Question

If the volume of the balloon is 500 m3m3 and the surrounding air is at 15.0 ∘C∘C, what must the temperature of the air in the balloon be for it to lift a total load of 290 kgkg (in addition to the mass of the hot air)? The density of air at 15.0 ∘C∘C and atmospheric pressure is 1.23 kg/m3

Answer 1

Answer:

Temperature of the air in the balloon = 272°C

Explanation:

Given:

Volume of balloon = 500 m³

Air temperature = 15° C = 273 + 15 = 288 K

Total weight = 290 kg

Density of air = 1.23 kg/m³

Find:

Temperature of the air in the balloon

Computation:

Density of hot air = Density of air - [Total weight / Volume of balloon]

Density of hot air = 1.23 - [290 - 500]

Density of hot air = 0.65 kg/m³

[Density of hot air][Temperature of the air in the balloon] = [Density of air][Air temperature ]

Temperature of the air in the balloon = [(1.23)(288)]/(0.65)

Temperature of the air in the balloon = 544.98

Temperature of the air in the balloon = 545 K

Temperature of the air in the balloon = 545 - 273 = 272°C