Why does the air in an air-conditioned room go out when the door is opened?

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Solution

The air inside the air-conditioned room is colder. Hence, it's denser and is at high pressure as compared to the air outside the room.
We know that the air moves from a region of high pressure to low pressure. Therefore, the air from the air-conditioned room (high pressure) goes out (low pressure) of the room when the door is opened.

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