The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of the soap bubble, the work done in doing so is given by

Step-by-step solution

The surface energy of a bubble E = Tension × surface area E = T × A For soap bubble E = 2 T × A E = 2 T × 4 π R 2 Here, R = radius of the bubble If the radius is doubled then we have E ′ = 2 T × 4 π R 2 E ′ = 2 T × 4 π 2 R 2 E ′ = 32 π R 2 T Work done = E ' - E ⇒   32 π R 2 T - 8 π R 2 T = 24 π R 2 T