Final answer:
Heating the gas in a hot air balloon causes it to become less dense than the cooler outside air, resulting in a buoyant force that makes the balloon rise. This is a result of the increased volume and decreased density of the heated air as explained by Charles's law.
Step-by-step explanation:
Heating the gas in an air balloon causes it to rise due to the principles of buoyancy and changes in density. According to Charles's law, when a gas like air is heated, its volume increases if the pressure is constant. Consequently, the density of the hot air inside the balloon decreases since density is inversely proportional to volume. The hot air inside the balloon becomes less dense than the cooler atmospheric air surrounding it. This difference in density means the hot air will rise, just like wood floats on water because it is less dense. As the air molecules inside the balloon heat up, they move faster and strike the walls of the balloon, causing it to expand as stated by the introduction to the concept of heated gases expanding. During this continuous heating process, the hot air balloon experiences a buoyant force which is the upward force exerted by the cooler, denser surrounding air, as seen in Figure 13.16 and other references provided. This buoyant force pushes the hot air balloon upward, allowing it to rise smoothly into the air, thus starting its journey into the skies as indicated in the 'How are hot air balloons able to move smoothly in the air?' section.
Convection currents are also a factor to consider, as the heated air rises due to being less dense, it creates a movement of air that can help carry the balloon upward further, exploiting the decrease in density relatively to its surrounding for lift as described in Figure 11.4.