{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw1_soln - Physics 313 Problem Set 1 Due Wednesday by the...

This preview shows pages 1–2. Sign up to view the full content.

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 float 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 PV = 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 filled 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 . 23 × 10 25 m - 3 Now, if the bottom neck of the balloon is open to the air, the pressure inside the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online