Hot air rises because it has expanded. It then displaces a greater volume of cold air, which

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Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it.

(a) Calculate the ratio of the buoyant force to the weight of 50.0°C air surrounded by 20.0°C air. 

(b) What energy is needed to cause 1.00 m3 of air to go from 20.0°C to 50.0°C? 

(c) What gravitational potential energy is gained by this volume of air if it rises 1.00 m3? Will this cause a significant cooling of the air?

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