Analytical expressions for the calculation of the thermodynamic properties of real air are presented. The expressions are derived from an equation of state proposed by Hirschfelder, et al. Although the region of interest is primarily that of low temperatures, the contribution of the vibrational energy is included, making the equations applicable to temperatures ranging from subcritical to 1500 K. Based on these equations, expressions are derived for the expansion of real air from fixed or variable plenum conditions, with the expansion of the air in the supply chamber ranging from isothermal to isentropic. It is shown that, compared with calculations based on perfect gas relations, the expansion of real air yields lower mass rate flows.

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