Page 5 of 5 Problem 4: A spherical helium filled balloon must be inflated to 150
ID: 1796508 • Letter: P
Question
Page 5 of 5 Problem 4: A spherical helium filled balloon must be inflated to 1500. m2 at sea level. As it rises in the earth's atmosphere, the volume of the balloon expands and the balloon will rise to a maximum altitude of 12.0 km, where the temperature is-46.6°F and the pressure is about 20.0 kPa. What assumptions did you make in each part. (a) (10 points) What will be its new volume at the 12.0 km altitude? (bX10 points) what is the buoyant force on the helium filled ballon at this alt of 125 kg and decr12.0 km ifthe empty balloon has a mass (i) what is the density of air at this altitude of 12.0 km?Explanation / Answer
(A) Applying P V / T = constant
(101.3 kPa) (1500 m^3) / (273 + 20) = (20 kPa) (Vf) / (273 - 43.7)
Vf = 5946 m^3
(b) (i) Fnet = Fb - m g =0
Fb = m g
mole of helium, (20 x 10^3) (5946) = n (8.314) (273 - 43.7)
n = 62376 mol
m = (125) + (62376 x 0.004) = 374.5 kg
Fb = 374.5 x 9.8 = 3670 N
(ii) Fb = V rho g
374.5 g = (5946)(rho)(g)
rho = 0.0630 kg / m^3
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