Archimedes principle..Need help?
N identical balloons are filled with 0.061 Kg-moles of He at 273K to a gauge pressure of 0.50 atm. How
many such balloons, N, each having an empty mass of 0.01 Kg, will be required to just float a 12 Kg object at
STP? Assume air is 100% N2. Use Archimedes principle.
- Lucas CLv 77 years agoFavorite Answer
Archimedes Principle says that if the set-up just floats, then its weight must be equal to the weight of the displaced air. First let's calculate the mass and volume of each fully-inflated balloon.
The empty mass of the balloon is 0.01 kg, and it contains 0.061 kg of helium (I assume you meant kg and not moles). That gives each balloon a total mass of 0.071 kg. Now let's work out the volume.
The molar mass of helium is 4.0026 g/mol, or 0.0040026 kg/mol. So a balloon with 0.061 kg contains 15.2 moles of helium:
0.061 kg He x (1 mol He / 0.0040026 kg He) = 15.2 mol
If the gauge pressure is 0.50 atm, then the total pressure inside the balloon must be 1.50 atm (since the ambient pressure is standard, or 1 atm). And the temperature inside the balloon is 273 K. We have enough information to calculate the volume of the balloon:
PV = nRT
V = nRT / P = (15.2 mol)(0.0821 L*atm/mol*K)(273 K) / (1.50 atm)
V = 227 L
So each balloon displaces 227 L of air. Let's calculate the mass of 227 L of air (in this case, pure N2, molar mass = 28.013 g/mol) at STP
PV = nRT
n = PV / RT = (1 atm)(227 L) / (0.0821 L*atm/mol*K)(273 K)
n = 10.1 mol
10.1 mol N2 x (28.013 g N2 / 1 mol N2) = 284 g N2 = 0.284 kg
So each 0.071 kg balloon displaces 0.284 kg of air, a difference of 0.213 kg. The buoyant force on each balloon is therefore equal to the weight of 0.213 kg. If you want to lift a 12 kg mass (with apparently negligible volume), then you need:
N = 12 kg / 0.213 kg = 56.4 balloons
Of course you can't have 0.4 balloon, so let's say 56 balloons and a 57th balloon that's a little under-inflated.
I hope that helps. Good luck!
- jimmymae2000Lv 77 years ago
Impossible to fill a balloon to .5 atm,(in the atmosphere).
- 4 years ago
Could you elaborate?
- 7 years ago
Please see link for answer