A rigorous approach for predicting the slope and curvature of the temperature–entropy saturation boundary of pure fluids

An accurate description of the geometry of the temperature-entropy (T–S) diagram is of fundamental importance for predicting the state of working fluids undergoing isentropic processes, as usually required for analyzing the performance of refrigeration and power generation systems. In this contribution, rigorous analytical expressions have been obtained for the first and second temperature derivatives of the entropy envelope along the vapor–liquid equilibrium (VLE) path of pure fluids. These relationships are valid from the triple point up o the critical state, and have been conveniently expressed in terms of Helmholtz’s energy, thus yielding a generalized method able to describe the geometry of the T–S diagram from typical equation of state (EOS) models. The customary classification of fluids in wet, isentropic or dry behavior has been reduced to a simple criterion based on a new dimensionless function ψ and how its value compares with the value of the isobaric heat capacity of the ideal gas. Applications are presented for cubic models of the van der Waals type, specific multi-parameter equations, molecular-based models, and virial density expansions. From these results it is concluded that dry behavior depends on the number of atoms that compose the molecule, and it will be generally observed in long-chained molecules.