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
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: Sep 3, 2024
- $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 2r.
$\therefore $ Area $A_2 = 4 \pi (2r)^2 = 16 \pi r^2$
Increase in surface area
$\Delta A = 2 (A_2 - A_1 ) $
$= 2(16 \pi r^2 - 4 \pi r^2) $
$= 2 4\pi r^2$
Energy spent,
$W = T \times \Delta A$
$ = T . 24 \pi r^2 $
$= 24 \pi T r^2\, J $
Under isothermal condition radius becomes 2r.
$\therefore $ Area $A_2 = 4 \pi (2r)^2 = 16 \pi r^2$
Increase in surface area
$\Delta A = 2 (A_2 - A_1 ) $
$= 2(16 \pi r^2 - 4 \pi r^2) $
$= 2 4\pi r^2$
Energy spent,
$W = T \times \Delta A$
$ = T . 24 \pi r^2 $
$= 24 \pi T r^2\, J $
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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.