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Pressure inside a balloon

by rubenhero
Tags: combined gas law, pressure
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rubenhero
#1
Dec3-11, 01:28 AM
P: 42
1. The problem statement, all variables and given/known data
g) A spherical balloon of radius R = 1.95 m is made from a material of mass M = 4.56 kg and is filled with helium gas at temperature T = 289 K. Assume the thickness of the balloon is negligible compared to the radius of the balloon, and the balloon just floats on air, neither rising nor falling. If the density of the surrounding air is ρ = 1.13 kg/m3, find P, the absolute pressure of the helium inside the balloon.
ASSUME: The balloon material displaces a negligible amount of air, and therefore creates no measurable buoyancy.


2. Relevant equations
M g = ρ V g, PV = nRT, Volume of sphere = 4/3(∏r3), n = total mass/molar mass


3. The attempt at a solution
V = 4/3(∏r3)
V = 4/3(∏1.953)
V = 31.05935577m3

M g = ρ V g
MHe g = 1.13 kg/m3 * 31.05935577m3 * g
MHe = 35.09707202 Kg = 35097.07202g

n = total mass/molar mass = total mass He/molar mass He
n = 35097.07202g/ (4g/mol)
n = 8774.268005 mol

P= (nRT)/V
P = (8774.268005 mol * 8.314 J/mol-K * 289K) / 31.05935577m3
P = 678775.745 Pa

I thought all the steps I took were right, but the answer I calculated is wrong. Any help with figuring out what I did wrong is appreciated!
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ehild
#2
Dec3-11, 01:37 AM
HW Helper
Thanks
P: 10,354
You ignored the mass of the balloon material, M(balloon)=4.56 kg.

ehild
rubenhero
#3
Dec3-11, 01:41 AM
P: 42
Wouldn't that mass be ignored if the balloon material displaces a negligible amount of air?

ehild
#4
Dec3-11, 02:09 AM
HW Helper
Thanks
P: 10,354
Pressure inside a balloon

The volume of the ballon material is ignored, but not its mass. It is given as 4.56 kg. The buoyant force is equal to the total weight: the sum of the (mass of balloon material + the mass of helium) times g.

ehild
rubenhero
#5
Dec3-11, 02:24 AM
P: 42
Thank you for your help ehild, that "ASSUME: The balloon material displaces a negligible amount of air, and therefore creates no measurable buoyancy. " part really confused me. I accounted for the mass of the balloon material and got an answer to be 590585.5565Pa, I put in 5.90e5Pa and it is the right answer.
ehild
#6
Dec3-11, 02:40 AM
HW Helper
Thanks
P: 10,354
Splendid!

ehild


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