hw1_soln - Physics 313 Problem Set 1 Due Wednesday...

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Physics 313 Problem Set 1 Due Wednesday September 13, 2006 by the end of class 1. Consider a hot air balloon with a volume of 1500 m 3 . It will Foat when its average density (including its payload) is less than the density of air. Suppose that the empty balloon plus its payload have a mass of 200 kg, and that the bottom neck of the balloon is open to the air. A What is the density of air at room temperature at ground level? Starting with P V = NkT , we get that the number density of air is N/V = P/kT . Multiplying the number density by the mass of one molecule gives the mass density. Air is roughly 75% N 2 (atomic mass 28) and 25% O 2 (atomic mass 32), which gives a mean atomic mass of 0 . 75 × 28+0 . 25 × 32 = 29. So one mole of air weighs 29 g, so one molecule weighs m = 29 g/ N A = 4 . 82 × 10 - 26 kg. So ρ = mN V = mP kT = (4 . 82 × 10 - 26 )(1 . 013 × 10 5 ) (1 . 38 × 10 - 23 )(293) = 1 . 21 kg / m 3 . B If the balloon is neutrally buoyant when full, what is the temperature of the air inside the balloon? Neutrally buoyant means the density of the ±lled balloon equals the density of air. If N is the number of air molecules inside the balloon, then the density of the balloon and payload (mass=200 kg) is ρ = 200 + mN V = 1 . 21 kg / m 3 . Plugging in V = 1500 m 3 and solving for N/V gives N V = 1 m ± 1 . 21 - 200 1500 ² = 2 . 23 × 10 25 m - 3 Now, if the bottom neck of the balloon is open to the air, the pressure inside the
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This note was uploaded on 03/11/2010 for the course PHYSICS 108 taught by Professor 0000 during the Fall '07 term at Clarke University.

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hw1_soln - Physics 313 Problem Set 1 Due Wednesday...

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