Isentropic exponents of real gases and application for the air at temperatures from 150 K to 450 K

Summary Three real gas isentropic exponentsk_Tv,k_rv,k_pT are introduced, which when used in place of the classical isentropic exponentk=c_p/c in the ideal gas isentropic change equations, the latter may describe very accurately the isentropic change of real gases. The usual practice of employing exponentk may lead to considerably incorrect results even when the value ofk corresponds to the correct local value ofc_p/c_v of the real gas under examination. The numerical values of the new exponents are calculated in the case of real air for temperatures from 150 K to 450 K and pressures from 1 bar to 1000 bar. It is seen that at low temperatures and high pressures the values of the new exponents differ considerably from the values of the classical exponentk. Therefore, the error resulting by approximating, as is usually the case, the behaviour of real gases by the ideal gas isentropic change equations in a stepwise fashion with exponentk instead of the new exponents, is considerable. It follows that exponentk, which appears in various relations in thermodynamics, fluid mechanics, gasdynamics, heat transfer etc., should be suitably replaced by combinations of the three exponents. Related numerical examples, made in the case of real air, showed that the use ofk leads (in the temperature and pressure ranges examined) to a 5% error in the calculation of blowby rate in internal combustion enginers, high pressure compressors or steam turbines and to a 50% error in the calculation of the isentropic expansion or compression.Nomenclature A_ij,B_i,N_ij,O_ij,Q_ij Coefficients - c Velocity - c_p Specific heat under constant pressure - c_v Specific heat under constant volume - h Specific enthalpy - k Isentropic exponent,k=c_p/c_v - k_pT Real gas isentropic exponent corresponding to the pair of variablesp,T - k_pv Real gas isentropic exponent corresponding to the pair of variablesp, v - k_Tv Real gas isentropic exponent corresponding to the pair of variablesT,v - M Mach number,M=c/ - p Pressure - p_c Pressure at the critical point - R Constant of the air,R=287.22 J/kg K - s Specific entropy - T Temperature - T_c Temperature at the critical point - v Specific volume - v_c Specific volume at the critical point - z Compressibility factor - Sound velocity - T Temperature incrementWith 14 Figures