How does temperature vary with height from floor to ceiling?

[SteveIzHxC]

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.

 

[Simon Bridge]

Welcome to PF;
Heat generally moves from hot places to cold places - a completely closed and thermally isolated box will eventually find thermal equilibium and have an even temperature throughout. To maintain a temperature gradient you have to apply heat someplace and remove it someplace else.

IRL the air in a room is not in thermal equilibrium with itself.
You can get very noticeable temperature gradients between floor and ceiling and even between different parts of the room at the same height.

 

[sophiecentaur]

The uneven temperature distribution in rooms is a factor that could be usefully addressed as an energy-saving strategy. I have a ceiling fan in my conservatory and it certainly warms the place up significantly on a cold night if you 'stir the air up a bit'.

 

[Simon Bridge]

Yeah I've experienced that - I had a high-ceilinged house and once climbed a ladder to check the temperature difference - in the evening after a hot day it could quite large. The ceiling fan would produce a rush of warm air.
I'd hate to have to model it though.

 

[Baluncore]

Fundamentally, the air on the floor will be the temperature of the floor. The air on the ceiling will be the temperature of the ceiling. That sets the gradient in the room.

The air in the room is only one part of a matrix of thermal flux paths. The floor, walls and ceiling all play a part by setting the boundary conditions. Radiation cross-couples all surfaces with all air masses. With equal temperature boundaries you would expect everything to equilibrate and there to be no significant temperature difference.

Things are different at night when the ceiling can be colder than the floor. Convection may then transfer heat from the floor to the ceiling in a “thermal siphon”, but only when the floor is hotter than the ceiling.

If you stir up the stagnant air in a room with a hot ceiling you will warm the floor and cool the ceiling. It might be better to install insulation to regulate your boundary conditions.

The air you breath out is made both warmer and wetter, two good reasons for it to rise, (Yes, wet air is lighter than dry air), so that respired air will condense water on a cold ceiling and can support mould growth there. The hot wet air is more obvious in a bathroom.

Sleep on a high bench in a snow cave, never on the floor, the floor is where the cold air and accumulating CO2 pools.

 

[NascentOxygen]

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?

Why don’t you measure it? Hang a thermometer on a string from a loop on the ceiling, arranged so that you can raise the thermometer from floor to ceiling by pulling on the string. Use black marker to draw 1 foot intervals on the vertical string. Read it from a distance using binoculars, or a tele lens on your camera.

Tell us what you find.