I was surprised by how few people knew the answer to this. So I thought I’d give four explanations at different levels of difficulty.
Level 1- Hot air is less dense than cold air so it rises.
Level 2- As you increase the temperature of air, the molecules of nitrogen, oxygen, carbon dioxide, etc… that make up the air begin to jostle around more. As a result, they bump into each other more frequently and start spreading out. This makes the air less dense since the same number of molecules are spread over a greater volume. Therefore, the warmer air rises.
Level 3- Upon heating air, the gaseous molecules are promoted to higher energy states. This results in molecules having more kinetic energy, especially for vibrating. As the amplitude of vibrations increases with energy, the molecules take up a greater volume in space. Therefore the density of the heated air decreases as molecules bounce off each other much more due to short range repulsive forces. Therefore the warmer air begins to rise.
Level 4- Upon applying energy to air by heating, various energy levels, in particular the vibrational energy states, are excited. This is because thermal energy is of a similar magnitude to vibrational energy levels, therefore the molecules’ vibrational states are readily promoted. The specific rovibrational state is of little consequence to the change in density. Modelling these vibrational states as an anharmonic oscillator (with any number of higher order corrections) shows clearly that as higher vibrational levels are occupied, the equilibrium bond length increases (we could go into the different vibrational modes here but seeing as most of the air is oxygen and nitrogen, i.e. diatomics, I think I’ll cut out that painful discussion). Therefore, each molecule occupies a greater volume in space, and in order to minimise repulsive interactions and maintain the lowest internal energy possible, the molecules spread out. Ergo, less dense so they rise.
Where did I lose you? If at all…