Calculating Mass of Helium in a Balloon

AI Thread Summary
To calculate the mass of helium in a balloon with a diameter of 20 m and a gauge pressure of 2.0 atm, the ideal gas law is applied. The calculation involves converting pressure to pascals and using the volume of the balloon, which is derived from its diameter. The initial calculation yields a mass of 2061 kg, but the expected answer is 2050 kg. The discrepancy suggests a potential rounding issue or slight variations in the constants used. Ensuring accurate constants and calculations is crucial for obtaining the correct mass of helium.
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Homework Statement



A balloon 20 m in diameter is filled with helium at a gauge pressure of 2.0 atm. A man is standing in a basket suspended from the bottom of the balloon. A restraining cable attached to the basket keeps the balloon from rising. The balloon (not including the gas it contains), the basket and the man have a combined mass of 150 kg. the temperature is 24oC that day and the barometer reads 760 mm Hg.

What is the mass of helium?

Homework Equations



pV = nRT

The Attempt at a Solution



(3 atm x 101325 Pa/atm)(4/3*pi*(10^3)) = (m/0.004)(8.314)(297.15)
m = 2061 kg

But the correct ans is 2050 kg. Anyone pls help? thanks
 
Last edited:
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Well, your math is right so if your constants are right then you have the right answer.
 

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