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r and T are the radius and surface tension of a soap bubble respectively. The energy required to double the diameter of the soap bubble at the same temperature is

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$12 π r^{2} T$

$4 π r^{2} T$

$2 π r^{2} T$

$24 π r^{2} T$

answer is D.

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Detailed Solution

To increase the surface energy
$\begin{array}{l} 2 (4 π R^{2} T - 4 π r^{2} T) \\ = 8 π T (R^{2} - r^{2}) = 8 π T (4 r^{2} - r^{2}) \\ = 24 π r^{2} T \end{array}$

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