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 : \(\frac{10}{1}\)
Based on the principle of volume conservation, we have \(\frac{4}{3}\pi R^3=1000\times\frac{4}{3}\pi r^3\implies r=\frac{R}{10}\)
The surface energy of 1000 droplets is calculated as \(1000\times T\times 4\pi[\frac{R}{10}]^2\)
\(=10(T\times4\pi R^2)\)
During the formation of a larger drop, the surface energy diminishes, leading to energy release and a subsequent temperature increase.
\(\therefore\frac{\text{total surface energy of 1000 droplets}}{\text{surface energy of big drop}}\)
\(=\frac{10(T\times4\pi R^2)}{T\times4\pi R^2}=\frac{10}{1}\)