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Resource: Floating and Sinking: Hot Air Balloons
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For example, an iron bar with the same dimensions as a wooden stick will weigh significantly more than the stick; it will have more mass. Although the two objects take up the same amount of space (they have the same volume), because one has more mass than the other, they must be composed differently inside.
The difference between two such objects is their density. The density of a material is determined by dividing an object's mass by its volume. This means that the greater the mass of a given volume of material, the higher the material's density.
For some materials, density remains almost fixed, regardless of environmental conditions. A block of steel, for example, has nearly the same density, whether it is at sea level or at an altitude of 3000 meters, and whether it is cooled to 0 degrees Celsius or warmed to 100 degrees Celsius. Since its volume barely changes when warmed that much, its density also stays almost the same.
In contrast, the density of gases varies dramatically under different environmental conditions. At higher temperatures, gas molecules move more rapidly and bump into each other more frequently. If maintained at same pressure while they are heated, they will expand, and decrease in density. The difference in the density of warm air inside a balloon and cool air outside the balloon causes a hot air balloon to rise and float.
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Source: NOVA Online Adventure: "Balloon Race Around the World"
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