Equation of State for the Thermodynamic Properties of 1,1,2,2,3-Pentafluoropropane (R-245ca)

An equation of state for the calculation of the thermodynamic properties of 1,1,2,2,3-pentafluoropropane (R-245ca), which is a hydrofluorocarbon refrigerant, is presented. The equation of state (EOS) is expressed in terms of the Helmholtz energy as a function of temperature and density, and can calculate all thermodynamic properties through the use of derivatives of the Helmholtz energy. The equation is valid for all liquid, vapor, and supercritical states of the fluid, and is valid from the triple point to 450 K, with pressures up to 10 MPa. Comparisons to experimental data are given to verify the stated uncertainties in the EOS. The estimated uncertainty for density is 0.1 % in the liquid phase between 243 K and 373 K with pressures up to 6.5 MPa; the uncertainties increase outside this range, and are unknown. The uncertainty in vapor-phase speed of sound is 0.1 %. The uncertainty in vapor pressure is 0.2 % between 270 K and 393 K. The uncertainties in other regions and properties are unknown due to a lack of experimental data.     

New Fundamental Equations of State with a Common Functional Form for 2,3,3,3-Tetrafluoropropene (R-1234yf) and <Emphasis Type="Italic">trans</Emphasis>-1,3,3,3-Tetrafluoropropene (R-1234ze(E))

New fundamental equations of state explicit in the Helmholtz energy with a common functional form are presented for 2,3,3,3-tetrafluoropropene (R-1234yf) and trans-1,3,3,3-tetrafluoropropene (R-1234ze(E)). The independent variables of the equations of state are the temperature and density. The equations of state are based on reliable experimental data for the vapor pressure, density, heat capacities, and speed of sound. The equation for R-1234yf covers temperatures between 240 K and 400 K for pressures up to 40 MPa with uncertainties of 0.1 % in liquid density, 0.3 % in vapor density, 2 % in liquid heat capacities, 0.05 % in the vapor-phase speed of sound, and 0.1 % in vapor pressure. The equation for R-1234ze(E) is valid for temperatures from 240 K to 420 K and for pressures up to 15 MPa with uncertainties of 0.1 % in liquid density, 0.2 % in vapor density, 3 % in liquid heat capacities, 0.05 % in the vapor-phase speed of sound, and 0.1 % in vapor pressure. Both equations exhibit reasonable behavior in extrapolated regions outside the range of the experimental data.     

Compressed Liquid Densities and Helmholtz Energy Equation of State for Fluoroethane (R161)

In this study, compressed liquid densities of Fluoroethane (R161, CAS No. 353-36-6) were measured using a high-pressure vibrating-tube densimeter over the temperature range from (283 to 363) K with pressures up to 100 MPa. A Helmholtz energy equation of state for R161 was developed from these density measurements and other experimental thermodynamic property data from the literature. The formulation is valid for temperatures from the triple point temperature of 130 K to 420 K with pressures up to 100 MPa. The approximate uncertainties of properties calculated with the new equation of state are estimated to be 0.25 % in density, 0.2 % in saturated liquid density between 230 K and 320 K, and 0.2 % in vapor pressure below 350 K. Deviations in the critical region are higher for all properties. The extrapolation behavior of the new formulation at high temperatures and high pressures is reasonable.     

A Thermodynamic Equation of State for Pentafluoroethane (R-125)

We developed a fundamental equation of state for pentafluoroethane (R-125, CHF₂CF₃) which is represented in terms of a non-dimensional Helmholtz free energy. The equation has been established on the basis of selected measurements of the pressure-density-temperature relation, speed of sound, heat capacities, and saturation properties. Linear and non-linear regression analysis was employed to determine the functional form and the numerical parameters. The equation represents all the thermodynamic properties of R-125 in the liquid and gaseous phases for temperatures between the triple point and 470 K, and pressures up to 35 MPa. The uncertainties are estimated to be about ±0.05% or 0.1 kPa for the vapor pressure, ± 0.05 % for the liquid and vapor densities, about ± 1 % for the isobaric and isochoric heat capacities in the liquid, and ± 0.5 % or ± 0.02 % for the speed of sound in the liquid and vapor, respectively.     

A Thermodynamic Property Model for Fluid Phase Hydrogen Sulfide

A Helmholtz free energy equation of state for the fluid phase of hydrogen sulfide has been developed as a function of reduced temperature and density with 23 terms on the basis of selected measurements of pressure–density–temperature (P, , T), isobaric heat capacity, and saturation properties. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from the triple point temperature (187.67 K) to 760 K at pressures up to 170 MPa. The uncertainty in density calculation of the present equation of state is 0.7% in the liquid phase, and that in pressure calculation is 0.3% in the vapor phase. The uncertainty in saturated vapor pressure calculation is 0.2%, and that in isobaric heat capacity calculation is 1% in the liquid phase. The behavior of the isobaric heat capacity, isochoric heat capacity, speed of sound, and Joule–Thomson coefficients calculated by the present model shows physically reasonable behavior and those of the calculated ideal curves also illustrate the capability of extending the range of validity. Graphical and statistical comparisons between experimental data and the available thermodynamic models are also discussed.     

An Equation of State for 1,1,1-Trifluoroethane (R-143a)

A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P––T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.     

A thermodynamic property formulation for nitrogen from the freezing line to 2000 K at pressures to 1000 MPa

A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of nitrogen from the freezing line to 2000 K at pressures to 1000 MPa is presented. A new vapor pressure equation and equations for the saturated liquid and vapor densities as functions of temperature are also included. The techniques used for development of the fundamental equation are those reported in a companion paper for ethylene. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (C _v), isobaric heat capacity (C _p), and velocity of sound are also included in that paper. The property formulation using the fundamental equation reported here may generally be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ± 2%, and velocity of sound values within ±2%. The fundamental equation is not intended for use near the critical point.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

A new equation of state for chlorodifluoromethane (R22) covering the entire fluid region from 116 K to 550 K at pressures up to 200 MPa

A new equation of state in the form of a fundamental equation explicit in the dimensionless Helmholtz free energy has been developed for chlorodifluoromethane (R 22). This equation, which contains 22 fitted coefficients, covers the entire fluid region from 116 K (triple point temperature) to 550 K at pressures up to 200 MPa. The mathematical form of the equation was determined with the help of a new method to optimize its structure. New pressure-density-temperature data in the liquid region and especially new vapour pressures and saturated liquid densities, as well as speed of sound data have been incorporated to extend the range of validity and to improve the accuracy of properties calculated with this equation beyond that of previous formulations. Independent equations are also included for the vapour pressure as well as for the saturated liquid and vapour densities. The uncertainty of the new wide-range equation of state can roughly be given as follows: ± 0.1% in density (with the exception of the critical region), ± 1% in heat capacity, ± 0.5% in speed of sound in the liquid and 0.1% in speed of sound in the gas phase. The new equation of state corresponds to the International Temperature Scale of 1990 (ITS-90).     

Equation of State for Normal Liquid Helium-3 from 0.1 to 3.3157 K

An equation of state for normal liquid ³He has been constructed in the form of Helmholtz free energy as a function of independent parameters—temperature, and density. The equation was fitted simultaneously to the collected experimental p-ρ-T, specific heat, sound velocity, isobaric expansion coefficient and isothermal compressibility coefficient from the world’s literature to accuracies comparable with reasonable experimental errors in the measured quantities. Extensive comparisons between the equation of state and experimental data have been made by a set of deviation plots. The state equation is valid in the region for temperatures from 0.1 K to T _c = 3.3157 K, and for pressures from vapor pressures to melting pressures.     

A Rational Helmholtz Fundamental Equation of State for Difluoromethane with an Intermolecular Potential Background

A new fundamental thermodynamic equation of state for difluoromethane was developed by considering the intermolecular potential behavior for improving the reliability in the gaseous phase. Reliable second and third virial coefficients are introduced in accordance with the principle of a unified relation of the intermolecular potential energy and the fundamental equation of state. The fundamental equation of state is able to provide reliable thermodynamic properties even at low temperatures or in the region near saturation where precise and accurate experimental data are not available. The estimated uncertainties of calculated properties from the equation of state are 0.07% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.35% in pressure for the supercritical region, 0.07% in vapor pressure, 0.2% in saturated-liquid density, 0.7% in saturated-vapor density, 0.01% in speed of sound for the gaseous phase, 0.7% in speed of sound for the liquid phase, and 0.6% in isochoric specific heat for the liquid phase. The equation is valid for temperatures from the triple point to 450 K and pressures up to 72 MPa.     

A thermodynamic property formulation for ethylene from the freezing line to 450 K at pressures to 260 MPa

A new thermodynamic property formulation based upon a fundamental equation explicit in Helmholtz energy of the form A=A(, T) for ethylene from the freezing line to 450 K at pressures to 260 MPa is presented. A vapor pressure equation, equations for the saturated liquid and vapor densities as functions of temperature, and an equation for the ideal-gas heat capacity are also included. The fundamental equation was selected from a comprehensive function of 100 terms on the basis of a statistical analysis of the quality of the fit. The coefficients of the fundamental equation were determined by a weighted least-squares fit to selected P--T data, saturated liquid and saturated vapor density data to define the phase equilibrium criteria for coexistence, C _v data, velocity of sound data, and second virial coefficients. The fundamental equation and the derivative functions for calculating internal energy, enthalpy, entropy, isochoric heat capacity (C _v), isobaric heat capacity (C _p), and velocity of sound are included. The fundamental equation reported here may be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ±3 %, and velocity of sound values within ±1 %, except in the region near the critical point. The fundamental equation is not intended for use near the critical point. This formulation is proposed as part of a new international standard for thermodynamic properties of ethylene.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa

A thermodynamic property formulation for standard dry air based upon experimental P––T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.     

A thermodynamic property formulation for cyclohexane

A formulation for the thermodynamic properties of cyclohexane is presented. The equation is valid for single-phase and saturation states from the melting line to 700 K at pressures up to 80 MPa. It includes a fundamental equation explicit in reduced Helmholtz energy with independent variables of reduced density and temperature. The functional form and coefficients of the ancillary equations were determined by weighted linear regression analyses of evaluated experimental data. An adaptive regression algorithm was used to determine the final equation. To ensure correct thermodynamic behavior of the Helmholtz energy surface the coefficients of the fundamental equation were determined with multiproperty fitting, Pressure-density-temperature (P-p-T) and isobaric heat capacity (C _p -P-T) data were used to develop the fundamental equation, SaturationP-p-T values, calculated from the estimating functions, were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Separate functions were used for the vapor pressure, saturated liquid density, saturated vapor density. ideal-gas heat capacity. and pressure on the melting curve, Comparisons between experimental data and values calculated using the fundamental equation are given to verify the accuracy of the formulation. The formulation given here may be used to calculate densities within ±0.1 %, heat capacities to within ±2 %. and speed of sound to within ± 1 %, except near the critical point.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A fundamental equation of state for 1,1-difluoroethane (HFC-152a)

A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable (p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado. U.S.A.     

A Thermodynamic Property Model for Fluid-Phase Propane

A fundamental equation of state for propane (R-290), formulated in terms of the non-dimensional Helmholtz free energy, is presented. It was developed based on selected reliable measurements for pressure-volume-temperature (PVT), isochoric and isobaric heat capacities, speed of sound, and the saturation properties which were all converted to ITS-90. Supplementary input data calculated from a virial equation for the vapor-phase PVT properties at lower temperatures and other correlations for the saturated vapor pressures and saturated vapor- and liquid-densities have also been used. The present equation of state includes 19 terms in the residual part and represents most of the reliable experimental data accurately in the range of validity from 85.48 K (the triple point temperature) to 623 K, at pressures to 103 MPa, and at densities to 741 kg·m^–3. The smooth behavior of the derived thermodynamic properties in the entire fluid phase is demonstrated. In addition, graphical and statistical comparisons between experimental data and the available thermodynamic models, including the present one, showed that the present model can provide a physically sound representation of all the thermodynamic properties of engineering importance.     

A thermodynamic property formulation for air. I. Single-phase equation of state from 60 to 873 K at pressures to 70 MPa

A revised interim formulation for the thermodynamic properties of air has been developed for calculating properties of the vapor and estimating properties for the liquid at temperatures as low as 60 K. The formulation incorporates separate equations for the calculation of bubble-point and dew-point pressures and densities and for the ideal-gas heat capacity. A new fundamental equation of state is given for vapor and liquid states of air based upon available experimental data and predicted values of isochoric heat capacity for the liquid using corresponding states methods. Procedures for predicting C _v are discussed. The fundamental equation for air is explicit in nondimensional Helmholtz energy. The terms of the fundamental equation were selected from a larger set of 75 proposed terms using a least-squares fitting procedure. Representative graphical comparisons of calculated property values to experimental measurements are given. The estimated accuracy of calculated densities is generally ± 0.2% except near the dew and bubble lines. Calculated heat capacities for the liquid must be considered only as estimates until substantiated by experimental measurements.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Experimental study of speed of sound in gaseous refrigerant R-507a

The speed of sound in gaseous refrigerants R-134a and R-507a is measured by the method of ultrasonic interferometer in a temperature interval from 293 to 373 K and pressure values from 0.01 to 0.5–2.9 MPa. The errors in measurement of the temperature, pressure, and speed of sound are ±20 mK, ±4 kPa, and ±(0.1–0.2)%, respectively. On the basis of the data obtained, the temperature dependence of the idealgas heat capacity is calculated. The results obtained are compared with calculation of speed of sound from the fundamental state equation for Helmholtz free energy.     

A Rational Fundamental Equation of State for Pentafluoroethane with Theoretical and Experimental Bases

A fundamental equation of state for pentafluoroethane was established on the basis of not only assessment of the experimental data but also by introducing parameters for virial coefficients having a theoretical background in statistical thermodynamics. The equation of state has a range of validity for temperatures from the triple point up to 500 K and pressures up to 70 MPa. The estimated uncertainties of the equation are 0.1% for the vapor pressure, 0.15% in density for the saturated-liquid phase, 0.5% in density for the saturated-vapor phase, 0.1% in density for the liquid phase, 0.1% in pressure for the gaseous phase, 0.5% in density for the supercritical region, 0.01% in speed of sound for the gaseous phase, 0.9% in speed of sound for the liquid phase, 0.5% in isobaric specific heat for the liquid phase, and 1.2% in isochoric specific heat for the liquid phase. The derived specific heats in the gaseous phase are close to the values from the virial equation of state with the second and third virial coefficients derived from intermolecular potential models and precise speed-of-sound measurements.     

A Generalized Model for the Thermodynamic Properties of Mixtures

A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.     

A Thermodynamic Property Model for Fluid-Phase Isobutane

A Helmholtz free energy equation of state for the fluid phase of isobutane (R-600a) has been developed on the basis of the ITS-90 temperature scale. This model was developed using selected measurements of the pressure–density–temperature (P, , T), isobaric heat capacity, speed of sound, and saturation properties. The structure of the present model consists of only 19 terms in its functional form, which is the same as those successfully applied to our recent modeling of R-290 and R-600, and a nonlinear fitting procedure was used to determine the numerical parameters of the present equation of state. Based on a comparison with available experimental data, it is recognized that the model represents most of the reliable experimental data accurately in the range of validity covering temperatures from 113.56 K (the triple-point temperature) to 573 K, at pressures up to 35 MPa, and at densities up to 749 kg·m^–3. Physically sound behavior of the derived thermodynamic properties over the entire fluid phase is demonstrated. The estimated uncertainties of properties calculated using the model are 0.2% in density, 1% in heat capacities, 0.02% in the speed of sound for the vapor, 1% in the speed of sound elsewhere, and 0.2% in vapor pressure, except in the critical region. In addition, graphical and statistical comparisons between experimental data and the available thermodynamic models, including the present one, showed that the model can provide a physically sound representation of all the thermodynamic properties of engineering importance.