Question

6) In the absence of turbulent mixing, the partial pressure of each constituent of air would fall off with PiPleMi8:/RT height above sea level in Earth's atmosphere as where Pi is the partial pressure of component i at height z, Po is the partial pressure of component i at sea level, g is the acceleration due to gravity, R is the gas constant, T'is the absolute temperature, and Mi is the molecular mass of component i. As a result of turbulent mixing, the composition of Earth's atmosphere is constant below an altitude of 100 km, but the total pressure changes with altitude as: where Mave is the mean molecular weight of air. At sea level: xN2-0.78084 and XHe 0.00000524 and T- 300. K a. Calculate the total pressure at 8.7 km, assuming a mean molecular mass of 28.9 g mol and that T-310K throughout this altitude range. b. Calculate the value that XN2/XHe (i.e., the ratio of the mole fractions of nitrogen to helium) would have at 8.7 km in the absence of turbulent mixing. Compare your answer with the correct value, and explain the deviation Hint(a): Be sure to check your units. What does the overall dimension of the argument of an exponential have to be? Hint(b): What is turbulent mixing, what does it mean for the gases?

Answer 1

Partial pressure of a molecule is air pressure multiplied by its mole fraction.

In 2nd part the deviation between the two values is due to turbulent mixing .

Partial pressure of a molecule is air pressure multiplied by its mole fraction. In 2nd part the deviation between the two values is due to turbulent mixing. We know P degree_air = 1.0125 times 10^5 Pa a) let total pressure will be p_tot. p_tot = p degree_air e^-M_avg middot gz/RT = 1.0125 times 10^5 pa exp (-28.9 times 10^-3 times 9.81 times 8.7 times 10^3/8.314 times 310) = 3.88 times 10^5 Pa b) we know that p x (i.e. mole fraction) P_N_2/P_H_e = x_N_2/x_H_e = 0.78084/5.24 times 10^-6 = 1.49 times 10^5 This is with turbulent mixing. P_N_2 = P degree_N_2 e^-m_N_2 gz/RT = 0.78084 times 1.0125 times 10^5 exp (-28.02 times 10^-3 times 9.81 times 8.7 times 10^3/8.314 times 300) = 3.03 times 10^4 Pa p_He = P degree_He e^M_He gz/RT = 5.24 times 10^-6 times 1.0125 times 10^5 exp (-4.003 times 10^-3 times 9.81 times 8.7 times 10^3/8.314 times 300) = 0.463 Pa x_N_2 = 6.54