where P is pressure, p is density, g is the acceleration of gravity and z is the vertical coordinate. We have two choices for describing dP/dz. For an ideal gas, PV = nRT where V is
The choices come in defining M for this mixture of gases. We might define M, for each gas separately, or we might define a mean value M = J2i XiA/I, where X, is the mole fraction of component i. The use of M, holds for P, of any individual species in the absence of any physical mixing (e.g., by turbulence or Brownian motion), while M would be used in the case of perfect mixing.
7.2.2 Scale Height
If we define a molecular weight for each constituent, then we can rearrange Equation (1). Because p = PM/RT, dP
neous only with respect to N2/ 02, 40Ar, and other long-lived gases).
In the case of a mixed atmosphere, M cannot be defined precisely since the composition is variable (especially due to water vapor). If dry air is assumed (which is a good approximation most of the time at altitudes above about 5 km), then M = 28.97 g/mol. If the atmosphere is assumed to be roughly isothermal, then from Equation (5) pressure falls off with altitude as
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