Two soap bubbles of radii r₁ and r₂ in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to

Step-by-step solution

In Iso-thermal process: p V= C . The pressure inside bubble is: p 1 / r and volume is: V r^3 . p V r^2 And n= p V R T , therefore number of moles of gas inside the bubble is proportional to the square of its radius n r^2 On combining bubbles, the total number of moles is conserved: Therefore, n₁+n₁=N r₁^2+r₂^2=R^2 The above result can also be obtained by total surface energy conservation: 2 (4 R^2 ) =2 (4 r₁^2 ) +2 (4 r₂^2 ) or R= r₁^2+r₂^2