We all know the air at the ceiling is warmer than the air at the floor because "hot air rises" due to the density gradient. But I started wondering how drastic is this effect actually? Noticeable, at all, say, in a normal 11 foot ceiling room? Make whatever assumptions you need (still air, no people in room, perfectly isolated room thermally from outside, etc.) Firstly I would just be interested in an estimate of the total difference, but further, could we calculate the temperature as a function of height? It should just be linear I guess.