First slide

Surface tension

Question

A soap bubble of initial radius r is to be blown up. The surface tension of the soap film is T. The surface energy needed to double the diameter of the bubble without change in temperature, is

Moderate

A

$24 {πr}^{2} T$
B

$12 {πr}^{2} T$
C

$6 {πr}^{2} T$
D

$36 {πr}^{2} T$

Solution

Change in area of one surface
$ΔA = 4 π [{(2 r)}^{2} - r^{2}] = 12 {πr}^{2}$
$∴$ Total change in area = $24 {πr}^{2}$
$T = \frac{ΔU}{ΔA} \Rightarrow ΔU = TΔA = 24 {πr}^{2} T$

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