Pressure At Surface And Scale Height

  1. Please can someone tell me if my thinking here is right...

    I've got a planet with an atmospheric pressure at 6km of 0.5 P0 and at 8km of 0.4 P0 (P0 = pressure at the surface).

    I want to work out the scale height of the atmosphere.

    Given scale height = λ

    and for height above surface = z

    P(z)=P(0)e(-z/λ)

    I could rearrange to show the pressure at the surface as:

    P(0)=P(z)/e(-z/λ)

    I could then use the relative pressure, assume P(0)=1 (as it will cancel out shortly) and height from each of the know quantities and set them equal to each other like this:

    0.4/e(-8000/λ) = 0.5/e(-6000/λ)

    A little mutliplication....

    0.4 e(-6000/λ) = 0.5 e(-8000/λ)

    Take the Log of both sides....

    (-6000/λ) log 0.4 = (-8000/λ) log 0.5

    But know I'm left with the λ cancelling out if I multiply both sides by λ. I'm sure I've gone wrong here somewhere. Probably something very simple. Can anyone advise? Have I made a simple mistake in my working or have I gone completely off the reservation and need to start again? I just need to end up with λ = xxx metres.

    Thank you.
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    hi bobbles22! :smile:
    nooo :wink:

    (-6000/λ) + log 0.4 = (-8000/λ) + log 0.5 :smile:
     
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