If W amount of work is required to form a bub | vedclass

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(D) The volume of a spherical bubble is given by $V = \frac{4}{3} \pi R^3$,which implies $R = \left( \frac{3V}{4\pi} \right)^{1/3}$.Therefore,$R^2 = \

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$\sqrt[3]{4} \, W$

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(D) The volume of a spherical bubble is given by $V = \frac{4}{3} \pi R^3$,which implies $R = \left( \frac{3V}{4\pi} ight)^{1/3}$.Therefore,$R^2 = \left( \frac{3}{4\pi} ight)^{2/3} V^{2/3}$,which means $R^2 \propto V^{2/3}$.The work done $W$ to form a soap bubble (which has two surfaces) is $W = T 	imes \Delta A = T 	imes 2(4\pi R^2) = 8\pi R^2 T$.Since $W \propto R^2$ and $R^2 \propto V^{2/3}$,we have $W \propto V^{2/3}$.Thus,$\frac{W_2}{W_1} = \left( \frac{V_2}{V_1} ight)^{2/3} = \left( \frac{2V}{V} ight)^{2/3} = 2^{2/3} = (2^2)^{1/3} = \sqrt[3]{4}$.Therefore,$W_2 = \sqrt[3]{4} \, W$.

If $W$ amount of work is required to form a bubble of volume $V$,then how much work is required to form a bubble of volume $2V$?

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