Archimedes' principle: an object experiences a lifting force (buoyant force) equal to the weight of the fluid being displaced by the object.
Helium (He)and hot air are lighter than the normal air near the ground level. If the balloon is filled with He or heater air, near the ground level, the normal air that the balloon displaced has a heavier weight that the weight of He or hot air inside the balloon. The net force is up, assuming the balloon itself is weightless (the balloon fabric is so thin that the weight is negligible). When the balloon reaches the upper atmosphere where the surrounding air is as light as the hot air, the balloon will stop ascending.
As humans, we are used to living at 1 atmosphere of pressure, so we rarely think about it. We normally don't feel the pressure on us because the human body is primarily made up of liquid, and liquids are basically non compressible. At times, we do notice changes of pressure, in our ears. You may have noticed your ears "popping" when flying, driving in the mountains, or even going up and down in an elevator. This is because our ears have an air space in them, and air, like all other gases, is compressible.
Boyle's Law states a gas will compress proportionately to the amount of pressure exerted on it. For example, if you have a 1 cubic foot balloon and double the pressure on it, it will be compressed to 1/2 cubic foot. Increase the pressure by 4, and the volume will drop to 1/4 the size etc. This theory was discovered by Sir Robert Boyle, a 17th century scientist. The theory known as Boyle's Law and it states: If the temperature remains constant, the volume of a given mass of gas is inversely proportional to the absolute pressure.
The reverse is also true and answers your question more directly. A half filled balloon at 2 atmospheres (14 ft underwater) will double its pressure when it rises to the surface at 1 atmosphere. It would therefore become a full balloon. That is why divers exhale when surfacing on Scuba.
because as you heat the gas, you cause the gas to expand on the container (whish is a balloon), this lowers the density, and a less dense fluid submersed in a denser fluid will rise, like an air bubble rises from underwater
Make the balloon capable of further expansion. That way as the balloon rises and the barometric pressure falls the balloon can expand and allow its internal gases to achieve a constantly decreasing density.
It would expand as the gases inside expand against the pressure of the skin of the balloon and the atmospheric pressure.
Hot air balloons are limited in altitude because of adiabatic cooling. As you ascend in the atmosphere, the air becomes cooler. This alone would not be able to stop a balloon rising if there were enough fuel to continuously heat the air. However, as the balloon rises, the hot gas inside the balloon also rises. Logical right? When the gas rises, reduced pressure allows the gas to expand and as gases expand, the also cool. So, there will come a point, or pressure, where it become increasingly difficult to heat the air faster than it cools due to expansion and the balloon will stop rising.
Simple...hot air rises..
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As you rise in elevation, the pressure around you decreases. This lower pressure would cause the balloon to expand, and burst if it was inflated to much originally. By starting it off only partly filled, it will expand to a normal size and not explode.
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