Question:
A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be
A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be
Updated On: Mar 19, 2025
- 2.8 × 10–4 J
- 1.5 × 10–3 J
- 1.9 × 10–4 J
- 9.4 × 10–5 J
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The Correct Option is A
Solution and Explanation
The correct answer is (A) : 2.8 × 10–4 J
\(r′ = \frac{r}{4}\)
⇒ ΔE = T(ΔS)
= T × 4π(nr′2 –r2), n = 64
= T × 4π × (4 – 1)r2
⇒ ΔE = 0.075 × 4 × 3.142 (3) × 10–4 J
= 2.8 × 10–4 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.