First slide

Surface tension

Question

A soap bubble has radius r.The surface tension of the soap film is T. The energy needed to double the radius of the bubble without change of temperature is

Easy

A

$4 {πr}^{2} T$
B

$2 {πr}^{2} T$
C

$12 {πr}^{2} T$
D

$24 {πr}^{2} T$

Solution

Surface area of bubble of radius r
${=4πr}^{2}$
Surface area of bubble of radius 2 r
$= 4 π (2 r)^{2} = 16 {πr}^{2}$
As the bubble has two surfaces, hence the total increase in surface area
$= 2 \times [16 {πr}^{2} - 4 {πr}^{2}] = 24 {πr}^{2}$
$∴ Energy needed = work done = 24 {πr}^{2} T$

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