Relative concentration vs. altitude

Discussion in 'Physics' started by boks, Jan 30, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    Earth's atmosphere has roughly four molecules of nitrogen for every oxygen molecule at sea level;
    more precisely, the ratio is 78:21. Assuming a constant temperature at all altitudes (not really very
    accurate), what is the ratio at an altitude of 10km? Explain why your result is qualitative reasonable.

    Hint; This problem concerns the number density of oxygen molecules as a function of height. The
    density is related in a simple way to the probability that a given oxygen molecule will be found at a
    particular height. You know how to calculate such probabilities.


    Any idea how to solve this?
     
    Last edited: Jan 31, 2009
  2. BillO

    Well-Known Member

    Nov 24, 2008
    985
    136
    At first glance, I'd be tempted to treat them like ideal gases, then use the ideal gas law and partial pressures to calulate the change in concentration with altitude.
     
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    PV = N k_B T, right?
     
  4. Alexei Smirnov

    Active Member

    Jan 7, 2009
    43
    1
    Use barometric formula at constant T for each gas separately:

    PN2(h)=PN2(0)*exp(-MN2*h*A)
    PO2(h)=PO2(0)*exp(-MO2*h*A)

    where A = g/kT (constant).

    Pressure ratio at height h is:
    PN2(h) / PO2(h) = PN2(0) / PO2(0) * exp( -(MN2-MO2)*h*A )

    The exponent with mass difference is responsible for pressure (or number of molecules) ratio change with altitude.

    Thanks,
    Alexei
     
  5. triggernum5

    Active Member

    May 4, 2008
    216
    0
    Does the ratio simply vary with the specific gravities?
     
  6. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    I found this formula, describing nanoparticles in air. I guess it then also can be used for gas molecules?

    [​IMG]
     
    Last edited: Feb 1, 2009
  7. Alexei Smirnov

    Active Member

    Jan 7, 2009
    43
    1
    and height
     
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