Question

In a soap bubble, pressure difference is

• A. $\frac{2S_{la}}{r}$
• B. $\frac{4S_{la}}{r}$
• C. $\frac{S_{la}}{r}$
• D. $\frac{8S_{la}}{r}$

Answer 1

Answer: (B)

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 $=16\pi r\Delta r{S}_{la}$...(i)
where, $S_{la}$ 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
$p=\frac{4S_{la}}{r}$
$\therefore$ Pressure difference in a soap bubble is
$p_i-p_0=\frac{4S_{la}}{r}$