Question

The excess pressure inside an air bubble of radius $r$ just below the surface of water is $P_{1}$. The excess pressure inside a drop of the same radius just outside the surface is $P_{2}$. If $T$ is surface tension then (a) $P_{1}=2 P_{2}$ (b) $P_{1}=P_{2}$ (c) $P_{2}=2 P_{1}$ (d) $P_{2}=0, P_{1} \neq 0$

Name: Problem 18, Chapter 10: Genius Physics (Class 11) - For IIT-JEE and CBSE
Uploaded: 2022-03-06T17:46:06-08:00
Duration: 1 min 1 s
Channel: Saman Zulfiqar
Description: The excess pressure inside an air bubble of radius r just below the surface of water is P1. The excess pressure inside a drop of the same radius just outside the surface is P2. If T is surface tension then (a) P1=2 P2 (b) P1=P2 (c) P2=2 P1 (d) P2=0, P1 ≠0

   The excess pressure inside an air bubble of radius $r$ just below the surface of water is $P_{1}$. The excess pressure inside a drop of the same radius just outside the surface is $P_{2}$. If $T$ is surface tension then
(a) $P_{1}=2 P_{2}$
(b) $P_{1}=P_{2}$
(c) $P_{2}=2 P_{1}$
(d) $P_{2}=0, P_{1} \neq 0$

Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal 1st Edition

Chapter 10, Problem 18

Instant Answer

Solved by Expert Saman Zulfiqar

03/06/2022

Step 1

Step 1: The excess pressure inside an air bubble is given by the formula $P_{1} = \frac{4T}{r}$, where $T$ is the surface tension and $r$ is the radius of the bubble. Show more…

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The excess pressure inside an air bubble of radius $r$ just below the surface of water is $P_{1}$. The excess pressure inside a drop of the same radius just outside the surface is $P_{2}$. If $T$ is surface tension then (a) $P_{1}=2 P_{2}$ (b) $P_{1}=P_{2}$ (c) $P_{2}=2 P_{1}$ (d) $P_{2}=0, P_{1} \neq 0$

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Key Concepts

Surface Tension

Surface tension is the force per unit length existing at the interface between two fluids due to molecular interactions. It is responsible for the minimization of surface area, giving rise to phenomena such as droplet formation, capillarity, and the stability of bubbles.

Laplace Pressure

Laplace pressure is the pressure difference across the curved surface of a bubble or drop, which arises from surface tension. It relates the excess pressure to the curvature of the interface, with the pressure difference increasing as the radius of curvature decreases.

Curvature of Interfaces

The curvature of an interface affects how surface tension influences pressure inside and outside a bubble or drop. In a bubble, having a double-curved interface, the excess pressure is higher compared to a drop, which has a single-curved interface. This distinction is crucial for understanding and comparing the excess pressures in each case.

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