If T is the surface tension of a soap solutio | vedclass

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Question

(C) soap bubble has two surfaces (inner and outer). The surface area of a spherical bubble of diameter $d$ is $A = 4\pi r^2 = 4\pi (d/2)^2 = \pi d^2$.

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) soap bubble has two surfaces (inner and outer). The surface area of a spherical bubble of diameter $d$ is $A = 4\pi r^2 = 4\pi (d/2)^2 = \pi d^2$.Since there are two surfaces, the total surface area is $A_{total} = 2 	imes \pi d^2 = 2\pi d^2$.The work done $W$ is equal to the change in surface energy: $W = T 	imes \Delta A$.Initial diameter $d_1 = D$, so initial area $A_1 = 2\pi D^2$.Final diameter $d_2 = 2D$, so final area $A_2 = 2\pi (2D)^2 = 8\pi D^2$.Change in area $\Delta A = A_2 - A_1 = 8\pi D^2 - 2\pi D^2 = 6\pi D^2$.Therefore, the work done is $W = T 	imes 6\pi D^2 = 6\pi D^2 T$.

If $T$ is the surface tension of a soap solution, the amount of work done in blowing a soap bubble from a diameter $D$ to $2D$ is (in $\pi D^2 T$)

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