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Barometric height distribution formula problem

  1. Nov 3, 2009 #1
    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
     
  2. jcsd
  3. Nov 4, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    show your working

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

    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

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