# 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.

# Modeling the Atmosphere, pt. 1

There’s a physics joke where a dairy farmer calls up the local university asking for some help improving his cow business. He ends up on the phone with a physicist, who assures the man that a solution can be found. Months later the farmer gets a call back. It’s the physicist, who says excitedly, “I can can help you, but my model only works for the case of spherical cows in a vacuum.”