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(A) soap bubble has two surfaces (inner and outer). The work done $W$ in increasing the radius of a soap bubble from $R_1$ to $R_2$ is given by the ch

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$24$

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(A) soap bubble has two surfaces (inner and outer). The work done $W$ in increasing the radius of a soap bubble from $R_1$ to $R_2$ is given by the change in surface energy.$W = T 	imes \Delta A 	imes 2$Where $T = S$ (surface tension) and $\Delta A = 4\pi R_2^2 - 4\pi R_1^2$.$W = S 	imes 2 	imes (4\pi R_2^2 - 4\pi R_1^2) = 8\pi S(R_2^2 - R_1^2)$.Given $R_1 = R$ and $R_2 = 2R$:$W = 8\pi S((2R)^2 - R^2) = 8\pi S(4R^2 - R^2) = 8\pi S(3R^2) = 24\pi R^2 S$.

The radius of a soap bubble is increased from $R$ to $2R$. The work done in this process in terms of surface tension $S$ is: (in $\pi R^2 S$)

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