Calculating Hot Air Balloon Volume & Lift

AI Thread Summary
The volume of the hot air balloon is calculated using the formula V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh), resulting in 2956.24 m³ with R=9m, h=15m, and r=1m. The balloon's mass is 750 kg, and at a height of 5000m with a temperature of 373 K, the pressure changes from p1 = 101300 Pa to p2 = 50650 Pa. The lift force is determined to be F = mg - 7350 N. Clarification is needed regarding the statement about not exceeding the temperature of the air inside by 100 degrees Celsius, as it is currently vague. Accurate calculations and clear parameters are essential for understanding hot air balloon dynamics.
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Homework Statement
We have to make a hot air balloon that can rise up to 5km and bring up 4 people. In total, the balloon weight is 750 kilogrammes. We cannot exceed the temperature of the air inside by 100 degrees C. We have to find how the temperature of air must change in order for the balloon to maintain a constant rising speed.
Relevant Equations
Fl = V (ρc - ρh) ag
Volume of hot air ballon
V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh) = 2956.24 m3

Balloon:
R=9m
h=15m
r=1m

m = 750 kg
H = 5000m
T = 373 K
p1 = 101300 Pa
p2 = 50650 Pa
M(air) = 0.029 kg/mol
F = mg - 7350 N
 
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You need to show more of an attempt at working this out. Also, "We cannot exceed the temperature of the air inside by 100 degrees C" is an ambiguous statement. Please clarify.
 
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