Suppose you have a large hot air balloon, open at the bottom but filled with air that is heated to 50 °C while the outside air is 10 °C. What can you say about the air inside the balloon and how much it can lift? The density of air is surprisingly high: 1.23 kg/m3, an average hot air balloon has a volume of 3000 m3 , and the acceleration of gravity is 9.8 m/s2.
Suppose you have a large hot air balloon, open at the bottom but filled with air that is heated to 50 °C while the outside air is 10 °C. What can you say about the air inside the balloon and how much it can lift?
The density of air is surprisingly high: 1.23 kg/m3, an average hot air balloon has a volume of 3000 m3 , and the acceleration of gravity is 9.8 m/s2.
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The density is higher by the factor (273 + 50)/(273+10) = 1.14 and therefore will not have a buoyant force and will not lift off the ground with any load. |
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The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.88 times the weight of the air it replaced, or about 32,000 N. |
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The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.12 times the weight of the air it replaced, or about 4300 N. |
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The density is the same but the pressure of the hot air is higher by (273 + 50)/(273+10) = 1.14 and that lifts the balloon. |
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The density is lower by the factor (10)/(50) = 0.2 and therefore will have a buoyant force of 0.8 times the weight of the it replaced, or about 29,000 N. |
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