A hot-air balloon does not rise because smoke pushes it. The principle is buoyancy: surrounding air exerts an upward force on any volume it displaces. The envelope is a large volume of air held in fabric open at the bottom.

The burner heats the air inside. Warm air expands; some leaves through the opening below. The same volume then holds less mass than the cooler air around it, so average density falls. If buoyancy covers the weight of envelope, basket, fuel and people, the balloon climbs.

The pilot fires the burner to climb or to stop a descent. To descend, the air is allowed to cool or a top valve is opened in a controlled way to release warm air. On landing the valve helps dump lift quickly. Temperature limits are those in the aircraft documents, not in an article.

There is no propeller or rudder for horizontal travel. The balloon moves with the air mass. By changing altitude the pilot can seek layers with different wind, but cannot pick an arbitrary route.

Flight depends on weather, visibility, terrain and a ground crew. The burner and high temperatures require training and certification. Improvised flame-carrying balloons are dangerous and can start fires.

This text describes the physical principle, not an operating procedure. Flight is only for authorised operators.

The photograph shows a balloon over a landscape, not a laboratory tank. It illustrates the envelope in flight, not a density experiment.

Image: MusikAnimal, hot-air balloon at sunrise over Cappadocia, Turkey. Wikimedia Commons, CC BY-SA 4.0. Cropped to 16:9. Licence. Original file.

Sources consulted: NASA Glenn — Buoyancy; Balloon flight | Encyclopaedia Britannica; FAA — Balloon Flying Handbook.