Atmospheric Density, exponential decay derivation

1. Nov 19, 2007

tony_cruz

I've read my lecture notes about 100x but can't even begin to see where this derivation can come from. A previous derivation was the equation
dP/dz = -gρ
(P = pressure, z = distance, g= acc due to grav, ρ = density)

If atmosphere can be treated as an isothermal ideal gas of constant mean molecular mass m, show that density drops exponentially with height,
ρ= [ρ0]e^-z/h
where h is a constant*

later i worked through to find it was the scale height ~8.5km but the value is unknown for this question.

2. Nov 19, 2007