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.     

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.     

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.     

Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol

In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.     

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 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%.     

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.     

A Thermodynamic Equation of State For the Critical Region of Ethylene

A fundamental equation of state that describes the behavior of the thermodynamic properties of ethylene in the vicinity of the critical point is formulated. Specifically, a crossover equation of state that takes into account not only the scaling laws at the critical point but also the analytical behavior far away from the critical point is presented. Analysis of different sets of data for the thermodynamic properties is made.     

A Rigorous Thermodynamic Property Model for Fluid-Phase 1,1-Difluoroethane (R-152a)

A new thermodynamic property model for the Helmholtz free energy with rational third virial coefficients for fluid-phase 1,1-difluoroethane (R-152a) was developed. The model was validated by existing experimental data for temperatures from the triple point to 450 K and pressures up to 60 MPa. Reasonable behavior of the second and third virial coefficients was confirmed from intermolecular potential models. The estimated uncertainties are 0.1% in density for the gaseous and liquid phases, 0.4% in density for the supercritical region, 0.05% in speed of sound for the gaseous phase, 2% in speed of sound for the liquid phase, and 1% in specific heat capacities for the liquid phase. From the reasonable behavior of the ideal curves and the third virial coefficients, the model can be assumed reliable in representing the thermodynamic properties not only at states with available experimental data but also at states for which no experimental data are available.     

Thermodynamic Validation of the Form of Unified Equation of State for Liquid and Gas

Proceeding from strict thermodynamic equations, a preferable structure of the unified equation of state (EOS) for liquid, gas, and fluid is determined. It is shown that the equation for the compressibility factor must contain the function of only one variable as one of the terms, namely, the function of volume (density). The physical meaning of this function as the compressibility factor is revealed with the temperature asymptotically tending toward infinity. It is shown that, in a wide range of parameters of state for fluids, the proposed three-parameter equation of state adequately describes the experimental data on the thermal properties of a number of monatomic (Ne, Ar, Kr, Xe), diatomic (N₂, O₂), and polyatomic (CO₂, NH₃, CF₄, CH₄, C₂H₄, C₂H₆, C₃H₈) substances. The proposed equation of state is compared to a number of other known three-parameter equations of state, and it is shown that the proposed equation described the thermal properties several times more accurately than the known equations.     

Methodology for Constructing the Equation of State and Thermodynamic Tables for a New Generation Refrigerant

Measurement Techniques - A unified fundamental equation of state has been developed for 2,3,3,3-tetrafluoropropene (R1234yf), a fourth-generation ozone-safe refrigerant, and a method for...     

An Equation of State for Fluoroethane (R161)

Fluoroethane (R161, C₂H₅F, 353-36-6) is a potential alternative refrigerant with excellent cycle performance, with zero ozone-depletion potential and low global warming potential. In this study, the thermodynamic property formulation for fluoroethane has been developed with the use of available experimental thermodynamic property data. In determining the equation of state, multiproperty fitting methods were used including single-phase pressure–density–temperature (pρT), vapor pressure, and saturated liquid-density data. The equation of state has been developed to conform to the Maxwell criterion for two-phase liquid–vapor equilibrium states, and is valid for temperatures from 130 K to 450 K, and pressures to 5 MPa. The extrapolation behavior of the equation of state at high temperatures and high pressures is reasonable. As there are very few compressed liquid-density experimental data published, the uncertainties in density of the equation of state are estimated to be 2.0 % in the compressed-liquid region and 0.5 % in the gas and supercritical regions. Uncertainties in vapor pressure are 0.5 % above 200 K and increase at lower temperatures. The uncertainties for all properties are higher in the critical region, except vapor pressure. Detailed comparisons between experimental and calculated data have been performed in this study.     

The Thermodynamic Properties of n-Tetradecane in Liquid State

Based on the sound velocity data, a grid algorithm is used to calculate the thermodynamic properties of a liquid. The density, isobaric expansion coefficient, isothermal compressibility, isobaric and isochoric heat capacities, enthalpy and entropy of liquid n-tetradecane were calculated in the ranges of temperature from 293 to 433 K and pressure from 0.1 to 140 MPa. The coefficients of the Tate equation are determined in the above-identified range of parameters. A table of the thermodynamic properties of n-tetradecane is presented.     

Thermodynamic Modeling of Gas-Phase PVTx Properties for the Ternary R-32/125/143a System

Experimental PVTx property data have been used to develop a thermodynamic model of the gas-phase PVTx properties for R-32/125/143a in terms of a truncated virial equation of state. It is developed on the basis of the experimental PVTx property data which were obtained by a group of the present authors. The present model represents the input data with a high reproducibility, i.e., within ±0.2% in pressure for each pure component, ±0.25% for binary mixtures except for R-32/143a, and ±0.3% for ternary mixtures. The present model covers a temperature range of 300 to 380K, pressures up to 4.5MPa, and densities up to 2.5 moldm^–3 at any composition of the present ternary system. The uncertainty of the present model is considered being within ±0.3% in pressure and ±0.3% in the second virial coefficient. The thermodynamic behaviors of the specific isobaric heat capacity, isochoric heat capacity, and speed of sound are also discussed, in addition to the examination of the temperature dependence of the second and third virial coefficients.     

Calculation of the Thermodynamic Properties of Diatomic Substances Based on the Ornstein-Zernike Equation

The new method of calculation of intermolecular distribution functions is used to calculate various thermodynamic properties of diatomic substances (oxygen, nitrogen, ethane). Good agreement is demonstrated between the calculation and experimental data.     

Thermodynamic Properties of Heavy n-Alkanes in the Liquid State: n-Dodecane

A grid algorithm based on sound speed data, was used to calculate the thermodynamic properties of liquid n-dodecane. The density, isobaric expansion coefficient, isothermal compressibility, isobaric and isochoric heat capacities, enthalpy, and entropy of liquid n-dodecane were calculated in the range of temperatures from 293 to 433 K and pressures from 0.1 to 140 MPa. Coefficients of the Tait equation were determined in the above-identified range of parameters. A table of the thermodynamic properties of n-dodecane is presented.     

An Equation of State for the Hard-Sphere Chain Fluid Based on the Thermodynamic Perturbation Theory of Sequential Polymerization

New equations of state for freely jointed hard-sphere chain fluids are developed. The equations of state are based on the thermodynamic perturbation theory. The new equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike theory. These RDFs are composed of a monomer reference term, the Carnahan–Starling or the Percus–Yevick expression, and an additional bond contribution. These equations of state are then extended to real fluids. To calculate the phase equilibrium properties of nonassociating chain fluids, a dispersion contribution is added to the repulsive hard-chain reference term. With the new equations of state of chain fluids supplemented with the dispersion term, the vapor pressures and the coexisting densities of several real fluids are calculated.     

Thermodynamic Properties of 1-Alkenes in the Liquid State: 1-Tetradecene

Thermodynamic properties of liquid 1-tetradecene have been calculated using a grid algorithm based on sound-speed data, obtained in a previous study over a wide range of temperatures and pressures. Since additional information such as densities and isobaric heat capacities at atmospheric pressure are needed for these calculations, the most reliable literature data and those obtained on the basis of structure–property correlations in the homologous series of 1-alkenes were used. Detailed tables, containing values of sound speed, density, isobaric, and isochoric heat capacities, isobaric expansion coefficient, isothermal compressibility, enthalpy, and entropy in the range of temperatures from 303 to 433 K and at pressures from 0.1 to 100 MPa, are given.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Thermodynamic Properties of Trifluoroiodomethane (CF13I)1

Studies of the thermodynamic properties of trifluoroiodomethane (CF₃I) are presented in this paper. The vapor–liquid coexistence curve of CF₃I was measured by visual observation of the meniscus. The critical temperature and the critical density of CF₃I were determined by considering not only the level where the meniscus disappeared but also the intensity of the critical opalescence. The correlation of the saturated density in the critical region was developed, and the exponent of the power law was determined. Correlations of the saturated vapor and liquid densities and the enthalpy of vaporization for CF₃I were also developed. The vapor pressure of CF₃I was measured at temperatures ranging from below the normal boiling point to the critical point, and a vapor pressure equation for CF₃I was developed, from which the normal boiling point of CF₃I was determined. The gaseous PVT properties of CF₃I were measured with a Burnett/isochoric method, and a gaseous equation of state for CF₃I was developed. The speed of sound of gaseous CF₃I was measured with a cylindrical, variable-path acoustic interferometer operating at 156.252 kHz, and the ideal-gas heat capacity and second acoustic virial coefficient were calculated. A correlation of the second virial coefficient for CF₃I was obtained by a semiempirical method using the square-well potential for the intermolecular force and was compared with the result based on PVT measurements. The surface tension of CF₃I was measured with a differential capillary rise method (DCRM), and the temperature dependence of the results was successfully represented to within ±0.13 mN·m^–1 using a van der Waals correlation.     

Review of the Thermodynamic Properties of Hydrogen Based on Existing Equations of State

Currently available equations of state (EOSs) for hydrogen are reviewed, and the data for the critical point, normal boiling point, and triple point are summarized. Through comparisons of PVT, saturated properties, heat capacity, and speed of sound among the latest EOSs for hydrogen, their features are discussed. The proper use of the EOSs, including a consideration of the nuclear isomers (ortho- and parahydrogen), is of great importance, especially for saturated properties, heat capacity, and speed of sound because these properties are different between the nuclear isomers. The present review concludes with recommendations for use of the EOSs for hydrogen.