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What is this equation?

  1. Sep 17, 2013 #1
    p(h) = (p0e)-(mgh/kT)

    where p0 is the atmosphere at sea level, m is the mass of an object at height h, g is the gravitational proportionality constant...

    is there a specific name for this equation? is this derived from the Boltzmann’s distribution law? Also, I'm really confused about what e is... Thank you!
  2. jcsd
  3. Sep 17, 2013 #2
    e is Euler's number, about 2.7. Search wiki for it.

    It's the pressure at a height, h at a temperature T. k is Boltzmann's constant.
  4. Sep 17, 2013 #3
    Also g is not the same thing as G. G is the gravitational proportionality constant, g is the acceleration due to gravity.
  5. Sep 17, 2013 #4

    Ken G

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    Also,the p_o should not be inside the parentheses. Only the e is being raised to that power. It is not a Boltzmann factor, that would be statistical physics. This is a solution to a force equation, the hydrostatic equilibrium that looks like dp/dh = -rho * g, where rho = mp/kT from the ideal gas law and p is gas pressure.
  6. Sep 17, 2013 #5


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    It's the Law of Atmospheres:
    http://www.cmmp.ucl.ac.uk/~als/teaching/1B28/Lecture notes/Lecture_8.pdf

    See p. 4 of the attachment.

    It predicts the number of gas molecules at a given height h, and consequently the pressure at that height in terms of the surface pressure Po.

    N.B.: k is indeed Boltzmann's constant.
  7. Sep 18, 2013 #6

    D H

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    And m is the mean molecular mass of air.
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