My NotesO Ask Your Teacher 5. ÷ 0112.5 points l Previous Answers ZinPhysLS3 11.

Question

My NotesO Ask Your Teacher 5. ÷ 0112.5 points l Previous Answers ZinPhysLS3 11. PO10. We consider a hot-air balloon of mass 241 kg (basket and envelope). The spherical envelope of the balloon has a diameter of 19 m when fully inflated. To what temperature (in °C) must the enclosed air be heated for the baloon to carry five standard men? Assume the surrounding air is at 20°C and is treated as an ideal gas. Use 29 g/mol for the molar mass of air. (Assume the mass of each standard man is 70 kg. Enter a number Need Help?Read It Submit Answer Save Progress Practice Another Version

Explanation / Answer

on balloon:

Fnet = Fb - m g = 0

Fb = V rho_out g

rho_out is the density of gas outside.

P V = n R T

P V = (m / M) RT

P M / R T = m / V = density

rho_out = (101325)(0.029) / (8.314)(273 + 20)

= 1.206 kg / m^3

V = 4 pi (19/2)^3 / 3 =3591.4 m^3

Fb = (1.206)(3581.4)(g) = 4331.18 g

m = (241 + (3581.4)(rho) + (5 x 70))

so (241 + (3581.4)(rho) + (5 x 70)) = 4331.18

rho = 1.044 kg / m^3

1.044 = P M / R T = (101325) (0.029) / (8.314 T)

T = 338.4 K or 65.4 deg C

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