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Barometric formula and height ratios

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Starting from the barometric formula for a thin, isothermal atmosphere, show that the ratio of the pressure P(z2) at height z2 to the pressure P(z1) at height z1 is given by

    P(z2)/P(z1) = e(-(z2-z1)/y) where y is the scale height

    2. Relevant equations
    Barometric formula: P(z) =P(0) e(-z/y)


    3. The attempt at a solution
    looks easy but i just can see how?
     
  2. jcsd
  3. Jan 16, 2012 #2

    Simon Bridge

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    If it looks easy, then you should be able to see how.
    Have you tried writing P(z1) and P(z2) in the barometric formula and just dividing them?

    aside: on notation:

    P(z)=P(0).exp(-z/y) ... in plain text, or, in LaTeX (worth learning)
    [tex]P(z)=P_0 e^{-z/y}[/tex]
     
    Last edited: Jan 16, 2012
  4. Jan 16, 2012 #3
    I'm afraid my algebra is a little rusty, how do you divide e(-z2/y) by e(-z1/y)?
     
  5. Jan 16, 2012 #4

    Simon Bridge

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    property of powers
    [tex]x^a x^b = x^{a+b}[/tex]... it's the same for the exponential function.
     
  6. Jan 16, 2012 #5
    got it... just clicked
     
  7. Jan 16, 2012 #6

    Simon Bridge

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    :) I get blind spots like that sometimes.
     
  8. Jan 16, 2012 #7
    Yeah, thanks for the memory jog :-)
     
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