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## Homework Statement

(1)The gas inside a spherical bubble expands slowly so that its radius is increases from R to 2R. Atmospheric pressure is ##P_0## and surface tension is S. The work done by the gas is ___________

## Homework Equations

work done against surface tension ##W_t = S.\Delta A## where A is the surface area and S is the surface tension.

## The Attempt at a Solution

initial area =##(4\pi R^2)##

final area = ## (4\pi(4R^2-R^2))##

so W against S is ##S.8\pi R^2##

but the answer given is ##\frac{25\pi P_0R^3}{3} + 24\pi S R^2##

where did the first term containing ##P_0## come from and why is the second term ##24\pi SR^2##