Question

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Derive the expression tor the excess pressure Inside a liquid drop.
Carries 2 Marks
Class 11 CBSE

Answer 1

Answer:

To Derive:

Expression for excess pressure inside a liquid drop.

Proof :

There is a pressure difference between the inside and outside of a liquid drop and hence , we get to see the bulging - spherical shapes of drops.

Let Excess pressure be ∆P

Now, let us consider a small amount of work done to move the surface by " δr "

distance :

∴ δW = Force × δr

=> δW = (Excess pressure × Area) × δr

=> δW = [∆P × 4πr²] × δr

Now , Let us consider slight increase in Surface energy due to small increase in Surface Area :

∴ δU = (Surface Tension) × (∆Surf. Area)

=> δU = T × [ 4π(r + δr)² - 4πr²]

=> δU = T × [4π (2r × δr) ]

.......... [ ignoring (δr)² term ]

Now, considering the fact that the work done is stored as increased Surface energy.

∴ δU = δW

=> T × [4π (2r × δr) ] = [∆P × 4πr²] × δr

=> ∆P = 2T/r

Hence the final answer is :

$excess \: press. = \frac{2T}{r}$