The following does not include all scientific details and parameters, only a com

Question

The following does not include all scientific details and parameters, only a common summary of "thoughts". What is scientifically wrong with this summary?

When you take your beer and tap the top of a friends beer bottle, the beer shoots out the top as the CO2 is taken out of solution and rebounds off the bottom of the bottle. If the liquid in the bottle does not have anything in solution, the tap on the top of the bottle results in the explosion of the bottom of the bottle. This is from the cavitation that was created at the bottom of the bottle, and the pressure wave that propogates through the liquid to collapse the cavitation. When the cavitation collapses, the momentum of the water that has now been shifted down hits the bottom and blows out the bottom of the bottle. It does not seem that the energy imparted with the relatively light tap on the top is enough to violently blow out the bottom of the bottle. Is there more energy in the collapse of a cavitation than the energy required to create the cavitation in the first place? Or is it just the momentum of the liquid that blows out the bottom of the bottle? Pits and dings in metal pump blades are caused by cavitation collapse. What is and where does that power come from?

Explanation / Answer

The cavitation does not produce more energy than you put in, it just doesn't take a great deal of energy to break glass. It takes a lot of force, but once the two pieces of glass are separated by a few angstroms, the force drops to zero, so the total work done in the process is not very large.

To estimate the energy, multiply the number of atoms on a surface by 1eV, which is a generous bond-energy. This doesn't take into account long-range forces, like Van-Der-Waals attraction, but I assume these effects are not much stronger. A circle of circumference 20cm and width .25 cm has an area of 5cm^2, which is 5*10^16 A^2. This gives a binding energy of the order .01 J, and your hand has plenty more energy than that.

As an aside, regarding the cavitation at the bottom, this is an interplay of the different speed of sound in air vs. glass. When you hit the glass, the sound in the glass reaches the bottom of the glass before the sound wave in the air can transmit the pulse to the water, so that you get an underpressure at the bottom.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.