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Mechanical Properties Of Fluids

Question
CBSEENPH11026263

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If  T  is the surface tension of soap solution, the energy spent in the blowing

  • 3 πTr2

  • 6πTr2

  • 12πTr2

  • 24 πTr2

Solution

D.

24 πTr2

Initially area of soap bubble

           A1 = 4π r2

Under isothermal condition radius becomes 2 r, Then, area

       A24π 2r2

            = 4 π. 4r2

        A2 = 16 πr2

Increase in surface area

       A = 2 A2 - A1

               = 2 16πr2 - 4πr2

         A = 24 π r2

Energy spent

         W = T × ΔA

              = T . 24π r2

         W = 24 πT r2 J