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

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SUMMARY

This discussion focuses on calculating the payload capabilities of a hot air balloon using Archimedes' Principle and the Ideal Gas Law. The key parameters include the temperatures of cold air (278K) and hot air (313K), and the balloon's radius of 10 meters. The pressure calculations yield P2 = 113.7 kPa based on the relationship P1V1/T1 = P2V2/T2. The mass of the air can be determined using the Ideal Gas Law, where n = m/M, with M being the molar mass of air components like O2 and N2.

PREREQUISITES
  • Understanding of Archimedes' Principle
  • Familiarity with the Ideal Gas Law (pV=nRT)
  • Basic knowledge of gas laws and pressure calculations
  • Ability to calculate molar mass of gases (O2 and N2)
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  • Learn about the Ideal Gas Law and its implications for gas behavior
  • Research methods to calculate the molar mass of air components
  • Explore practical examples of hot air balloon payload calculations
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Students studying physics, engineers involved in aerodynamics, and anyone interested in the principles of buoyancy and gas laws in relation to hot air balloon design.

barry3rd
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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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