Question:

A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing

Updated On: Jun 23, 2023
  • $3 \, \pi \, Tr^2$
  • $6 \, \pi \, Tr^2$
  • $12\, \pi \, Tr^2$
  • $24 \, \pi \, Tr^2$
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The Correct Option is D

Solution and Explanation

Initially area of soap bubble $ A_{1}=4 \pi r^{2}$ Under isothermal condition radius becomes $2 r$. Then, area $ A_{2}=4 n(2 r)^{2} $ $=4 n .4 r^{2} $ $=16 \pi r^{2} $ Increase in surface area $ \Delta A =2\left(A_{2}-A_{1}\right) $ $=2\left(16 \pi r^{2}-4 \pi r^{2}\right)$ $=24 \pi r^{2} $ Energy spent $W =T \times \Delta A $ $=T .24 \pi r^{2} $ or $W =24 \pi T r^{2} J$
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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.