Chapter 1 SOlucionario WHITE
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Chapter 1 • Introduction 1.1 A gas at 20°C may b e rarefied if it contains less than 1012 molecules per mm3. If Avogadro‘s number is 6.023E23 molecules per mole, what air pressure does this represent? Solution: The mass of one molecule of air may be computed as Then the density of air containing 1012 molecules per mm3 is, in SI units, moleculesg10 4.81E23 moleculemm gkg4.81E11 4.81E5 m m Finally, from the perfect gas law, Eq. (1.13), at 20°C = 293 K, we obtain the pressure: 232 kgmpRT4.81E5 287 (293 K). ms K ns4.0Pa 1.2 The earth‘s atmosphere can be modeled as a uniform layer of air of thickness 20 km and average density 0.6 kg/m3 (see Table A-6). Use these values to estimate the total mass and total number of molecules of air in the entire atmosphere of the earth. Solution: Let Re be the earth‘s radius ≈ 6377 km. Then the total mass of air in the atmosphere is ta vg avg e32 m dVol(Air Vol)4R(Air thickness) (0.6 kg/m)4(6.377E6 m)(20E3 m) Dividing by the mass of one molecule ≈ 4.8E−23 g (see Pr ob. 1.1 above), we obtain the total number of molecules in the earth‘s atmosphere: molecules m(atmosphere)6.1E21 gramsN m(one molecule)4.8E23 gm/molecule Ans.== ≈− 1.3E44 molecules 2 Solutions Manual • Fluid Mechanics, Fifth Edition
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