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

Abstract

Three real gas isentropic exponentskTv,krv,kpT are introduced, which when used in place of the classical isentropic exponentk=cp/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 ofcp/cv 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.