Question

The mass of a hot-air balloon and its occupants is 295 kg (excluding the hot air inside the balloon). The air outside the balloon has a pressure of 1.01 x 105 Pa and a density of 1.29 kg/m3. To lift off, the air inside the balloon is heated. The volume of the heated balloon is 568 m3. The pressure of the heated air remains the same as that of the outside air. To what temperature in kelvins must the air be heated so that the balloon just lifts off? The molecular mass of air is 29 u.

Answer 1

T = 457.2 K

Step-by-step explanation:

mass of balloon (Mb) = 295 kg

pressure of outside air (Pa) = 1.01 x 10^{5}

density of air (ρ) = 1.29 kg/m^{3}

volume (v) = 568 m^{3}

molecular mass of air (m) = 29 u

F = mg = ρvg

(Mb + Ma)g = ρvg

(Mb + Ma) = ρv

295 + Ma = 1.29 x 568

Ma = 437.72 kg = 437.72 x 10^{3} g

number of moles (n) = mass / molar mass

number of moles (n) = 437.72 x 10^{3} / 29 = 15,093.8 moles

from the ideal gas law pv = nRT

T =
`(pv)/(nR)`

T =
`(1.01 x 10^(5) x 568)/(15,093.8 x 8.314)`

T = 457.2 K