Why does hot air rise?

I find it amazing that the best anyone can do here is "hot air rises because its lighter". Its hardly an explanation, because it does not explain where the force that pushes the hot air up comes from.

Here's the real explanation.

The pressure in the atmosphere falls as you go upwards, because there is less air above you pushing down. This is why air pressure is lower up a mountain.

Consider a metre cube of air. The pressure at the bottom of the cube is higher than that at the top of it, by ro.g.h where ro is the density of air (about 1 kg per cubic metre), g is the acceleration of gravity (10 m/s/s) and h is our 1 metre cube side. This means there is a force pushing the cube of air upwards of ro.g.h times the area of the cube - ie 1m x 1m. This makes 10 Newtons pushing up. But our cubic metre of air (1 kg mass) weighs 10 Newtons, so it goes nowhere.

Now consider a cubic meter of warm air at the same point. If its density (because its warm) is say 10% lower than the surrounding air, then the force up will still be 10 Newtons, but its weight down will only be 9 Newtons - so up it goes.

Exactly the same applies in water. So stones sink because the pressure difference created as above is much lower than the weight down.

Heat is energy. When we say something is hot, we really are saying it has a lot of stored energy.

What does this energy do?

Matter is made up of incredibly small pieces called atoms and molecules. Atoms and molecules are always moving.

The more energy these atoms and molecules have, the faster they move. The faster they mover, the more space they take up.

If something is hot, it weighs the same as if it were cold, but it just takes up more space.

This leads us to the concept of density. Because hat air takes up more space than cold air, hot aur has a smaller density.

Less dense hot air will "float" above the more dense cold air.

Heat causes air molecules to vibrate. The vibration pushes the molecules away from each other, i.e. the air expands. So heated air has less molecules per cubic meter than cool air and is therefore lighter. Since air can flow, the heavier air flows downward pushing the lighter air upward.

A stone sinks in water because a cubic centimeter of stone weighs more than the same amount of water. Again, water can flow so the stone sinks.

It has to do with the density of specific molecules that make up the air. Cool air has more moisture in it which is water. The suspended water particles have a higher density then the molecules found in dry air which causes it to sink below the dryer air. Just like sugar in a glass of tea, or like you said a stone in water.

As people have said, hot air is less dense. The air molecules in hot air are spread farther apart than air molecules in cold air, because the warmer the air, the faster the air molecules move, and so when it's hot enough, they just zip apart.

Hot air expands and become less dense therefore the density of the cold air pushes downard because of the higher density same thing with stones and water stone is denser then water...

Since it's lighter than cold air--less dense--the cold air falls (gravity pulls it) and that leaves no place for the hot air. It is displaced by the cold air, so it gets pushed up.

um hot air rises cause its lighter than cool air, stones sink because they are dense and have a lot of mass

Because it is less dense than cold air.

It's all about density. Anything mroe dense than water sinks in water. Helium is less dense than air, so helium baloons rise.

Becouse, density of hot air is low, so, it rises up.

No, stone sinks because density of stone is higher than that of water.

Reltionship in both the cases is "density", not the temperature, as u doubt.