Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is T , the density of the liquid is ρ and L is its latent heat of vaporisation.)

Step-by-step solution

Let the radius of the drop at time t = t be r and at an instant t = t + d t be r - d r As surface area is given by, A = 4 π r 2 , ∴ decrease in surface area is, d A = 4 π 2 r d r ∴ Decrease in surface energy during time d t is, d U = T d A = T · 8 π r d r           . . . 1 Decrease in volume during time d t is, d V = 4 π r 2 d r ∴ Decrease in mass during time d t is, d m = ρ d V = 4 π ρ r 2 d r ∴ Heat required in vaporisation i