diffusion
- 73
- 0
I haven't had extensive experience in solving DE's just yet; I'm curious as to where the P(0) term comes from between the 4th and 5th expressions in the following derivation:
http://en.wikipedia.org/wiki/Barometric_formula#Derivation
My attempt follows:
[itex]\frac{dP}{P} = - \frac{M g\,dz}{kT}[/itex]
[itex]\int\frac{1}{P}dP = - \int\frac{M g}{kT}dz[/itex]
[itex]P = e^{-\int\frac{M g}{kT}dz}[/itex]
[itex]P = e^{-Mgz/kT}[/itex]
Clearly I'm missing something obvious, but I don't know what exactly.
http://en.wikipedia.org/wiki/Barometric_formula#Derivation
My attempt follows:
[itex]\frac{dP}{P} = - \frac{M g\,dz}{kT}[/itex]
[itex]\int\frac{1}{P}dP = - \int\frac{M g}{kT}dz[/itex]
[itex]P = e^{-\int\frac{M g}{kT}dz}[/itex]
[itex]P = e^{-Mgz/kT}[/itex]
Clearly I'm missing something obvious, but I don't know what exactly.