User:Milton Beychok/Sandbox

$P_{\mathrm {h} }=P_{0}\cdot \left({\frac {T_{0}-L\cdot h}{T_{0}}}\right)^{\frac {g\cdot M}{R\cdot L}}$

which, for the parameter values below, then becomes:

$P_{\mathrm {h} }=P_{0}\,\cdot {\bigg (}{\frac {T_{0}-6.5h}{T_{0}}}{\bigg )}^{5.2558}$

Given an air pollutant concentration at sea-level atmospheric pressure, the concentration at higher altitudes can be obtained from this equation:

$C_{\mathrm {h} }=C_{0}\,\cdot {\bigg (}{\frac {T_{0}-6.5h}{T_{0}}}{\bigg )}^{5.2558}$

where:
L	= atmospheric temperature lapse rate = 6.5 K/km
h	= altitude, km
g	= Earth's surface gravitational acceleration = 9.80665 m/s2
M	= Molecular weight of air = 28.9644 g/mol
R	= Universal gas constant = 8.314472 J/(mol • K)
P 0	= absolute atmospheric pressure at sea level (in any selected pressure units)
P h	= absolute atmospheric pressure at altitude h (in the same pressure units as P 0)
C	= Air pollutant concentration, in mass per unit volume at sea level atmospheric pressure P 0 and specified temperature T0 (commonly 288.15 K)
C h	= Concentration, in mass per unit volume at altitude h and specified temperature T0