Calculating Hot Air Balloon Volume & Lift

In summary, the volume of a hot air balloon can be calculated by multiplying the balloon's radius squared by pi (π) and then multiplying that by the height of the balloon. The lift capacity of a hot air balloon is dependent on several factors, including the size of the balloon, the temperature of the air inside the balloon, and the weight of the basket, passengers, and fuel. The lift of a hot air balloon is directly affected by the temperature of the air inside the balloon, with hot air producing more lift than cold air. The maximum altitude a hot air balloon can reach depends on various factors, with specialized balloons being able to reach heights of 20,000 feet or more. The lift of a hot air balloon is affected by
  • #1
Desperate
1
0
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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  • #2
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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