Radius of a soap bubble is 'r', surface tension of soap solution is T. Then without increasing the temperature, how much energy will be needed to double its radius

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Radius of a soap bubble is 'r', surface tension of soap solution is T. Then without increasing the temperature, how much energy will be needed to double its radius

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$4 {πr}^{2} T$

$12 {πr}^{2} T$

$24 {πr}^{2} T$

$2 {πr}^{2} T$

answer is D.

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Detailed Solution

$W = 8 πT (R_{2}^{2} - R_{1}^{2}) = 8 πT [{(2 r)}^{2} - {(r)}^{2}] = 24 {πr}^{2} T$

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