First slide

Surface tension and surface energy

Question

A number of droplets, each of radius r, combine to form a drop of radius R. If T is the surface tension, the rise in temperature will be

Moderate

A

$\frac{2 T}{r}$
B

$\frac{3 T}{R}$
C

$2 T [\frac{1}{r} - \frac{1}{R}]$
D

$3 T [\frac{1}{r} - \frac{1}{R}]$

Solution

$\frac{4}{3} {πR}^{3} = n \times \frac{4}{3} {πr}^{3} or R^{3} = {nr}^{3}$
Energy evolved $= (n \times 4 {πr}^{2} - 4 {πR}^{2}) T$
Now, $θ = \frac{Q}{VρS} = \frac{Q}{V} = (In C.G.S. system, ρ = 1 and S = 1)$
$∴ θ = \frac{[n \times 4 {πr}^{2} - 4 {πR}^{2}] T}{\frac{4}{3} {πR}^{3}}$
$= \frac{3 T [{nr}^{2} - R^{2}]}{R^{3}} = 3 T [\frac{{nr}^{2}}{{nr}^{3}} - \frac{R^{2}}{R^{3}}] = 3 T [\frac{1}{r} - \frac{1}{R}]$

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