1st year physic help - hot air balloons

AI Thread Summary
The discussion focuses on calculating the average temperature of the air inside a hot air balloon using principles of buoyancy and gas laws. The buoyancy force is determined to be equal to the weight of the balloon and its passengers, leading to a calculation of the required density of the cooler air outside. The volume of the balloon is calculated, and the density of the cooler air is found to be 0.066 kg/m³. The participant questions whether it is valid to assume that the pressure inside the balloon matches the outside pressure of 90 kPa and discusses the relationship between temperatures and densities of the air inside and outside the balloon. The analysis is on track for determining the air temperature in the balloon.
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1st year physics help - hot air balloons...

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question:

The buoyancy force that pushes the balloon upward is proportional to the density of the cooler air outsider the balloon and the volume of the balloon, and can be expressed as

force buoyancy = denisty(ofcoolair)*g*volume(ofballoon)

where g is the gravitational constant.

Consider a 20-m-diameter hot-air balloon that, together with its cage, has a mass of 80 kg when empty. This balloon is hanging still in the air at a location where the atmospheric pressure and temperature are 90 kPa and 15 o C, respectively, while carrying three 65 kg people. Determine the average temperature of the air in the balloon.

this is what I have so far...

The buoyancy force required for the balloon to hang still in the air is equal to the force exerted downwards by the weight of the balloon so:

Force buoyancy, Fb = mass*gravity = 275*9.81 = 2697.75 N
Therefore:

denisty(ofcoolair)*g*volume(ofballoon) = 2697.75 N

volume(of balloon) = 4/3*pi*10^3 = 4188.79 m^3

density(ofcoolair) = 0.066 kg m^3

I know that for the balloon to be hanging still:

density(ofcoolair) = density(ofhotair)

Is it ok to assume that the pressure inside the balloon is the same as the outside (90kPa)? I'm also assuming that V1 = V2. Which would give me the expression:

T2/T1 = n1/n2

Am I heading in the right direction?
 
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