How Does Turbulent Mixing Affect Atmospheric Pressure with Altitude?

[speny83]

In the absence of turbulent mixing, the partial pressure of each constituent of air would fall off with height above sea level in Earth's atmosphere as Pi=P_0ie^−Migz/RT where Pi is the partial pressure at the height z, P_0i is the partial pressure of component i at sea level, g is the acceleration of gravity, R is the gas constant, T is the absolute temperature, and M_i is the molecular mass of the gas. As a result of turbulent mixing, the composition of Earth's atmosphere is constant below an altitude of 100 km, but the total pressure decreases with altitude as P=P₀e^{−M_avegz/RT} where M_ave is the mean molecular weight of air. At sea level, x_N2= 0.78084 and x_He= 0.00000524 and T= 300. K.


Im not really sure where to start with this. I figured maybe just start with the exponent of e and I am confused right off the bat. using the info give it would be e^(28.9 g mol^-1)(9.81m s^-2)(6500m)/(300k)(R)...so I am not sure what R to use, also i sort of remember something about e not being able to be raised to something with units and i end up with all kinds of units left all over the place?

 

[Office_Shredder]

Well if e can't be raised to something with units, then R better have units of g /(K mol s² m²).

Noting that g/(m² s²) is almost the units for a joule (replace gram with kilogram, which you should be able to figure out how to do in the original statement), and I'd say what you have is the good ol' fashion gas constant in J/(mol K)

http://en.wikipedia.org/wiki/Gas_constant

 

[speny83]

I had no idea that was equivalent. the book I've been using does not mention that, guess that was supposed to be something i remembered from HS about 15 years ago! But I am correct about the e power unit thing, at least something is still in there haha!

thanks