(Just thought I'd post this as a reminder of some relevant science...)
I'm going to go over your question bit by bit. Explain some of the language of your question, and then analyze the final answer. My explanations assume prior knowledge of the atomic reality of gases but little else.
First off "heat rises" is a term that should be avoided in a physics discussion. The term "heat" is referring to the transfer of thermal energy from one place to another. It is not a state-quantity. For instance, state quantities are things that are qualities of the matter it self. For instance mass is a state quantity. So is charge. These are the same regardless of other place and time. While "heat" is a description of change, not a description of state. We say a pan on the stove heated up. Or better still a flow of heat from the flame into the pan caused the pan to have a higher temperature. If we said the pan on the stove has heat, that is incorrect, the pan on the stove has thermal energy (a mesure of the mass and temperature of the object), and a temperature.
Reminder: temperature is a mesure of the average kinetic energy of a substance.
Rephrase: Does hot (greater temperature) air rise? Or is it displaced by cold (lower temperature) air?
First: Why does anything fall and rise in a gravitational field? Well it must have a force pushing it up. To change its potential energy (U=mg) a force must act on it.
What is the force that causes a fluid or gas to rise and fall? In all cases it can be described as a pressure.
Pressure is always a relative thing, this is because it isn't pressure that causes things to rise and fall it is a pressure difference or gradient. So what is important is the net pressure, or pressure difference.
First of all this is an important point. If the pressure in a volume is all the same: nothing changes. No air moves (besides individual particles that will move due to brownian motion).
So how can I create a pressure difference to cause one bit of air to rise? To be pushed up?
1) The easiest way is to control how packed the air is, its density. A greater packed group of molecules will have more atoms in a smaller space so it if each molecule is moving at the same speed more collisions occur between the edge of its volume (these changes in momentum cause a force) and it will exert more force: greater pressure.
2) But how do we mesure how fast the particles are going in volume of something? Because if the atoms move faster then there will be greater changes in momentum and more force. Temperature is the mesure of this, the average kinetic energy describes in essence how fast the particles are going.
What does 1) and 2) tell us? Well pressure is controlled by the speed of the particles, and how many of them are in the space. In thermodynamics the equation PV=nRT is used. R is a constant. n is the number of mol (a measure of the number of particles). This says the pressure and volume (V) are related to temperature (speed) and the amount (n).
This says that a hotter volume of the same substance will need to expand to maintain its outward pressure. A colder thing will contract. This is the process of hotter and colder liquids and gases becoming less dense or more dense.
FINAL (Q and A): A: Does hotter air rise? B: Or does cold air displace the hot air causing it to rise?
Well let's test the fist one, hotter implies that it is hotter then something. So if it is hotter then the air around it, the air will expand, the pressure will decrease (since PV is constant) and high pressure, lower density air will push it up: displacing it. Here we see the issue with the question: both A and B are true. If B were not, and cold air wasn't available then there would be no difference in densities, no difference in pressures, and nothing would change. You can not have A without B, and B without A, and mostly this is because a pressure gradient is necessary for changes to occur.
Could you have two gases where the hotter of the two was on the bottom? Yes. A light gas like helium, less dense because its molecules hate each other (personified; sorry), will float all the way out of the earth's atmosphere, leaving hot desert air below.
source:
http://physics.stackexchange.com/questions/6329/does-hot-air-really-rise
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