-Z/Zo 3 The density of air as a function of altitude above sea level is modeled as p(z) = poe` where po = 1.2 kg/m³, and zo = 16, 855 m. A spherical balloon with radius r = 0.2 m is filled with Helium gas (MH₂ = 4 g/mol) to STP (P = 1 atm, T = 273 K). What is the maximum height the balloon can float up to assuming constant pressure and temperature within the balloon? Assume that the density of air is constant across the volume of the balloon for a specific height, and that the balloon's rubber has negligible mo

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Chapter5: Analysis Of Convection Heat Transfer
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The density of air as a function of altitude above sea level is modeled as p(z) = Pᵒe¯z/zo, where Po = 1.2
kg/m³, and Zo 16, 855 m. A spherical balloon with radius r = 0.2 m is filled with Helium gas (MHe = 4
g/mol) to STP (P = 1 atm, T = 273 K). What is the maximum height the balloon can float up to
assuming constant pressure and temperature within the balloon? Assume that the density of air is
constant across the volume of the balloon for a specific height, and that the balloon's rubber has
negligible mass.
Transcribed Image Text:The density of air as a function of altitude above sea level is modeled as p(z) = Pᵒe¯z/zo, where Po = 1.2 kg/m³, and Zo 16, 855 m. A spherical balloon with radius r = 0.2 m is filled with Helium gas (MHe = 4 g/mol) to STP (P = 1 atm, T = 273 K). What is the maximum height the balloon can float up to assuming constant pressure and temperature within the balloon? Assume that the density of air is constant across the volume of the balloon for a specific height, and that the balloon's rubber has negligible mass.
a (°℃−¹)
Material
Gold
Copper
Aluminum
1.65×10-5
2.3x10-5
Stainless Steel 1.75×10-5
Water
Ethyl Alcohol
Ice
1 atm = 1.01×105 Pa
NA = 6.022×102³ particles/mol
R = 8.3145 J/(mol K)
kB = 1.38×10-23 J/K
o = 5.67 × 10-8W/(m²K4)
c (J/(kg K)) C (J/(mol K)) | Lf (J/kg) Lv (J/kg) density (kg/m³)
129
25
19,300
8,960
2,700
7,500
4190
75
1,000
3.33×105 22.6×105
1.09×105 8.79×105
2400
110
790
2090
37.6
917
Transcribed Image Text:a (°℃−¹) Material Gold Copper Aluminum 1.65×10-5 2.3x10-5 Stainless Steel 1.75×10-5 Water Ethyl Alcohol Ice 1 atm = 1.01×105 Pa NA = 6.022×102³ particles/mol R = 8.3145 J/(mol K) kB = 1.38×10-23 J/K o = 5.67 × 10-8W/(m²K4) c (J/(kg K)) C (J/(mol K)) | Lf (J/kg) Lv (J/kg) density (kg/m³) 129 25 19,300 8,960 2,700 7,500 4190 75 1,000 3.33×105 22.6×105 1.09×105 8.79×105 2400 110 790 2090 37.6 917
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