Question
Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, the density of liquid is ρ and L is its latent heat of vaporisation.
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ρL/T
-
-
T/ρL
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2T/ρL
Solution
D.
2T/ρL
Decrease in surface energy = Heat required in vapourisation.... (i)
Decrease in surface energy = T x ΔA
= 2T x 4πrdr [ For two surface]
heat required in vapourisation = Latent heat
= ML = V x ρL
= (4πr2dr) ρL
Now from eq (i)
2T x 4πrdr = 4πr2ρL
r = 2T/ρL
