Question:
A mercury drop of radius $1 \,cm$ is sprayed into $10^{6}$ drops of equal size. The energy expended in joule is (surface tension of mercury is $460 \times 10^{-3}\,N / m$ ):
A mercury drop of radius $1 \,cm$ is sprayed into $10^{6}$ drops of equal size. The energy expended in joule is (surface tension of mercury is $460 \times 10^{-3}\,N / m$ ):
Updated On: Jun 23, 2023
- $0.057$
- $5.7$
- $5.7 \times 10^{-4}$
- $5.7 \times 10^{-6}$
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The Correct Option is A
Solution and Explanation
$R =1 \,cm , n =10^{6}$
$\Delta \bigcup=4 \pi R ^{2}\left( n ^{1 / 3}-1\right) T$
$=4 \pi \times 10^{-4}\left(10^{2}-1\right) 460 \times 10^{-3}$
$=0.057\, J$
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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.