Let n number of little droplets of water of surface tension S (dyne/cm), all of the same radius r cm combine to from a single drop of radius R heat, while using cgs system of units answer the following questions.
The energy released is

Options

A. `Sxx4 pi nr^(2)`
B. `Sxx4 pi R^(2)`
C. `S 4 pi R^(2)[n^(1//3) - 1]`
D. `S 4 pi R^(2) [n^(2//3) - 1]`

Answer

C

Explanation

As, volume of n small drop = volume of big drop
S0, `nxx(4)/(3)pi r^(3) =(4)/(3)pi R^(3)`
or `nr^(3) = R^(3)` or `r=R//n^(1//3`
The energy released = Surface tension x decrease in surface area
`=Sxx[nxx4pi r^(2) - 4pi R^(2)]`
`=Sxx4pi[nr^(2) - R^(2)]=Sxx4pi[(nR^(2))/(n^(2//3)) - R^(2)]`
`=Sxx4pi R^(2)[n^(1//3)-1]`