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.     

Equation of State for the Thermodynamic Properties of <Emphasis Type="Italic">trans</Emphasis>-1,3,3,3-Tetrafluoropropene [R-1234ze(E)]

An equation of state for the calculation of the thermodynamic properties of the hydrofluoroolefin refrigerant R-1234ze(E) is presented. The equation of state (EOS) is expressed in terms of the Helmholtz energy as a function of temperature and density. The formulation can be used for the calculation of all thermodynamic properties through the use of derivatives of the Helmholtz energy. Comparisons to experimental data are given to establish the uncertainty of the EOS. The equation of state is valid from the triple point (169 K) to 420 K, with pressures to 100 MPa. The uncertainty in density in the liquid and vapor phases is 0.1 % from 200 K to 420 K at all pressures. The uncertainty increases outside of this temperature region and in the critical region. In the gaseous phase, speeds of sound can be calculated with an uncertainty of 0.05 %. In the liquid phase, the uncertainty in speed of sound increases to 0.1 %. The estimated uncertainty for liquid heat capacities is 5 %. The uncertainty in vapor pressure is 0.1 %.     

Thermodynamic Properties for R-404A

An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m^–3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.     

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.     

A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol

A formulation for the thermodynamic properties of ethanol (C₂H₅OH) in the liquid, vapor, and saturation states is presented. The formulation is valid for single-phase and saturation states from 250 to 650K at pressures up to 280MPa. The formulation includes a fundamental equation and ancillary functions for the estimation of saturation properties. The experimental data used to determine the fundamental equation include pressure-density-temperature, ideal gas heat capacity, speed of sound, and vapor pressure. Saturation values computed from the ancillary functions were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Comparisons between experimental data and values computed using the fundamental equation are given to verify the uncertainties in the calculated properties. The formulation presented may be used to compute densities to within ±0.2%, heat capacities to within ±3%, and speed of sound to within ±1%. Saturation values of the vapor pressure and saturation densities are represented to within ±0.5%, except near the critical point.     

Density and speed of sound of R-406A refrigerant in the vapor phase

The speed of sound and the density of the gaseous R-406A refrigerant within the temperature range 293–373 K and at the pressures from 0.05 MPa up to 0.6–2.3 MPa were investigated by means of an ultrasound interferometer and a constant volume piezometer. The measurement errors for the temperature, the pressure, and the speed of sound were ±20 mK, ±4 kPa, and ±(0.1–0.3)%, respectively. The approximation dependences of the investigated properties of the R-406A vapor are obtained and their errors are estimated. The obtained results are compared with the calculations using the REFPROP software.     

Thermodynamic property representation for the R-32/125 binary system by a new cubic equation of state

Thermodynamic properties of the R-32/125 binary system are modeled by a new cubic equation of state which was developed and applied to the pure R-32 and R-125 in a previous paper by the present authors. The essential thermodynamic properties such as PVTx properties, vapor-liquid equilibrium, enthalpy, entropy, isobaric specific heat, and speed of sound are well represented by the new model simultaneously for the liquid phase, the gas phase, and the two-phase region of the R-32/125 binary system. The developed model is valid for the entire range of compositions, and a pressure-enthalpy diagram for a R-32/125 mixture with 50 mass% of R-32 is illustrated as an example. The new model was also compared with other reported models in refrigeration cycle calculations.     

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.     

Thermodynamic properties of the R-415A refrigerant in the vapor phase and on the condensation line

The speed of sound in the R-415A refrigerant vapor and its density and pressure on the condensation line were measured by the ultrasonic interferometer and constant-volume piezometer methods within a range of temperatures from 293 to 373 K and pressures from 0.04 to 0.5–2.45 MPa. The temperature, pressure, density and speed of sound measurement errors were ±20 mK, ±4 kPa, and ±(0.1–0.2)%, respectively. The temperature dependence of the ideal-gas heat capacity was calculated on the basis of the obtained data. The obtained results were compared with the properties calculated by the REFPROP software.     

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.     

Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a

A mixture model explicit in Helmholtz energy has been developed that is capable of predicting thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, and R-152a. 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 equation that is applied to all mixtures used in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate thermodynamic properties of mixtures, including dew and bubble point properties and critical points, generally within the experimental uncertainties of the available measured properties. It incorporates the most accurate published equation of state for each pure fluid. The estimated uncertainties of calculated properties are ±0.25% in density, ±0.5% in the speed of sound, and ±1% in heat capacities. Calculated bubble point pressures are generally accurate to within ±1%.     

Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements

The speed of sound in gaseous hydrogen bromide (HBr) and boron trichloride (BCl₃) was measured using a highly precise acoustic resonance technique. The HBr speed-of-sound measurements span the temperature range 230 to 440 K and the pressure range from 0.05 to 1.5 MPa. The BCl₃ speed-of-sound measurements span the temperature range 290 to 460 K and the pressure range from 0.05 MPa to 0.40 MPa. The pressure range in each fluid was limited to 80% of the sample vapor pressure at each temperature. The speed-of-sound data have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacities as a function of temperature with a relative standard uncertainty of 0.1%. The heat capacities agree with those calculated from spectroscopic data within their combined uncertainties. The speeds of sound were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on the hard-core square-well intermolecular potential model and the second based on the hard-core Lennard–Jones intermolecular potential model. The resulting virial equations of state reproduced the speed-of-sound measurements to 0.01% and can be expected to calculate vapor densities with a relative standard uncertainty of 0.1%. Transport properties calculated from the hard-core Lennard–Jones potential model should have a relative standard uncertainty of 10% or less.     

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.     

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%.     

Vapor Pressure, Speed of Sound, and PVT-Properties of R-404a in the Vapor Phase

The density (300–363 K, up to 3.5 MPa) and speed of sound (293–373 K, 7.5–480 kPa) in gaseous R-404a have been studied by an isochoric piezometer method and an ultrasonic interferometer, respectively. The pressures of the saturated vapor along the dew line were measured from 298 to 330 K. The experimental uncertainties of the temperature, pressure, density, and speed-of-sound measurements were estimated to be within ±20 mK, ±1.5 kPa, ±0.15%, and ±(0.1–0.2)%, respectively. On the basis of the obtained data, the isobaric molar heat capacity of R-404a was calculated for the ideal-gas state. An eight-coefficient Benedict–Webb–Rubin equation of state has been developed for the gaseous phase of R-404a.     

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 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.     

Special Equations of State for Methane,Argon, and Nitrogen for the Temperature Range from 270 to 350 K at Pressures up to 30 MPa

In order to describe the thermodynamic behavior of methane, argon, and nitrogen in the so-called “natural-gas region,” namely, from 270 to 350 K at pressures up to 30 MPa as accurate as possible with equations of a very simple form, new equations of state for these three substances have been developed. These equations are in the form of a fundamental equation in the dimensionless Helmholtz energy; for calculating the pressure or the density, the corresponding equations explicit in pressure are also given. The residual parts of the Helmholtz function representing the behavior of the real gas contain 12 fitted coefficients for methane, 8 for argon, and 7 for nitrogen. The thermodynamic relations between the Helmholtz energy and the most important thermodynamic properties and the needed derivatives of the equations are explicitly given; to assist the user there is also a table with values for computer-program verification. The uncertainties when calculating the density ρ, the speed of sound w, the isobaric specific heat capacity c _p, and the isochoric specific heat capacity c _v are estimated as follows. For all three substances it is Δρ/ρ≤±0.02 % for p≤ 12 MPa and Δρ/ρ ≤ ±0.05% for higher pressures. For methane it is Δw/w≤±0.02% for p≤10 MPa and Δw/w≤+-0.1% for higher pressures; for argon it is Δw/w?-0.1 % for p≤ 7 MPa, Δw/w≤±0.3 % for 7 <p≤30 MPa; and for nitrogen it is Δw/w≤±0.1% for p≤1.5 MPa and Δw/w±0.5% for higher pressures. For all three substances it is Δc _p/c _p≤±1 % and ΔC _v/C _v≤±1 % in the entire range.     

Study on Isochoric Specific Heat Capacity of Liquid R-410A and HFE-347pcf2

The isochoric heat capacity (c _v ) of R-410A [a mixture of 49.81 mass% difluoromethane (HFC-32) + 50.19 mass% pentafluoroethane (HFC-125)] and 1,1,2,2-tetrafluoroethyl-2,2,2-trifluoroethylether (HFE-347pcf2) was measured at temperatures from 277 K to 400 K and at pressures up to 30 MPa. The reported density measurements for R-410A and HFE-347pcf2 are in the single-phase region and cover a density range above 0.92 g·cm^?3 and 1.33 g·cm^?3, respectively. The measured data of R-410A are compared with data reported by other researchers. Also, the measured data of R-410A are examined with an available equation of state. As a result, it is found that the present c _v data for R-410A agree well with those by other researchers and the calculated values with the equation of state in the measurement range except near the critical isochore.     

Thermophysical Properties of a Refrigerant Mixture of R365mfc (1,1,1,3,3-Pentafluorobutane) and Galden<Superscript>®</Superscript> HT 55 (Perfluoropolyether)

This work presents a comprehensive experimental study of various thermophysical properties of an azeotropic refrigerant mixture of 65 mass% R365mfc (1,1,1,3,3-pentafluorobutane) and 35 mass% Galden^? HT 55 (perfluoropolyether). Light scattering from bulk fluids has been applied for measuring both the thermal diffusivity and the speed of sound in the liquid and vapor phases under saturation conditions, between 293 K and the liquid–vapor critical point at 450.7 K. Furthermore, the speed of sound has been measured for the superheated-vapor phase along nine isotherms, between 393 and 523 K and up to a maximum pressure of about 2.5 MPa. For temperatures between 253 and 413 K, light scattering by surface waves on a horizontal liquid–vapor interface has been used for simultaneous determination of the surface tension and kinematic viscosity of the liquid phase. With light scattering techniques, uncertainties of less than ±2.0%, ±0.5%, ±1.5%, and ±1.5% have been achieved for the thermal diffusivity, sound speed, kinematic viscosity, and surface tension, respectively. In addition to vapor-pressure measurements between 304 and 448 K, the density was measured between 273 and 443 K using a vibrating-tube method. Here, measurements have been performed in the compressed- and saturated-liquid phases with uncertainties of ±0.3% and ±0.1%, respectively, as well as for the superheated vapor up to a maximum pressure of about 3 MPa with an uncertainty between ±0.3% and ±3%. Critical-point parameters were derived by combining the data obtained by different techniques.