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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

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$24 {πr}^{2} T$

$12 {πr}^{2} T$

$6 {πr}^{2} T$

$36 {πr}^{2} T$

answer is A.

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Detailed 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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