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Q.

The work done in blowing a soap bubble of volume V is W. Then the work done in blowing a soap bubble of volume 2V will be $2^{\frac{2}{n}} W$ .Find n.

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answer is 3.

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Detailed Solution

$W = ΔU = T \times 4 {πr}^{2} But V = \frac{4}{3} {πr}^{3} \Rightarrow r = {(\frac{3 V}{4})}^{1 / 3} \begin{array}{l} If volume = 2 V \Rightarrow radius r^{'} = 2^{\frac{1}{3}} r \\ ∴ W = T \times 4 π {(2^{1 / 3} r)}^{2} = T 4 π 2^{2 / 3} r^{2} = 2^{2 / 3} W \end{array}$

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