The relationship between the temperature and volume of a gas, which is known as Charles' law, provides an explanation of how hot-air balloons work.
In a hot air balloon, the gas expands when heated and hence the volume increases which helps it fly. This happents at a constant pressure. When a given weight of hot air occupies a larger volume than the same weight of cold air. Hot air is therefore less dense than cold air. Once the air in a balloon gets hot enough, the net weight of the balloon plus this hot air is less than the weight of an equivalent volume of cold air, and the balloon starts to rise. When the gas in the balloon is allowed to cool, the balloon returns to the ground.