(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The envelope and basket of a hot-air balloon have combined mass of 331 kg. The spherical envelope of the balloon has a radius of 10 m when fully inflated. What is the maximum mass of the passengers the balloon can carry when the temperature of the gas is 108 o C? Use M(air) = 29 g/mol. Assume that the surrounding air is at 25 o C and is treated as an ideal gas.

2. Relevant equations

Fbuoyancy = ρVg (density times volume times acceleration due to gravity)

3. The attempt at a solution

Not entirely sure if a buoyant force is acting here, but it makes sense as that's what we're learning.

Attempt:

Volume at 25 degrees = 4/3πr^3 = 4188 m^3

(101330Pa)(4188m^3) = n (8.314)(298K)

n = 171317 moles

(171317mol - n hotair) = (171317mol)(298K)/(381K)

n hotair = 37321 mol

171317 - 37321 = 133995 mol

(133995mol/m^3)(0.029kg/mol) = 3885 kg/m^3

Now assuming that is the density, I was trying to plug that into the buoyancy formula and calculate the force. However my force ends up way too big. The correct answer in the end should be 751 kg. Any help is appreciated!

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# Buoyancy force of a hot-air balloon

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