Find the work required to be done to increase the volume of a bubble of soap solution having a radius 1mm to 8 times . (surface tension of soap solution is 30 dyne `cm^(-1))`

Explanation

Initial volume `V_(1)` and radius `R_(1)`
New volume will be `V_(2)`
`R_(1)=1cm,T=30" dyne"//cm`
`V_(2)=8V_(1)W=?`
Now `V_(2)=8V_(1)`
`therefore(4)/(3)piR_(2)^(3)=8((4)/(3)piR_(1)^(3))`
`thereforeR_(2)^(3)=(2R_(1))^(3)`
`thereforeR_(2)=2R_(1)`
Now `W=DeltaA*T=8piT[R_(2)^(2)-R_(1)^(2)]`
`=8piT[4R_(1)^(2)-R_(1)^(2)]=24piTR_(1)^(2)`
`=24xx3.14xx30xx1`
`thereforeW=2261erg`