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A balloon supports a total load of 185 kg at normal pressure (76 cm Hg) and temperature 27 deg C. If its volume stays constant, what load can it carry when it rises to an altitude where the barometric pressure is 45 cm Hg and the temperature is -7 deg C?
- 181.46 kg
- 214.15 kg
- 219.07 kg
- 123.54 kg
Correct answer: 123.54 kg
Solution
At fixed volume V, mass of displaced air = rho_air*V, and rho_air is proportional to P/T. The total upthrust equals weight of displaced air. The carried load is reduced because air density falls at altitude. Working through the proportionality with the given numbers yields about 123.54 kg.
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