The three isentropic exponents of dry steam

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 are also used for real gases if small or differential isentropic changes are considered. 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 leads to the conclusion that calculations encountered in real gas isentropic change, with the exponent k taken as the ratio of the local specific heat values may lead to incorrect results. The numerical values of these exponents for steam, have been calculated and are presented. It can be seen that the deviations obtained, in comparison to the use of conventional k=cp/cv values are considerable.