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1.0125, representative of a generic heavy fluorocarbon. The van der Waals gas exhibits a very large inversion zone. Outside this zone, the fundamental derivative quickly increases, reaching values close to 3 already at a short distance from the transition line, and tends to the perfect gas value when the specific volume tends to infinity. A more accurate model is the the Martin-Hou equation of state [3], which provides a realistic description of the gas behavior and of the inversion zone size: −5.475T p= RT +A2 +B2T+C2e c (V −b) (V −b)2 −5.475T +A3 +B3T+C3e c (V −b)3 (Eq. (V −b)5 7) + A4 (V −b)4 + B5T where the coefficient Ai, Bi, Ci, are functions of the particular gas considered, Tc is the critical temperature, and b is the co-volume. Such equation, involving five virial terms and satisfying ten thermodynamic constraints, ensures high accuracy with a minimum amount of experimental information. A power law is used to model variations the low-density specific heat with temperature. It is not possible to explicitly relate the pressure with the internal energy, that requires often an iterative method to compute thermodynamic properties. In the Figure 1b, the Amagat (p-v) diagram of a real gas modelled through the Martin-Hou equation of state, namely, heavy fluorocarbon pf-perhydrouorene (commercial name PP10) is reported. On the contrary with respect to the vdW equation (see Figure 1a), the inversion zone for PP10 is much more reduced. Nevertheless, the increase of Γ outside the inversion zone for increasing pressure is much slower. For further details concerning the evaluation of the coefficients Ai, Bi, Ci see [43]. 35PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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