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 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.     

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 HFC-32 (difluoromethane)

An 18-coefficient modified Benedict–Webb–Rubin equation of state of HFC-32 (difluoromethane) has been developed, based on the updated available PVT measurements, heat capacity measurements and speed of sound measurements. Correlations of vapor pressure and saturated liquid density are also presented. The correlations have been developed based on the reported experimental saturation properties data. This equation of state is effective both in the superheated gaseous phase and compressed liquid phase at pressures up to 70 MPa, densities to 1450 kg/m³, and temperatures from 150 to 475 K, respectively.     

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.     

Thermodynamic properties of CHF2CF2CH2F, 1,1,2,2,3-pentafluoropropane

We report the thermodynamic properties of 1,1,2,2,3-pentafluoropropane (known in the refrigeration industry as HFC-245ca) in the temperature and pressure region commonly encountered in thermal machinery. The properties are based on measurements of the vapor pressure, the density of the compressed liquid, the refractive index of the saturated liquid and vapor, the critical temperature, the speed of sound in the vapor phase, and the capillary rise. From these data we deduce the saturated liquid and vapor densities, the equation of state of the vapor phase, the surface tension, and estimates of the critical pressure and density. The data determine the coefficients for a Carnahan-Starlings-DeSantis (CSD) equation of state. The CSD coefficients found in REFPROP 4.0 are based on the measurements reported here.     

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).     

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.     

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.     

Die Schallgeschwindigkeit als thermodynamische Zustandsgröße

In the limit of small amplitudes and low frequencies, the speed of sound is a quantity describing the thermodynamic state of the fluid under consideration. Similar to other state variables like pressure, temperature and density, the speed of sound is well accessible by experiment to a high degree of precision. Because of the thermodynamic interelationship between the slope of the thermal property surface (p, ?, T-surface), the speed of sound and the caloric variables of state, the speed of sound plays a major role in establishing fundamental equations of state for fluids. Unlike thermal property data, speed of sound data is rather scarce, especially in the homogeneous liquid high pressure region.     

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.     

An equation of state for 1,1-difluroethane (HFC 152a)

An equation of state for 1,1-difluoroethane (HFC 152a, CH₃CHF₂) has been developed on the basis of reliable experimental data including PVT, liquid C_p, and saturated-liquid-density data measured by our group. It is a non-dimensionalized virial equation whose functional form is the same as that originally developed for 1,1,1,2-tetrafluoroethane (HFC 134a) in our group. The effective range is for pressures up to 15 MPa, temperatures from 230 to 450 K, and densities to 1000 kg m⁻³. The equation represents reliable PVT measurements within ± 1% in pressure for the superheated vapour and supercritical fluid, while within ±0.5% in density for the compressed liquid. In addition, it should be noted that the equation represents the other essential thermodynamic properties including vapour pressures, saturated-liquid/ vapour densities, isobaric/isochoric specific heats and sound velocity in both the liquid and gaseous phase of HFC 152a.     

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.     

Equation of state for gaseous propane determined from the speed of sound

An equation of state in the form of a truncated virial series has been developed for gaseous propane. Second, third, and fourth virial coefficients and their temperature derivatives were calculated from model two- and three-body intermolecular potentials, the parameters of which were fitted to experimental values of the speed of sound in the gas; no other data were used. The resulting model predicts accurately thermal and caloric properties of the gas over a wide range of temperatures at densities up to about one-quarter of the critical. The second and third (but not the fourth) virial coefficients are in very close agreement with directly measured values. To facilitate rapid calculation of thermodynamic properties, a look-up table for the virial coefficients and their temperature derivatives is provided together with a recommended means of interpolation.     

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 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 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.     

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.     

Application of nonlinear regression in the development of a wide range formulation for HCFC-22

An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based onP--T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.