Calculating Mass of Helium in a Balloon

In summary, the conversation is about finding the mass of helium in a balloon filled with helium at a specific gauge pressure and temperature, with a man and basket attached to it. The equation used is pV = nRT and the final answer should be 2050 kg according to the correct answer.
  • #1
titanium90
4
0

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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  • #2
Well, your math is right so if your constants are right then you have the right answer.
 

FAQ: Calculating Mass of Helium in a Balloon

How do you calculate the mass of helium in a balloon?

The mass of helium in a balloon can be calculated by using the ideal gas law, which states that the product of pressure and volume is equal to the number of moles of gas multiplied by the universal gas constant and the temperature. The number of moles of helium can be determined by dividing the volume of the balloon by the molar volume of helium at the given temperature and pressure.

What are the necessary measurements for calculating the mass of helium in a balloon?

To calculate the mass of helium in a balloon, you will need to know the volume of the balloon, the pressure inside the balloon, the temperature of the helium, and the molar volume of helium at the given temperature and pressure.

Can the mass of helium in a balloon change over time?

Yes, the mass of helium in a balloon can change over time as helium is a gas and can escape from the balloon. The rate at which helium escapes will depend on the material of the balloon and other external factors such as temperature and pressure.

How does the temperature affect the mass of helium in a balloon?

The temperature can affect the mass of helium in a balloon as it influences the volume of the gas. When the temperature increases, the volume of the helium will also increase, leading to a decrease in the mass of helium in the balloon.

What is the significance of calculating the mass of helium in a balloon?

Calculating the mass of helium in a balloon is important for understanding the behavior of gases and for practical applications such as in the fields of meteorology and balloon flight. It can also help in determining the amount of helium needed for a specific balloon size and in ensuring the safety of the balloon by not exceeding its lifting capacity.

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