What happens to the buoyant force when a hot plume of gases cools to the surrounding air temperature?

When a hot plume of gases cools to the surrounding air temperature, the buoyant force acting on the plume effectively becomes zero. This phenomenon occurs because buoyancy relies on the difference in density between the heated gases and the cooler surrounding air.

Initially, when the gases are hot, they are less dense than the surrounding air, which generates a buoyant force that causes the gases to rise. However, as these gases cool and their temperature equals that of the surrounding air, their density increases to match that of the air. When both the plume and the surrounding air are at the same temperature, the buoyant force ceases to exist because there is no longer a difference in density to create upward lift. Consequently, the hot plume will no longer rise and will instead settle, leading to the conclusion that the buoyant force becomes zero.