Question

Derive Laplace’s law for spherical membrane of bubble due to surface tension

Answer 1

Expression for excess pressure inside a bubble:

Free surface of drops or bubbles are spherical in shape. 

Let, P_i = inside pressure of a drop or air bubble

P_o = outside pressure of bubble 

r = radius of drop or bubble.

Let the radius of drop increases from r to r + Δr so that inside pressure remains constant.

Initial area of drop A₁ = 4πr² , Final surface area of drop A₂ = 4π(r+Δr)²

Increase in surface area,

As Δr is very small, the term containing Δr² can be neglected.

ΔA = 8πrΔr

Work done by force of surface tension,

In case of soap bubble, there are two free surfaces in contact with air.

Excess pressure, P_i - P_o = \(\frac{4T}{r}\)

Equation (2) represents excess pressure inside a drop or air bubble. It is also called Laplace’s law of spherical membrane.