In increasing the area of a film of soap solution from 50 cm 2 to 100 cm 2 , 3 . 0 × 10 - 4 J of work is done. Calculate the value of surface tension of the soap solution.

Given: Initial area = 50 cm 2 Final area = 100 cm 2 Work done = 3 . 0 × 10 - 4 J Find: Surface Tension of the soap solution Solution: Change in area △ A = Final area - Initial area △ A = 100 cm 2 - 50 cm 2 = 50 cm 2 △ A = 50 × 10 - 4 m 2 We know, w = T 2 △ A T = w 2 △ A T = 3 · 0 × 10 - 4 2 × 50 × 10 - 4 J / m 2 T = 3 × 10 - 2 J / m 2 OR T = 3 × 10 - 2 N / m → Relation between work, surface tension and change in area.

The surface area of a soap-bubble is 2 . 0 × 10 - 3 m 2 . How much work will be done in blowing the bubble to twice its surface area ?

Surface area of soap-bubble = 2 × 10 - 3 m Find: Work will be done in blowing (change) the bubble to twice its surface area. Solution: Initial surface area = 2 . 0 × 10 - 3 m 2 Initial surface area = 2 × 2 . 0 × 10 - 3 m 2 Change in surface area ( △ A ) = 2 × 2 . 0 × 10 - 3 - 2 . 0 × 10 - 3 = 2 . 0 × 10 - 3 m 2 We know that w = T × 2 △ A T = Surface tension of soap solution = 310 × 10 - 2 N / m ] W = 3 . 0 × 10 - 2 × 2 × 2 . 0 × 10 - 3 J w = 12 × 10 - 5 J or 1 . 2 × 10 - 4 J w = 1 . 2 × 10 - 4 J .