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

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Archimedes' Principle is applied to determine the payload capacity of a hot air balloon by comparing the mass of cold air and hot air. Given the temperatures of cold air at 278K and hot air at 313K, along with a balloon radius of 10, the pressure calculations yield P2 as 113.7 kPa. The equation pV=nRT is used to derive the mass of the air, where n equals mass divided by molar mass. The challenge lies in accurately calculating the mass using the ideal gas law, considering the composition of air primarily consists of O2 and N2. Understanding these principles is crucial for determining the balloon's payload capabilities.
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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
 
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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.
 

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