A pioneer aeronaut is planning the design of a hot-air balloon. What volume of air, in m³, at 100°C should be used if the balloon is to have a lifting power of 200 kg. The ambient temperature and pressure are 25°C and 1 atm, and the average molecular weight of air is 29 g/mol, whereas that of the hot air is 32 g/mol (due to the presence of some carbon dioxide). (Note that the lifting power is equal to the difference in the masses, for a given volume, of the surrounding air and the gas (hot air) inside the balloon.)

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R = 0.08205 L atm mol-1 K-1

T(K) = T (°C) + 273.15

A pioneer aeronaut is planning the design of a hot-air balloon.
What volume of air, in m³, at 100°C should be used if the balloon
is to have a lifting power of 200 kg. The ambient temperature and
pressure are 25°C and 1 atm, and the average molecular weight
of air is 29 g/mol, whereas that of the hot air is 32 g/mol (due to
the presence of some carbon dioxide).
(Note that the lifting power is equal to the difference in the masses, for
a given volume, of the surrounding air and the gas (hot air) inside the
balloon.)
Transcribed Image Text:A pioneer aeronaut is planning the design of a hot-air balloon. What volume of air, in m³, at 100°C should be used if the balloon is to have a lifting power of 200 kg. The ambient temperature and pressure are 25°C and 1 atm, and the average molecular weight of air is 29 g/mol, whereas that of the hot air is 32 g/mol (due to the presence of some carbon dioxide). (Note that the lifting power is equal to the difference in the masses, for a given volume, of the surrounding air and the gas (hot air) inside the balloon.)
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