Barometric height distribution formula problem

[8614smith]

Homework Statement

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 10^o 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].

Homework Equations

pV=Nk_BT

The Attempt at a Solution

how can a thickness be defined in terms of a density? and does mass density just mean density? I've integrated the barometric height formula between 0 and infinity and got to:

lnp(h) = -mg/k_bT . h

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

which can't be right having researched it its around 9km

 

[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

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