The pressure inside a soap bubble and outside it are not identical due to the surface of tension of the soap bubble.
To calculate this pressure difference, let’s first consider an air bubble inside a liquid. If the pressure difference is ΔP , then the work done to increase the radius of bubble from r to ( r + Δr) is given by:
W = F Δr = (4 πr2 )ΔP . Δr
while the change in area,
ΔS = 4π (r + Δr)2 – 4πr2
= 8 πr Δr
From the definition of surface tension
$ \displaystyle T = \frac{W}{\Delta S} $
$ \displaystyle T = \frac{4\pi r^2 \Delta P \Delta r }{8\pi r \Delta r} $
$ \displaystyle \Delta P = \frac{2 T}{r} $
For a soap bubble in air, there are two surfaces, and so,
$ \displaystyle \Delta P = 2 (\frac{2 T}{r}) = \frac{4T}{r} $
Exercise : Two soap bubbles of different radii (r, R : r < R) are connected by means of a tube. What will happen to the larger bubble ?
Also Read:
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Surface Tension Surface Energy Angle of contact Capillarity & Ascent Formula Viscosity , Stoke’s Law & Terminal Velocity Poiseuille’s formula |