Editing Barometric formula (section)

==Derivation==
The barometric formula can be derived using the [[ideal gas law]]:
<math display="block"> P = \frac{\rho}{M}  {R^*} T</math>

Assuming that all pressure is [[Hydrostatic pressure|hydrostatic]]:
<math display="block"> dP = - \rho g\,dz</math>
and dividing this equation by <math> P </math> we get:
<math display="block"> \frac{dP}{P} = - \frac{M g\,dz}{R^*T}</math>

[[Integral|Integrating]] this expression from the surface to the altitude ''z'' we get:
<math display="block"> P = P_0 e^{-\int_{0}^{z}{M g dz/R^*T}}</math>

Assuming linear temperature change <math>T = T_0 - L z</math> and constant molar mass and gravitational acceleration, we get the first barometric formula:
<math display="block"> P = P_0 \cdot \left[\frac{T}{T_0}\right]^{\textstyle \frac{M g}{R^* L}}</math>

Instead, assuming constant temperature, integrating gives the second barometric formula:
<math display="block"> P = P_0 e^{-M g z/R^*T}</math>

In this formulation, ''R<sup>*</sup>'' is the [[gas constant]], and the term ''R<sup>*</sup>T''/''Mg'' gives the [[scale height]] (approximately equal to 8.4&nbsp;km for the [[troposphere]]).

(For exact results, it should be remembered that atmospheres containing water do not behave as an ''ideal gas''. See [[real gas]] or [[perfect gas]] or [[gas]] for further understanding.)