barometric height distribution formula problem

[8614smith]

1. The problem statement, all variables and given/known data
Consider the earth’s atmosphere assuming it is a mixture containing 79% N2 and 21% O2 gas. Furthermore, assume that the atmosphere is at an average constant temperature of 10o Celsius and that the acceleration due to gravity is g = 9.81 ms-2.

Using the barometric height distribution formula integrate over the atmosphere’s mass density
(from sea-level [height ‘0’] to very great heights [‘infinity’]) and thereby determine the earth’s atmosphere’s effective thickness [in terms of the density at sea-level].

2. Relevant equations
pV=NkBT


3. The attempt at a solution
how can a thickness be defined in terms of a density? and does mass density just mean density? ive integrated the barometric height formula between 0 and infinity and got to:

lnp(h) = -mg/kbT . h

h = -ln(p) kbT/mg = -97975m

which cant be right having researched it its around 9km
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[lanedance]

show your working

the integral will probably be over density as a function of height
I = \int_0^{infty} dh. \rho(h)

each part of the integral effectively adding up density times height, to get the "average" thickness based on sea level density, just divide by sea level density

h_{average} = \frac{\int_0^{infty} dh. \rho(h)}{\rho_{sea level}}