Question

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

Answer 1

To estimate the air pressure when the can is crushed, use the ideal gas law considering the volume, temperature, and amount of steam. The exact calculation may be complex due to rapid changes occurring during cooling.

Step-by-step explanation:

The calculation of the air pressure at which a can is crushed can be approached by first considering the can's volume, the amount of water turned into steam within the can, and the temperature change involved. As the water vapor condenses into a much smaller volume of liquid water, the pressure inside the can reduces, possibly going below the external atmospheric pressure. Consideration should also be given to the kinetic-molecular theory, which links the motion of molecules to temperature and pressure.

To calculate the pressure, you could use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the amount of gas (in moles), R is the ideal gas constant, and T is the temperature in Kelvin. By assessing the change in conditions (pressure and temperature before and after), you can estimate the internal pressure at the moment the can collapses. You need to know the initial volume of the steam, the temperature that the water was boiled at, and assume that atmospheric pressure is 1.00 atm when the can is sealed.

However, due to the complexity of rapidly changing conditions during the quenching process, including heat transfer, phase transition of water, and deformation of the can, an exact calculation in a classroom setting may not be feasible without simplifying assumptions.