\times T\times 4\pi[\frac{R}{10}]^2$
$=10(T\times4\pi R^2)$
Surface energy will decrease in the process of formation of bigger drop, hence energy is released and temperature increases
$\therefore\frac{\text{total surface energy of 1000 droplets}}{\text{surface enrgy of big drop}}$
$=\frac{10(T\times4\pi R^2)}{T\times4\pi R^2}=\frac{10}{1}$