Question:

A spherical liquid drop of radius $R$ is divided into eight equal droplets. If surface tension is $T$, then work done in the process will be

Updated On: Jun 23, 2023
  • $2\pi R^2T$
  • $3\pi R^2T$
  • $4\pi R^2T$
  • $2\pi RT^2$
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The Correct Option is C

Solution and Explanation

Let r be radius of each small droplets. Since the volume remains the same $\therefore \frac{4}{3}\pi\,R^{3}=8 \times \left(\frac{4}{3}\pi r^{3}\right)$ $r=\frac{1}{2}R$ Surface area of big droplet $=4\pi R^{2}$ Surface area of 8 small droplets $=8 \times 4 \pi r^{2}$ Increase in surface area $=8\times 4\pi r^{2}-4 \pi R^{2}$ $=4\pi (8r^{2}-R^{2})$ $=4\pi\left[8\left(\frac{1}{2}R\right)^{2}-R^{2}\right]=4\pi\left[R^{2}\right]$ $=4\pi R^{2}$ Work done = Surface tension x increase in surface area $=T \times (4\pi R^{2})$ $=4 \pi R^{2}T$
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Notes on Surface Tension

Concepts Used:

Surface Tension

The amount of energy required to increase the liquid's surface area by one unit area is known as surface tension. In other words, it is a property of the liquid surface to resist force.

Surface tension is defined as,

The ratio of the surface force F to the length L along which the force acts.

Mathematically, the surface tension formula can be expressed as follows:

T=F/L

Where,

  • F is the force per unit length
  • L is the length in which force act
  • T is the surface tension of the liquid

Read More: Detergents and Surface Tension

Factors affecting surface tension:

  • Impurities: The surface tension decreases with the addition of impurities.
  • Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
  • Temperature: The surface tension of a liquid reduces as the temperature rises.

The Unit of Surface Tension:

The SI unit of Surface Tension is Newton per Meter or N/m.