Problem 8: Hot air balloons float because the air inside an inflatable compartment is heated. Consider such a balloon that has an inflatable compartment of maximum volume 1960 m3 and a basket with passengers of total mass 280 kg. Part (a) To what temperature, in Celsius degrees, would the air inside the balloon have to be heated in order for the balloon to lift off the ground? Assume the molar mass of air is 28.97 g/mol and its density is 1.20 kg/m3. Part (b) When the balloon reaches the highest point of its flight (around 2000 m), the air pressure has dropped to 80% of the pressure at ground level, and the density has dropped to 85% of the previous value. What temperature, in degrees Celsius, must the air in the balloon be to keep it floating at this altitude?
Problem 8: Hot air balloons float because the air inside an inflatable compartment is heated. Consider such a balloon that has an inflatable compartment of maximum volume 1960 m3 and a basket with passengers of total mass 280 kg.
Part (a) To what temperature, in Celsius degrees, would the air inside the balloon have to be heated in order for the balloon to lift off the ground? Assume the molar mass of air is 28.97 g/mol and its density is 1.20 kg/m3.
Part (b) When the balloon reaches the highest point of its flight (around 2000 m), the air pressure has dropped to 80% of the pressure at ground level, and the density has dropped to 85% of the previous value. What temperature, in degrees Celsius, must the air in the balloon be to keep it floating at this altitude?
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