Question

A soap bubble of radius $r$ is in vaccum. The number of moles of gas trapped in the soap bubble is proportional to

• A. $r^0$
• B. $r^1$
• C. $r^2$
• D. $r^3$

Answer 1

The correct option is C $r^2$


Say $T$ is the surface tension, and $t$ is the temperatire.
$P_{inside}=P_{outside}+\frac{4T}{r}$
$n=\frac{PV}{Rt}=\frac{(P_0+\frac{4T}{r})\frac{4\pi }{3}{r}^3}{Rt}$
But $P_0=0$
$n=\frac{\frac{16\pi }{3}T{r}^2}{\underset{}{Rt}}\Rightarrow n\propto r^2$