A bubble of air is suspended in clean water at ambient pressure and temperature.
A. How do the pressure and the number of molecules inside the bubble scale with the radius R of the bubble? Assume the surface tension \gamma is known and you can model the bubble/air as an ideal gas.
B. Find the minimum radius of the bubble so that the ideal gas law is valid? (hint: the volume fraction of the atoms inside the bubble has to be << 1)
C. If we add surfactant to water to lower the surface tension to 0.5* \gamma, identify the minimum radius of the bubble in part (B).