When heat is lost to the air, some is absorbed by nitrogen, some is absorbed by oxygen, and a tiny amount is absorbed by argon, carbon dioxide, water vapor, and trace gases. You can write
where xO2 and xN2 are moles of oxygen and moles of nitrogen per mole of air, and Cp(O2) and Cp(N2) are the constant pressure molar heat capacites for pure oxygen and nitrogen gases.
Heat absorbed by one mole of air = heat absorbed by O2 + heat absorbed by N2 + ... = xO2Cp(O2)T + xN2Cp(N2) T + ...
Assume that air is 21% oxygen, and 79% nitrogen by volume. If you can assume that the air behaves ideally, Avogadro's law says that the volume fraction for each gas is also its mole fraction. Since the heat absorbed by one mole of air should be Cp(air) times the change in temperature, you should be able to quickly estimate the heat capacity of air given Cp data for oxygen and nitrogen at the temperature you're interested in.
Assuming again that the air behaves ideally, the mole density (moles per unit volume) of air should be P/RT. You can convert the the mole density to a mass density using the molecular weight of air. The average molecular weight of a mixture is easy to calculate if you know the mole fractions of each component in the mixture:
M(mix) = x1M1 + x2M2 +...where xi and Mi are the mole fractions and molecular weights for the i-th component in the mixture. This is exactly how average atomic weights are computed from isotopic masses and abundances...
Author: Fred Senese email@example.com
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Last Revised 08/17/15.URL: http://antoine.frostburg.edu/chem/senese/101/thermo/faq/print-heat-capacity-air.shtml