The amount of work done in blowing a soap bub | vedclass

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Question

(B) soap bubble has two surfaces (inner and outer). Therefore,the total surface area of a soap bubble of radius $r$ is $A = 2 	imes (4\pi r^2) = 8\pi

Vedclass · Accepted Answer

$2\pi(D^2 - d^2)T$

Vedclass · Answer

(B) soap bubble has two surfaces (inner and outer). Therefore,the total surface area of a soap bubble of radius $r$ is $A = 2 	imes (4\pi r^2) = 8\pi r^2$.Initial radius $r_1 = d/2$,so initial area $A_1 = 8\pi(d/2)^2 = 2\pi d^2$.Final radius $r_2 = D/2$,so final area $A_2 = 8\pi(D/2)^2 = 2\pi D^2$.The change in surface area is $\Delta A = A_2 - A_1 = 2\pi(D^2 - d^2)$.The work done $W$ is given by $W = T 	imes \Delta A$.Substituting the values,$W = T 	imes 2\pi(D^2 - d^2) = 2\pi(D^2 - d^2)T$.

The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ($T=$ surface tension of solution).

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