Question

Surface tension is numerically equal to the surface energy. 

1. Dine surface tension. 

2. Derive an expression for the rise of liquid in a capillary tube.

Answer 1

1. Liquids acquire a free surface when poured in a container. These surfaces possess some additional energy. This phenomenon is known as surface tension. 

2. When a drop is split into tiny droplets, the surface area increases. So work has to be done for splitting the drop. 

Let R be radius of the drop and r the radius of the droplets: 

R = 1 × 10^-3 m 

surface area of the drop = 4πR² 

= 4π × (1 × 10^-3)² 

= 4π × 10^-6 m²

Volume of the drop = Volume of 10⁶ droplets

∴ Surface area of million droplets =10⁶ × 4π ²

= 10⁶ × 4π(1 × 10^-5)² 

= 4π × 10^-4 m²

∴ Increase in surface area = 4π × 10^-4 – 4π × 10^-6 

= 3.96π × 10^-4 m² 

∴ Energy expended = 3.967π × 10^-4 × S 

= 3.96π × 10^-4 × 72 × 10^-3 J 

= 8.95 × 10^-5 J.