The work done in blowing a soap bubble of vol | vedclass

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Question

(A) The volume of a soap bubble is given by $V = \frac{4}{3} \pi r^3$,which implies $r = (\frac{3V}{4\pi})^{1/3}$.The work done $W$ in blowing a soap

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$2^{2/3} W$

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(A) The volume of a soap bubble is given by $V = \frac{4}{3} \pi r^3$,which implies $r = (\frac{3V}{4\pi})^{1/3}$.The work done $W$ in blowing a soap bubble of radius $r$ is equal to the surface tension $T$ multiplied by the change in surface area. Since a soap bubble has two surfaces (inner and outer),the total surface area is $2 	imes (4 \pi r^2) = 8 \pi r^2$.Thus,$W = 8 \pi r^2 T$.Substituting the expression for $r$,we get $W = 8 \pi (\frac{3V}{4\pi})^{2/3} T$.This shows that $W \propto V^{2/3}$.For a bubble of volume $2V$,the new work $W'$ is given by $\frac{W'}{W} = (\frac{2V}{V})^{2/3} = 2^{2/3}$.Therefore,$W' = 2^{2/3} W$.

The work done in blowing a soap bubble of volume $V$ is $W$. The work required to blow a soap bubble of volume $2V$ is [where $T$ is the surface tension of the soap solution].

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