Answer to Question #152784 in Classical Mechanics for Ru

Question

What is the excess pressure inside a soap bubble that is 5cm in diameter, assuming 0.026Nm-1 as the surface tension of the soap solution?

Answer 1

$\text{Laplace formula}$

$\Delta{P}=\sigma(\frac{1}{R_1}+\frac{1}{R_2})$

$\text{we assume that the thickness of the bubble film can be neglected:}$

$R_1 =R_2$

$\text{taking into account the fact that the soap bubble has two surfaces }$

$\text{-the inner and the outer, then:}$

$\Delta{P}=2*\sigma(\frac{1}{R}+\frac{1}{R})=\frac{4*\sigma}{R}$

$\text{where:}$

$\sigma= 0.026\text{ (surface tension)}$

$R=0.025 \text{ (radius bubble in metrs }R = \frac{d}{2})$

$\Delta{P}=\frac{4*\sigma}{R}=\frac{4*0.026}{0.025}= 4.16 \ Pa$

Answer: 4.16 Pa excess pressure inside a soap