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You put a can with water at its base on a hot plate and allow the water to heat. Once steam is visible from the opening on top of the can, you quickly flip the can upside down into a bowl of water with gloves or tongs. The can will be crushed by the atmospheric pressure.

I know by heating the can, we boiled the water inside it. The process of boiling turned the water into vapor. And since the water vapor molecules are much more spread out than the water molecules, they take more space and are forcing the molecules of air out from the can. And when we put the can in the cold water, we suddenly cooled it. That cooling caused the water vapor in the can to condense, creating a partial vacuum. Because of that, the pressure outside of the can became much greater than the pressure inside, and that pressure difference crushed the can.

However, my point of confusion is...

How may someone calculate the air pressure of which the can is crushed before or after impact?

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How may someone calculate the air pressure of which the can is crushed before or after impact?

The outside air pressure is one atmosphere. The pressure in the can is one atmosphere as long as there is a way for air to come in and out, and as long as you heat the can gradually.

After the can is crushed, the gas pressure in the can is one atmosphere again (once water has had time to flow in and out).

When you submerge the can in the ice bath, the gas pressure inside the can depends on the remaining volume and the remaining amount of water in the gas phase.

If we assume that condensation of the water is fast and the liquid water is slow to enter the can and the can has not been crushed yet, you would be able to estimate the pressure inside as the vapor pressure of water at the current temperature of the gas. The temperature is difficult to estimate (it is $\pu{100 ^\circ C}$ when the water is boiling, and $\pu{0 ^\circ C}$ on the surface of the ice water). If we just assume room temperature, the vapor pressure is 0.0231 atm, i.e. 1/50th of the outside ambient pressure.

You get a sense of the pressure difference by looking at the volume of the can before and after crushing. Ideally, you could also measure how much water made it into the can, testing the hypothesis that entry of water is slow compared to the crushing of the can (either process will decrease the vapor volume).

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