This work reviews the available data on thermodynamic properties of carbon dioxide and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. The function for the residual part of the Helmholtz free energy was fitted to selected data of the following properties: (a) thermal properties of the single-phase region (ppT) and (b) of the liquid-vapor saturation curve (Ps> p', p") including the Maxwell criterion, (c) speed of sound w and (d) specific isobaric heat capacity c p of the single phase region and of the saturation curve, (e) specific isochoric heat capacity c v' (f) specific enthalpy h, (g) specific internal energy u, and (h) Joule-Thomson coefficient /-t. By applying modern strategies for the optimization of the mathematical form of the equation of state and for the simultaneous nonlinear fit to the data of all these properties, the resulting formulation is able to represent even the most accurate data to within their experimental uncertainty. In the technically most important region up to pressures of 30 MPa and up to temperatures of 523 K, the estimated uncertainty of the equation ranges from ± 0.03% to ± 0.05% in the density, ± 0.03% to ± 1 % in the speed of sound, and ± 0.15% to ± 1.5% in the isobaric heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation. Without a complex coupling to a scaled equation of state, the new formulation yields a reasonable description even of the caloric properties in the immediate vicinity of the critical point. At least for the basic properties such as pressure, fugacity, and enthalpy, the equation can be extrapolated up to the limits of the chemical stability of carbon dioxide. Independent equations for the vapor pressure and for the pressure on the sublimation and melting curve, for the saturated liquid and vapor densities, and for the isobaric ideal gas heat capacity are also included. Property tables calculated from the equation of state are given in the appendix.

In a preceding project, functional forms for "short" Helmholtz energy equations of state for typical nonpolar and weakly polar fluids and for typical polar fluids were developed using simultaneous optimization. In this work, the coefficients of these short forms for the equations of state have been fitted for the fluids acetone, carbon monoxide, carbonyl sulfide, decane, hydrogen sulfide, 2-methylbutane (isopentane), 2,2-dimethylpropane (neopentane), 2-methylpentane (isohexane), krypton, nitrous oxide, nonane, sulfur dioxide, toluene, xenon, hexafluoroethane (R-116), 1,1-dichloro-1-fluoroethane (R-141b), 1-chloro-1,1-difluoroethane (R-142b), octafluoropropane (R-218), 1,1,1,3,3-pentafluoropropane (R-245fa), and fluoromethane (R-41). The 12 coefficients of the equations of state were fitted to substance specific data sets. The results show that simultaneously optimized functional forms can be applied to other fluids out of the same class of fluids for which they were optimized without significant loss of accuracy. The high numerical stability of the functional forms resulted in successful fits for fluids that previously could not be described by accurate empirical equations of state. For R-41, it is shown that the accuracies can be increased further by fitting the temperature exponents in addition to the coefficients of the equation of state, provided that highly accurate experimental data are available. Typical uncertainties of properties calculated using the new equations are 0.2 % in density, 1 % to 2 % in heat capacity and liquid-phase speed of sound, and 0.2 % in vapor pressure. Where data are available, uncertainties in vapor-phase sound speeds are generally less than 0.1 %.

A new formulation for the thermodynamic properties of nitrogen has been developed. Many new data sets have become available, including high accuracy data from single and dual-sinker apparatuses which improve the accuracy of the representation of the pT surface of gaseous, liquid, and supercritical nitrogen, including the saturation states. New measurements of the speed of sound from spherical resonators yield accurate information on caloric properties in gaseous and supercritical nitrogen. Isochoric heat capacity and enthalpy data have also been published. Sophisticated procedures for the optimization of the mathematical structure of equations of state and special functional forms for an improved representation of data in the critical region were used. Constraints regarding the structure of the equation ensure reasonable results up to extreme conditions of temperature and pressure. For calibration applications, the new reference equation is supplemented by a simple but also accurate formulation, valid only for supercritical nitrogen between 250 and 350 K at pressures up to 30 MPa. The uncertainty in density of the new reference equation of state ranges from 0.02% at pressures less than 30 MPa up to 0.6% at very high pressures, except in the range from 270 to 350 K at pressures less than 12 MPa where the uncertainty in density is 0.

This work reviews the available data on thermodynamic properties of argon and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz energy. The functional form of the residual part of the Helmholtz energy was developed by using state-of-the-art linear optimization strategies and a new nonlinear regression analysis. The new equation of state contains 41 coefficients, which were fitted to selected data of the following properties: ͑a͒ thermal properties of the single phase (pT) and ͑b͒ of the liquid-vapor saturation curve ͑p s , Ј, Љ͒ including the Maxwell criterion, ͑c͒ speed of sound w, isochoric heat capacity c v , second and third thermal virial coefficients B and C and second acoustic virial coefficient ␤ a. For the density, the estimated uncertainty of the new equation of state is less than Ϯ0.02% for pressures up to 12 MPa and temperatures up to 340 K with the exception of the critical region and less than Ϯ0.03% for pressures up to 30 MPa and temperatures between 235 and 520 K. In the region with densities up to half the critical density and for temperatures between 90 and 450 K the estimated uncertainty of calculated speeds of sound is in general less than Ϯ0.02%. The new formulation shows reasonable extrapolation behavior up to very high pressures and temperatures. Independent equations for the vapor pressure, for the pressure on the sublimation and melting curve and for the saturated liquid and saturated vapor densities are also included. Tables for the thermodynamic properties of argon from 84 to 700 K for pressures up to 1000 MPa are given.

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