First slide

Surface tension

Question

Assume that liquid drop evaporates by decreasing in its surface energy so that its temperature remains unchanged. The surface tension of liquid drop is T, density of liquid is ρ and L is latent heat of vapouration of liquid. What should be the minimum radius of the drop for this to be possible

Difficult

A

T/ρL
B

3T/ρL
C

ρL/T
D

2T/ρL

Solution

Let r be the minimum radius of a drop of liquid. Therefore its surface energy, U = 4πr²T . If a thin layer of liquid of thickness t evaporates, then necessary latent heat to be supplied = ( 4πr²t).ρ.L.
Decrease in surface energy = 4πr²T - 4π(r - t)².T $\large \simeq$ 8πrt.T(r>>t)
Temperature of the drop will not change if, (8πrt)T = 4πr²t.ρ.L. ⇒ r = 2T/ρ.L

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