First slide

Surface tension

Question

Two spherical soap bubbles of radii r₁ and r₂ in vacuum coalesce under isotherm al conditions. The resulting bubble has a radius R such that

Easy

A

$R = (r_{1} + r_{2}) / 2$
B

$R = [r_{1} r_{2} / (r_{1} + r_{2})]$
C

$R = \sqrt{(r_{1}^{2} + r_{2}^{2})}$
D

${R=r}_{1} + r_{2}$

Solution

The bubbles coalesce in vacuum and hence there is no change in temperature, So, the surface energy does not change. This means that surface area remaining unchanged. Hence
$4 {πr}_{1}^{2} + 4 {πr}_{2}^{2} = 4 {πR}^{2} or R = {(r_{1}^{2} + r_{2}^{2})}^{1 / 2}$

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