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Q.
In a soap bubble, pressure difference is
Mechanical Properties of Fluids
Solution:
A soap bubble is as shown in figure, differs from a drop and a cavity as it has two interfaces.
When radius of bubble is increased by radius $\Delta r$, the increase in the surface area of the bubble $=8 \pi r \Delta r$.
So, effective increase in surface area of the soap bubble $=2 \times 8 \pi r \Delta r=16 \pi r \Delta r$
External work done in increasing the surface area of the soap bubble
$=$ Increase in surface energy $=16 \pi r \Delta r S_{l a}\,\,\,$...(i)
where, $S_{l a}$ is the surface tension of liquid-air interface.
But, work done $=p \times 4 \pi r^{2} \Delta r\,\,\,$...(ii)
From Eqs. (i) and (ii), we get
$p=\frac{4 S_{l a}}{r}$
$\therefore$ Pressure difference in a soap bubble is
$p_{i}-p_{0}=\frac{4 S_{l a}}{r}$
