Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air and $S$ the change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, which of the following relation is correct ?
- 4PV + 3ST = 0
- 3PV + 4ST = 0
- 2PV + 3ST = 0
- 3PV + 2ST = 0
The Correct Option is B
Solution and Explanation
$\left( P +\frac{4 T }{ r _{1}}\right) \frac{4}{3} \pi r _{1}^{3}+\left( P +\frac{4 T }{ r _{2}}\right) \frac{4}{3} \pi r _{2}^{3}$
$=\left( P +\frac{4 T }{ r }\right) \frac{4}{3} \pi r ^{3}$
$PV +\frac{4 T }{3}\left(4 \pi r _{1}^{2}+4 \pi r _{2}^{2}-4 \pi r ^{2}\right)$
$3 pv +4 TS$
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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.