All Problems

Liquids. Capillary effects

Problem 2.181

Find the work to be performed in order to blow a soap bubble of radius \(R\) if the outside air pressure is equal to \(p_{0}\) and the surface tension of the soap water solution is equal to \(\alpha\).

Reveal Answer
A′=F+pVln⁡(p/p0), where F˙=8πR2α,p=p0+4α/R,V=4/3πR3A^{\prime}=F+p V \ln \left(p / p_{0}\right), \text { where } \dot{F}=8 \pi R^{2} \alpha, \quad p=p_{0}+4 \alpha / R, V={ }^{4} /_{3} \pi R^{3}
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