How Does Archimedes' Principle Determine the Payload of a Hot Air Balloon?

[barry3rd]

Archimedies Principle!

Homework Statement

Hot air balloon question. We are not given the density nor are we able to look it up.
cold air is 278K, hot air is 313K
radius of balloon = 10
What is its payload capabilities?!

Homework Equations

payload = mass of cold air - mass of hot air
pV=nRT
P1V1/T1 = P2V2/T2

The Attempt at a Solution

P1 = 101 kpa which i think is a constant
P2 = P1x(T2/T1)
= 101x(313/278)
=113.7 kpa

working this into the pV = nRT is where the trouble is

 

[katchum]

Fill in n=m/M?

You know V, T. So you can calculate m. For M you have O2 and N2 in the air. Use Mendeljev.