An Accurate Vapor Pressure Equation with Good Extrapolation Characteristics

A new vapor pressure equation that has only three adjustable parameters and a simple form is presented in this paper. The equation is valid over the entire range from the triple point to the critical temperature for a chemically diverse set of compounds. It can represent the experimental data with an accuracy comparable to the Wagner vapor pressure equation. The advantage of the new equation is that it can be used to extrapolate well from a small amount of data in the usual range to the entire vapor–liquid coexistence region both up to the critical temperature and down to the triple point. Satisfactory results are presented for more than 40 substances in tables, and it has been shown that the new vapor pressure equation is generally valid in a wide range.     

Thermodynamic properties of n-pentane

Specific volumes and isobaric heat capacity measurements are reported for n-pentane. The measurements were made in the liquid and vapor phases at temperatures ranging from the triple point (173 K) to the onset of dissociation temperature (700 K) and pressures up to 100 MPa including a wide region around the critical point. We are able to fit our data, as well as those of a number of other authors, to a single equation of state with 30 constants. This equation yields the density of n-pentane in the temperature range from 280 to 650 K at pressures up to 80 MPa and the caloric properties up to 500 K. Additional experimental investigations of the thermodynamic properties are required for temperatures above 500 K. Interpolating equations for the caloric properties on the saturated line and in the critical region are also presented.     

PVT Measurements on tetrafluoroethane (R134a) along the vapor-liquid equilibrium boundary between 288 and 373 K and in the liquid state from the triple point to 265 K

For the investigations of the gas-liquid phase equilibria, a new apparatus has been developed capable of simultaneously determining the pressure and the liquid and vapor densities using Archimedes' principle. The relative measurement uncertainties of the liquid and vapor densities of R134a (purity, 99.999%) at 313 K are 2×10^–4 and 7×10^–4, respectively (95% confidence level). For the measurements in the liquid region along nine quasi-isochores at pressures up to 5 MPa, an isochoric apparatus was used. The relative measurement uncertainty ofpv/(RT) is less than 1×10^–3. In addition to the investigation of the (p, v, T) properties, the temperature and pressure at the triple point and the vapor pressure between the triple point and 265 K were measured. On the basis of these data, a vapor pressure correlation has been developed that reproduces the measured vapor pressures within the uncertainty of measurement. The results of our measurements are compared with a fundamental equation for R134a, which is based on the measurements of other research groups.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 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.     

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 n-hexane

Specific volumes and isobaric heat capacity measurements are reported for n-hexane. The measurements were made in the liquid and vapor phases at temperatures from the triple point and also cover a wide region around the critical point. The thermal, caloric, and acoustic data from our own investigation as well as those of a number of other authors are fitted to a single equation of state with 32 constants. This equation yields to all thermodynamic properties of n-hexane in the temperature range 180 to 630 K and pressures up to 100 MPa. The data in the critical region have been analyzed in terms of a scaled equation of state.     

Subatmospheric vapor pressures evaluated from internal-energy measurements

Vapor pressures were evaluated from measured internal-energy changes in the vapor+liquid two-phase region, ΔU ⁽²⁾. The method employed a thermodynamic relationship between the derivative quantity (ϖU ⁽²⁾/ϖV) _T and the vapor pressure (p _σ) and its temperature derivative (ϖp/ϖT)_σ. This method was applied at temperatures between the triple point and the normal boiling point of three substances: 1,1,1,2-tetrafluoroethane (R134a), pentafluoroethane (R125), and difluoromethane (R32). Agreement with experimentally measured vapor pressures near the normal boiling point (101.325 kPa) was within the experimental uncertainty of approximately ±0.04 kPa (±0.04%). The method was applied to R134a to test the thermodynamic consistency of a publishedp-p-T equation of state with an equation forp _σ for this substance. It was also applied to evaluate publishedp _σ data which are in disagreement by more than their claimed uncertainty.     

Thermodynamic properties of CFC alternatives: A survey of the available data

The thermodynamic properties of ten halogenated hydrocarbons are collected from a variety of sources, including unpublished data. Considered are the triple point, normal boiling point and critical point parameters, and the temperature dependence of the vapour pressure, saturated liquid density and ideal gas heat capacity. Also considered are the single-phase p-V-p data. The saturation liquid density and ideal gas simple correlations. The fluids, which are potential alternatives to the fully halogenated chlorofluorocarbons, are R23, R32, R125, R143a, R22, R134a, R152a, R124, R142b and R123.     

PVT Measurements for Pure Ethanol in the Near-Critical and Supercritical Regions

The PVT properties of pure ethanol were measured in the near-critical and supercritical regions. Measurements were made using a constant-volume piezometer immersed in a precision thermostat. The uncertainty of the density measurements was estimated to be 0.15%. The uncertainties of the temperature and pressure measurements were, respectively, 15 mK and 0.05%. Measurements were made along various near-critical isotherms between 373 and 673 K and at densities from 91.81 to 497.67 kg · m⁻³. The pressure range was from 0.226 to 40.292 MPa. Using two-phase PVT results, the values of the saturated-liquid and -vapor densities and the vapor pressure for temperatures between 373.15 and 513.15 K were obtained by means of an analytical extrapolation technique. The measured PVT data and saturated properties for pure ethanol were compared with values calculated from a fundamental equation of state and correlations, and with experimental data reported by other authors. The values of the critical parameters (T _C,P _C,ρ _C) were derived from the measured values of saturated densities and vapor pressure near the critical point. The derived values of the saturated densities near the critical point for ethanol were interpreted in term of the “complete scaling” theory.     

Thermodynamic properties of 1-chloro-1,2,2,2-tetrafluoroethane (R124)

The critical temperature and pressure, vapor pressure, and PVT relations for gaseous and liquid 1-chloro-1,2,2,2-tetrafluoroethane (R124) were determined experimentally. The vapor pressure was measured in the temperature range from 278.15 K to the critical temperature. The PVT measurements were carried out using two types of volumeters in the temperature range from 278.15 to 423.15 K, at pressure up to 100 MPa. The numerical PVT data of gaseous state are fitted as a function of density to a modified Benedict-Webb-Rubin equation. The pressure-volume relations of the liquid at each temperature are correlated satisfactorily as a function of pressure by the Tait equation. The critical density and saturated vapor and liquid densities are also determined and some of the thermodynamic properties are derived from the experimental results.     

Ideal-gas and saturation properties of methanol

Properties of the ideal gas have been considered in detail and new equations for the ideal-gas heat capacity enthalpy, and entropy are given which are valid from 100 to 1000 K. Saturation-curve data have been reviewed and an equation for the vapor pressure is given which covers the whole range from the triple point to the critical point. A tentative equation for the saturated liquid density is also given. The necessity for new experimental measurements is discussed.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).     

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.     

Predicting the High-Pressure Phase Equilibria of Binary Mixtures of n-Alkanes Using the SAFT-VR Approach

The phase behavior of selected alkane binary mixtures is studied using SAFT-VR, a version of the statistical associating fluid theory for potentials of variable attractive range (SAFT). We treat the n-alkane molecules as chains formed from united-atom hard-sphere segments with square-well potentials of variable range to describe the attractive interactions. We use a simple relationship between the number of carbon atoms in the n-alkane molecule and the number of segments in the united atom chains in order to predict the phase behavior of n-butane with other n-alkanes. The calculated vapor pressures and saturated liquid densities of the pure components are fitted to experimental data from the triple point to the critical point. These optimized parameters are rescaled by the respective experimental critical points and used to determine the critical lines and phase behavior of the mixtures. We use the Lorentz-Berthelot combining rule for the unlike interactions. We predict the phase behavior of n-butane + n-alkane binary mixtures, concentrating mainly on the critical region. The gas-liquid critical lines predicted by SAFT-VR for the n-alkane mixtures are in excellent agreement with the experimental data, and improve significantly on the results obtained with the simpler SAFT-HS approach where the attractive interactions are treated at the mean-field level.     

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.     

Equation for compressibility factor and density of saturated n-alkanes (C1–C10) vapor, parahydrogen, and water at the boiling line

An equation is obtained for calculating the compressibility factor and saturated vapor density of n-alkanes (C₁–C₁₀), parahydrogen, and water at temperatures of the triple point up to critical point. The calculation error is close to that for experimental data.     

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.     

Measurements of the refractive index of alternative refrigerants

Measurements of coexistence curves of the refractive index of HCFC-22, HFC23, HFC-32, HFC-125, and HFC-152a have been carried out in the range from ambient to critical temperature. Near the critical temperature the refractive index has distribution in both the vapor and the liquid phases in the test cell. Thus the values at the boundary between vapor and liquid are selected at those of saturated vapor and liquid, respectively. The values of the critical temperature and critical refractive index for each substance are estimated. The refractive index is related to density by the Lorentz-Lorenz equation. In the case of HFC-32 the value of the LL function is assumed to be constant in the limited region near the critical point, and the values of density of saturated vapor and liquid are calculated and are compared with the experimental values of density obtained byPVT measurement.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

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.