How much energy is required to double the rad | vedclass

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(A) soap bubble has two surfaces (inner and outer). The work done $W$ in changing the radius from $R_1$ to $R_2$ is given by $W = 2 	imes T 	imes \D

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$24$

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(A) soap bubble has two surfaces (inner and outer). The work done $W$ in changing the radius from $R_1$ to $R_2$ is given by $W = 2 	imes T 	imes \Delta A$,where $\Delta A$ is the change in surface area.Initial surface area $A_1 = 4\pi R^2$.Final surface area $A_2 = 4\pi (2R)^2 = 16\pi R^2$.Change in area $\Delta A = A_2 - A_1 = 16\pi R^2 - 4\pi R^2 = 12\pi R^2$.Since there are two surfaces,the total change in area is $2 	imes 12\pi R^2 = 24\pi R^2$.Therefore,the work done is $W = T 	imes (24\pi R^2) = 24\pi R^2 T$.

How much energy is required to double the radius of a soap bubble of radius $R$ and surface tension $T$ (in $\pi R^2 T$)?

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