A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

Let n droplets each of radius r coalesce to form a big drop of radius R.∴ Volume of  n droplets =   Volume of big dropn×43πr3=43πR3n=R3r3          . . . . (i) Volume of big drop, V=43πR3      . . . . (ii) Initial surface area of n droplets, Ai=n×4πr2=R3r3×4πr2(Using . . . (i)) =4πR3r=43πR33r=3Vr  (Using . . . . . (ii))Final surface area of big dropAf=4πR2=43πR33R=3VR  (Using . . . . (iii))Decrease in surface area ΔA=Ai−Af=3Vr−3VR=3V1r−1R∴  Energy released = Surface tension × Decrease in surface area =T×ΔA=3VT1r−1R