Question

Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of the soap solution is 30 dyn/cm.

Answer 1

Data : r₁ = 1 cm, r₂ = 2 cm, T = 30 dyn/cm

Initial surface area = 2 × 4πr₁²

Final surface area = 2 × 4πr₂²

∴ Increase in surface area

= 2 × 4πr₂² – 2 × 4πr₁² = 8π(r₂² – r₁²)

∴ The work done 

= surface tension × increase in surface area

= T × 8π(r₂² – r₁²)

= 30 × 8 × 3.142 × [(2)² – (1)²] 

= 2262 ergs