What force keeps a hot air balloon in the air?

Answer 1

It has nothing to due with "convection" or any other motion of the air. (If it did, then how would you explain floating helium balloons, which are at the same temperature as the air?)

The pressure of the air around you (even perfectly still air) decreases with altitude. It's well known, for example, that the air pressure at the top of a mountain is much less than at the mountain's base--that's why you need breathing equipment up there. The difference is caused by the weight of the air itself--lower locations have a greater mass of air weighing down on them than higher locations, and that produces pressure.

Even within a room, there's a SLIGHT difference in air pressure between the floor and the ceiling. The air pressure at the floor is slightly greater. That difference produces a small upward force called "buoyancy" on EVERY object in the room, including you. Air pressure pushes on you from all directions; but the pressure on your feet (pushing up) is slightly greater than the pressure on your head (pushing down). This isn't enough to make you float, but it is enough to reduce your measured weight by a small amount.

The amount of buoyancy acting on an object depends on an object's VOLUME. For a typical adult human (in typical air), the buoyant force on their body is around 3 ounces. That means the number you see on the bathroom scale is about 3 ounces less than your "real" weight.

It also means that if your "real" weight (due to gravity's pull) were less than 3 ounces, the buoyant force would overcome gravity, and you would float away! So the trick to floating is to reduce your weight (your mass), while increasing your volume (to increase the buoyant force). Both of those actions decrease your density. It turns out that if you decrease your density to the point that you're less dense than the air around you, the buoyant force will exceed the gravitational pull, and you'll float.

So that's what hot air balloons do. Hot air is less dense (has fewer molecules per cubic meter) than cold air, so that reduces the balloon's weight. But because those molecules are moving fast, they have enough pressure to expand the balloon, increasing its volume (and hence increasing the buoyant force). When the buoyant force exceeds the weight, the balloon rises.

Answer 2

A hot air balloon stays in the air due to the principle of buoyancy. The heated air inside the balloon is less dense than the surrounding cooler air, causing the balloon to float upwards. By controlling the temperature of the air inside the balloon, the pilot can control its altitude.