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The can collapses instantly.
The water inside the can is boiled. The water takes up more space as a gas than as a liquid, and this forces much of the air out of the can. When the heat is removed, the water returns to its liquid state and air, under normal circumstances, would be able to fill the space in the can again.
However, the can is inverted into cool water, preventing this from happening. The water does return to its liquid state very quickly because of the cool water bath. However, this same water prevents air from coming in, leaving whatever little air happened to be in the can after immersion the task of filling the entire leftover space. Because there is less gas per unit area inside the can than outside the can, the pressure inside the can is less than the pressure outside the can.
The greater pressure outside of the can pushes in on the can, and the lesser pressure inside of the can is unable to push back with equal force. The can, as a result, collapses.
This material is based upon work supported by the National Science Foundation under Grant Number 1246120