Question

At what elevation in kilometres above sea level is the density of air 78% of that at sea level? Assume a temperature of 22°C. (Consider that the average molar mass of air is 29 g/mol.)

Answer 1

Please let me know if this is fine. Thanks.

We are temperature lapse rate is zero, or temperature is constant, then rho = rho_b exp [-2M (h - h_b)/R T_b] where rho_b is density of sea level, g is acceleration due to gravity, h - h_0 is height from sea level, T_b temperature. rho/rho_b = 78/100 = exp [-9.8 times 0.029 times Delta h/8.314 times (273 + 22)] Delta h = -(ln 78/100) times 8.31 times (273 + 22)/9.8 times 0.029 where we used, m = 29 g/mol = 0.029 kg/mole R = 8.314 N middot m/(mole middot k) g = 9.8 m/s^2, T = (273 + 22) k Delta h = 2144.21 meter = 2.144 km