Air Pressure at Altitude

The sheet shows a derivation for the variation in Pressure with change in Altitude.  Actually, Temperature also changes with altitude, something known as the “Lapse Rate”. In order to take that into account, it is needed to solve two differential equations simultaneously (beyond the scope of this sheet – although only slightly).   The eigenvalue, (Mw g)/(R T), is frequently shown by dividing both numerator and denominator by Avogadro’s number, NA.  That results in mass in the numerator, mass=Mw/NA, and Boltzmann’s constant, k=R/NA, in the denominator.  The eigenvalue then becomes mg/kT.