If hot air rises and cool air falls, how does an open window downstairs end up cooling the upstairs in winter?
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Hot air rises and cool air falls, but hot air and cool air next to one another also mix together and warm/cool one another to some extent. The rising/falling effect is not strong enough to resist mixing from typical air currents.
As people move around the building, and as random air currents flow, the hot air upstairs gets mixed with cold air flowing in from downstairs. It’s also directly cooled by contact with the downstairs air.
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