Question

At what elevation in kilometres above sea level is the density of air 68% of that at sea level? Assume a temperature of 11°C. (Consider that the average molar mass of air is 29 g/mol.)

Answer 1

Density of air above sea level = 0.68 x 1.20 = 0.816 kg/m^3

Pressure, P = (0.816 x 8.314 x 284) /0.029 = 66438.61 Pa

Ln(P/Po) = - mgh/kT

Ln(66438.61/101325) = - (0.029 x 9.8 x h) /(1.38 x 10^-23 x 284)

-0.422 = - 7.25 x 10^19 h

Height h = 5.82 x 10^-21 x 6.02 x 10^23/1000 = 3.50 km

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