# Pressure At Surface And Scale Height

by bobbles22
Tags: atmospheric pressure, barometric formula, scale height
 P: 13 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.
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