2.When Felix Baumgartner made his parachute jump from the upper atmosphere, he w

Question

2.When Felix Baumgartner made his parachute jump from the upper atmosphere, he was at an
elevation of 39km where the temperature is 250K. At this height the helium ?lled balloon was
roughly spherical and had a diameter of 130m (radius 65m).
a)In class we derived the expression P = P0e^-z/z0 for pressure vs elevation, where z0=8000m. Estimate the pressure at z=39km, and then determine how many moles of helium
gas are in the balloon.
b)at ground level and at 300 K the density of air is 1.29kg/m3 and for helium 0.178kg/m3. What
are the air and helium gas densities at 39km and where the temperature is 250K (using the
pressure calculated in (a))?
c)Using the previous results, ?nd the mass of the capsule+payload+balloon used to get to 39km
elevation, given that the ballon and payload were neutrally buoyant at this elevation.

Explanation / Answer

a) P = Po * e^-39000/8000 = 7.64*10^-3 Po = 7.64*10^-3*1.013*10^5 = 773.932 Pa

V = (4/3)*pi*R^3 = (4/3)*3.14*(130/2)^3 = 1.149763e+6 m^3

P*V = n*R*T

n = P*V/RT = (773.932*1.149763e+6)/(8.314*250)

n = 428.11565e+3

b) Po/do*To = P/d*T

for air d = P*do*To/Po*T = (7.64*10^-3*1.29*300)/(250) = 0.011827 kg /m^3

for Helium   d = P*do*To/Po*T = (7.64*10^-3*0.178*300)/(250) = 0.001632 kg /m^3

c) M = d*V = 0.011827*1.149763e+6 = 13598.247001 Kg

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