If T is the surface tension,the amount of wor | vedclass

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(B) soap bubble has two surfaces (inner and outer). The surface area of a spherical bubble of radius $r$ is $A = 4\pi r^2$.Since there are two surface

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

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(B) soap bubble has two surfaces (inner and outer). The surface area of a spherical bubble of radius $r$ is $A = 4\pi r^2$.Since there are two surfaces,the total surface area is $A_{total} = 2 	imes 4\pi r^2 = 8\pi r^2$.The work done in increasing the radius from $r_1$ to $r_2$ is given by $W = T 	imes \Delta A_{total}$.Here,the initial radius $r_1 = d/2$ and the final radius $r_2 = D/2$.Initial surface area $A_1 = 8\pi (d/2)^2 = 2\pi d^2$.Final surface area $A_2 = 8\pi (D/2)^2 = 2\pi D^2$.Work done $W = T(A_2 - A_1) = T(2\pi D^2 - 2\pi d^2) = 2\pi T(D^2 - d^2)$.

If $T$ is the surface tension,the amount of work done in blowing a soap bubble from a diameter $d$ to diameter $D$ is

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