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A container filled with air under pressu...

A container filled with air under pressure `P_(0)` contains a soap bubble of radius `R` the air pressure has been reduced to half isothermally and the new radius of the bubble becomes `(5R)/(4)` if the surface tension of the soap water solution. Is S, `P_(0)` is found to be `(12nS)/(R)`. Find the value of n.

Text Solution

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`(P_(0)+(4S)/(R))((4)/(3)piR^(3))=((P_(0))/(2)+(4Sxx4)/(5R))xx(4)/(3)pi((5R)/(4))^(3)impliesP_(0)+(4S)/(R)=((P_(0))/(2)+(16S)/(5R))(125)/(64)impliesP_(0)=(96S)/(R)`
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