Thermodynamics - convection current

please could someone help explain the mechanism of a convection current as I keep finding conflicting explanations. Is a convection current caused by differences in density or differences in pressure? Most seem to say it is caused by differences in density (more specifically buoyancy) since you cannot get a convection current in zero gravity. However, could someone help explain the following:

If you take a house on a cold winters day then hot air in the house will rise due to differences in density and some of this air will find some way of escaping out the top of the house. When this warm air escapes, as far as I know, this causes cooler air from outside to be drawn in neat ground level (e.g. under your door). Surely this mechanism is caused by pressure differences? Why else would the cold air come inside the house? If it didn't then you would eventually create a vacuum no? I know it's not possible but if you completely stopped hot air leaving the top of your house would this completely stop drafts at the bottom of the house since a draft is just cold air coming in to replace the escaping hot air? Or vica versa, if you completely blocked cold air coming into your house at ground level would this have the knock on effect of stopping hot air escaping near the top?

Thanks to anyone who can help out!

• Ideal gas law says $P\propto\rho$ (also works for relativistic gases and polytropes). Therefore, it can be viewed as either. – Kyle Kanos Feb 17 '14 at 15:07
• @KyleKanos: At the interface between a region of hot gas and a region of cold gas such as occurs in thermal convection, there is a discontinuity in $\rho$ but no discontinuity in $P$, so $P\propto\rho$ is not applicable. The reason is because the temperature is non-constant in convection, so $P=\rho RT$ has $T$ and $\rho$ compensating each other. – DumpsterDoofus Feb 17 '14 at 17:16
• So your saying that for convection temperature and density change to keep pressure constant? But when warm air leaves a house near the top and cold air enters does this have nothing to do with pressure? Or is this not to do with convection? – user37250 Feb 17 '14 at 17:31
• @user37250: The easiest way to think of it is in terms of a density difference, with the convective force being essentially the same as the force which lifts a balloon. Your reasoning about the house is probably valid, and there is probably a pressure difference which draws in cold air at the bottom and pushes the hot air out of the top. The force due to the atmospheric pressure gradient is given by $-\nabla p$, which ordinarily would counteract the gravity force $\rho g$, but when you heat up a gas, $\rho$ changes, so the balance is disturbed, and the gas is lifted. – DumpsterDoofus Feb 17 '14 at 17:33