Modeling the Atmosphere, pt. 3

Pressure (y-axis) as a function of height (z-axis)

Parts one and two of modeling the atmosphere derived a way to describe atmospheric pressure as a function of altitude, assuming a constant temperature and acceleration due to gravity throughout the ideal gas. In this installment of Modeling the Atmosphere, the same function will be derived, this time using the Boltzmann distribution.

Modeling the Atmosphere, pt. 2

The previous Modeling the Atmosphere post derived an expression for describing the change in pressure $dP$ with respect to change in altitude $dz$ in terms of density $\rho$ and acceleration due to gravity $g$:

$\frac{dP}{dz} = -\rho g$

This equation is short to write, but it is not particularly useful. Before applying it to real-life situations, it must be transformed into the barometric equation.