Water has the greatest density at

Answer 1:

Hot air rises because when you heat air (or any other gas for that matter), it expands. When the air expands, it becomes less dense than the air around it. The less dense hot air then floats in the more dense cold air much like wood floats on water because wood is less dense than water.

This floating effect in a less dense medium is called a buoyant force or a displacement force.

We can model what I just said with a little physics. Consider the air to be an ideal gas (this is a good approximation which neglects the interaction of air molecules with each other).

How does air density vary with altitude

The pressure P, volume V, amount of gas N, and temperature T can all be related by the ideal gas equation as
P*V=N*R*T
where R is the ideal gas constant (8.314 in units of J/(mol*K)).

Say you start with an amount of air N at pressure P, volume V₁, and Temperature T₁ and heat it in a balloon (we will neglect the mass and elastic properties of the balloon for simplicity) to temperature T₂.

The ideal gas equation can be rewritten as
P*V₁/(N*T₁) =R=P*V₂/(N*T₂)
which with a little

when air is heated what happens to its density

when air is cooled does the density increase