Isentropic Expansion and the Three Isentropic Exponents of R152a

Abstract The isentropic change of an ideal gas is described by the well known relations pvk = const., Tv(k-1) = const. and p(1-k)Tk = const., where the exponent k is defined as the ratio of the constant pressure to the constant volume specific heat, k = Cp/Cv. The same relations can be used for real gases only if the differential isentropic changes under consideration are small. A better examination of the differential isentropic change shows that for p, v, T systems, there are three different isentropic exponents corresponding to each pair formed out of the variables p, v, T. These three exponents noted kT,p, kT,v, kp,v after the corresponding pair of variables used, are interconnected by one relation, and accordingly only two out of the three are independent. The analysis of the present paper shows the numerical values of these exponents as well as the isentropic expansion ratios for R152a in the vapor phase, presented in diagram form. It can be seen that the deviations of the three isentropic exponents relative to the conventional k = Cp/Cv values are considerable and depend upon the initial pressure and the stage of the expansion. Additionally, the effect of the three isentropic exponents on the ideal gas relations describing the isentropic expansion ratios is examined, in order to develop simple yet more accurate relations without having to resort to the complex real gas state equations.