A hot air balloon rises when the air filled in the balloon
it is able to displace a volume of air that has a mass greater than the mass of the
balloon. This follows from Archimedes' Principle. The balloon continues to rise till the
condition mentioned earlier is satisfied. When the mass of the air displaced by the
balloon is equal to the mass of the balloon, it floats.
As
you can see from the values in the graph, air expands when it is heated. The expansion
means a decrease in density as density is given by mass/volume. You can see by the
points on the graph (278,110), (283, 112), (288, 114), (293,116), (298, 118), (303, 119)
that a point with a higher x-coordinate also has a higher
y-coordinate.
Atmospheric air cools as the altitude
increases. The balloon will rise till a certain altitude based on the temperature of the
gas filled in it. If the temperature of the gas is increased, it rises higher; on the
other hand, if the temperature of the gas filled in it is lowered, it drops to a lower
altitude.
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