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Since theoretically hot air moves upwards and the cooler air moves downwards, I was wondering if there is a steady or unsteady tiny increase in temperature of a room as we move from the floor of the room to the ceiling. I mean are the temperatures at the floor and roof different by at least a small fraction?

Ignore the heating of roof by sunlight and thus the heating of ceiling and also ignore the cooling of floor by the earth below the floor and assume the doors, windows and vents in the room are sealed shut.

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    $\begingroup$ This is a famous question debated by Loschmidt and Maxwell. It would be nice to have a clear and definitive answer written up on this site, but I would beware of hasty or simplistic answers. Your statement of it seems to be opposite to what Loschmidt claimed, which was that the temperature would be lower near the ceiling. Is there some physical reasoning behind your expectation? In any answers, it would be nice to have an explanation of why, e.g., this is different from the variation of temperature of the earth's atmosphere with height. $\endgroup$
    – user4552
    Nov 17, 2019 at 15:21
  • $\begingroup$ @BenCrowell Explanation: Since theoretically hot air moves upwards and the cooler air moves downwards, I thought maybe hotter air in the room moves upwards causing a temperature difference between the regions near the ceiling and that near the floor. I've added this explanation to the question. $\endgroup$
    – Somanna
    Nov 17, 2019 at 16:02
  • $\begingroup$ @BenCrowell: Why is this interesting, because it has been debated centuries ago? The solution is a buoyant instability, and has tens of articles on this physics.se Hot air doesn't always rise, only sufficiently hot air, that reverses the entropy gradient with height, will always rise. $\endgroup$ Nov 17, 2019 at 16:30
  • $\begingroup$ @AtmosphericPrisonEscape: If you think this has already been asked and answered on this site, then please vote to close as a duplicate, giving the earliest Q&A that you think is the same. Then we would all be able to see the link you have in mind. $\endgroup$
    – user4552
    Nov 17, 2019 at 19:27
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    $\begingroup$ @ChiralAnomaly: My understanding of the way things are supposed to work is that if there is a later duplicate question that attracts a superior answer, you vote to close that later question as a duplicate, and you leave a comment on the answer asking the author to delete it and copy the content over to the original question. We don't want a proliferation of questions all asking the same thing. $\endgroup$
    – user4552
    Nov 17, 2019 at 21:51

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Yes, there will be temperature differ by a tiny fraction. Hot air being less dense (hence lighter) will move upwards whereas cold air being relatively denser (hense heavier) will sink down.

However the difference will be very tiny, not enough to be noticeable unless the physical conditions are changed (altered). The average temperature of room though will remain almost equal considering you could change the height of the room.

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    $\begingroup$ It is very noticeable if you have a mezzanine 20 feet above you. At my work if you turn the downward ceiling fan positioned over the warehouse area off up in the mezzanine will be room temperature but downstairs in the warehouse area will be outside temperature. Turn on the fan and then it is the same temperature. Like 8-10C difference. $\endgroup$
    – DKNguyen
    Mar 26, 2022 at 18:24

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