Ensure that the altitude is in kilometers. There are 3,280 feet in one kilometer. Therefore, divide the given elevation in feet by 3,280 to identify the elevation in kilometers.
Calculate the temperature of the air at the given elevation. This is accomplished by multiplying the elevation by the lapse rate, designated as 6.5 K/km, and subtracting the resulting value by the temperature in degrees Kelvin at sea level, which is established as 288 K.
Calculate the air pressure at the given elevation. The pressure is calculated as the elevation, in kilometers, multiplied by the lapse rate of 6.5 K/km. This value is then divided by the temperature at sea level, or 288K, and the resulting value is subtracted from 1. Finally, this new value is raised to a power of 5.3, thereby identifying the air pressure at a given elevation with units of Pascals.
Identify the air pressure at the given elevation using the previously calculated variables. The density of the air is equal to the product of the calculated pressure at the respective elevation and the molar mass of dry air (28.9 g/mol,) divided by the product of the calculated air temperature at the respective elevation and the universal gas constant, R (8.31 J/mol*K.) Thus, the final equation is given as:
Air density = (Air Pressure* Molar Mass of Air) / (Absolute Temperature * R)