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.

Explanation

A big drop is formed by coalescing 1000 small droplets. Let R be the radius of the big drop and r that of each droplet. Since the volume of the big drop is equal to the total volume of all the 1000 droplets
`(4)/(3) pi R ^(3) = 1000 xx (4)/(3) pi r ^(3)`
`r = (R )/(10)`
The surface energy of 1000 droplets is
`= 1000 [ T xx 4pi r ^(2)]`
`= 1000 [T xx 4pi ((R)/(10)) ^(2)]`
`= 10 (T xx 4pi R ^(2))`
The surface energy of the big drop is
`T xx 4 xx R ^(2).` Thus, surface energy will decrease.
Now.
Total surface energy
`("of 1000 droplets")/("surface energy of the big drop") = (10 (T xx 4pi R ^(2)))/( T xx 4 pi R ^(2)`
`= 10:1`