Question

Derive an expression for excess pressure inside a liquid drop and bubble.

Answer 1

Firstly let me tell you that soap bubbles have 2 free surfaces and it's formula is 4T/r

What is excess pressure?

In a curved liquid surface, pressure exerted on concave side of the liquid surface is greater than the pressure exerted on the convex side.Therefore a pressure difference is developed and this pressure difference is known as Excess pressure.

let's derive a formula,
let a drop of radius 'r' having internal and external pressure as Pi and Po respectively.
So,according to the definition,
P ex =Pi - Po
If the radius of the drop is changed from 'r' to (r+dr)then
Work done= F.dr
{ since F = (P ex.A) }
=( P ex.A)dr
=( P ex 4πr²)dr
Now,
change in surface area =
final - initial
=4π(r + dr)² - 4πr²
= 8πrdr( bcoz dr² is negligible)
so by the definition of surface energy,
T = W/∆A
4πr²P ex.dr/8πrdr
P ex = Pi - Po
= 2T/r
and since soap bubble have 2 free surfaces,
P ex = 4T/r

Here,
P ex = Excess pressure
W = work done
A = cross section area

Answer 2

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