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A vessel filled with air under pressue `p_(0)` contains a soap bubble of diameter `d`. The air presuue have been reduced `n`-fold, and the bubbled diameter increased `r`-fold is othermally. Find the surface tension of the soap water solution.

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For the air enclosed in the bubble we have
`pV=nRT`
`implies(p_(0)(8T)/d)pi/6d^(3)=(p_(0)/n+(8T)/(rd))pi/6r^(3)d^(3)`
`impliesp_(0)+(8T)/d=(p_(0)r^(3))/n+(8Tr^(2))/d`
`impliesp_(0()1-r3/n)=(8T)/d(r^(3)-1)impliesT=1/8p_(0)d xx(1-(r^(3))/n)/(r^(2)-1)`
`impliesp_(0)(1-(r^(3))/n)=(8T)/d(r^(2)-1)impliesT=1/8p_(0)d xx(1-(r^(3))/n)/(r^(2)-1)`

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