Calculating Hot Air Balloon Volume & Lift

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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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Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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