A hot-air balloon stays aﬂoat because hot air at atmospheric pressure is less dense than cooler air at the same pressure.If the volume of the balloon is 500 m3 and the surrounding air is at 60◦F. What is the maximum load (including the weight of balloon, but excluding the weight of the hot air) the balloon can lift if the hot air is at 400◦F? The air density at 60◦F is 1.23 kg/m3.
F = ma
Fbuoyant = ρDF × g × VDF
pV = nRT
The Attempt at a Solution
1) My first thought is to apply Newton's Second Law:
2) ρoutgVB = (mballoon + mload + ρinVHotAir)g
F = ma ⇒ FB - Fg = 0
[Where ρout = air density outside of balloon and ρinVHotAir = mass of the air in the balloon]3) From here I can find ρin using the ideal gas law, VHotAir = VB, and I can isolate mballoon + mload but what is throwing me for a loop is the fact that it does not state this is an ideal gas and the say exclude the weight of the hot air. Would I just exclude ρinVHotAir from step two then?