(B) soap bubble has two surfaces (inner and outer), so its total surface area is $2 \times 4 \pi R^2 = 8 \pi R^2$.Initial surface energy $E_i = T \tim

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(B) soap bubble has two surfaces (inner and outer), so its total surface area is $2 \times 4 \pi R^2 = 8 \pi R^2$.Initial surface energy $E_i = T \times (8 \pi R^2) = 8 \pi R^2 T$.When the radius is doubled, the new radius becomes $R' = 2R$.The new surface area is $2 \times 4 \pi (2R)^2 = 2 \times 4 \pi (4R^2) = 32 \pi R^2$.Final surface energy $E_f = T \times (32 \pi R^2) = 32 \pi R^2 T$.Work done $W = E_f - E_i$.$W = 32 \pi R^2 T - 8 \pi R^2 T = 24 \pi R^2 T$.

Class 11 Physics Mechanical Properties of Fluids Surface Energy

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The radius $R$ of the soap bubble is doubled under isothermal conditions. If $T$ is the surface tension of the soap bubble, the work done in doing so is given by (in $\pi R^2 T$)

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A
$32$
B
$24$
C
$8$
D
$4$

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The radius $R$ of the soap bubble is doubled under isothermal conditions. If $T$ is the surface tension of the soap bubble, the work done in doing so is given by (in $\pi R^2 T$)

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