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.     

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 practical density equation for saturated vapor of helium-3 from 0.01 K to the critical point

Based on the ideal gas state equation and the saturated vapor pressure equation of helium-3, a saturated vapor density equation is proposed, which can be applied for calculating the saturated vapor density of helium-3 from 0.01 K to the critical temperature. Above 1.4 K, the average deviation between the results by this equation and experimental data is about 0.66% and the maximum is 2%. Below 1.4 K, the results of this work show a comfortable agreement with those by virial state equation (the deviations are generally within 0.1%). Based on this new vapor density equation, the compressibility factor of saturated vapor is determined and the vaporization heat is calculated.     

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.     

Chempak: Physical-Properties Database Structure and Development

Chempak (commercial physical properties database and properties estimation software) gives the thermodynamic and transport properties of pure compounds as functions of temperature and pressure for both liquid and vapor phases. Compound liquid properties are defined from the melting to the critical points. Vapor properties are defined from the melting point to 1300 K. The user may define up to 50 mixtures of compounds drawn from the database. In addition, the user may add up to 100 additional compounds defined by using the same techniques employed to construct the main database. Vapor properties are defined by the use of the Lee–Kesler and the Wu and Stiel equations of state. Vapor viscosity and thermal conductivity are defined using corresponding states methods. Liquid thermodynamic properties (except specific heat) are derived from the equation of state. All other liquid properties are defined by setting 11 data values from the melting to the critical point. The resulting property data arrays are interpolated against temperature.     

PR状态方程推算液体多种热力学性质

在汽液平衡区域对ｐｅｎｇ－Ｒｏｂｉｎｓｏｎ立方型状态方程（ＰＲＥｏＳ）及其参数α（Ｔｒ）作了数学分析。结果说明，ＰＲＥＯＳ由于本身的局限而难以兼顾对两相密度、焓值和热容的推算精度。函数α（Ｔｒ）可以用不同的方法得到，当α（Ｔｒ）采用热容数据拟合得到时，则可以较好地同时计算液体的蒸发焓（△Ｈ＿ｖ）和热容偏差（△Ｃ＿ｐ）。本文对Ｃ＿２Ｈ＿６和ＨＣｌ作了举例计算。     

Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13)

Measurements of the molar heat capacity at constant volume C _v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, , T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, , T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C _v predictions with measurements was found. Published C _v(, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C _v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.     

The thermal conductivity and heat capacity of gaseous argon

This paper presents new absolute measurements of the thermal conductivity and of the thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. We measured seven isotherms in the supercritical dense gas at temperatures between 157 and 324 K with pressures up to 70 MPa and densities up to 32 mol · L^–1 and five isotherms in the vapor at temperatures between 103 and 142 K with pressures up to the saturation vapor pressure. The instrument is capable of measuring the thermal conductivity with an accuracy better than 1% and thermal diffusivity with an accuracy better than 5%. Heat capacity results were determined from the simultaneously measured values of thermal conductivity and thermal diffusivity and from the density calculated from measured values of pressure and temperature from an equation of state. The heat capacities presented in this paper, with a nominal accuracy of 5%, prove that heat capacity data can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be invaluable when applied to fluids which lack specific heat data or an adequate equation of state.     

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 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.     

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.     

Vapor-Phase Helmholtz Equation for HFC-227ea from Speed-of-Sound Measurements

This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of 900 cm³ at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.     

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.     

Vapor–Liquid Equilibrium Measurements for Binary Mixtures Containing 1,1,1,2,3,3,3-Heptafluoropropane (HFC-227ea)1

Isothermal vapor–liquid equilibrium data for two binary mixtures of alternative refrigerants were determined by using an apparatus applying recirculating vapor and liquid. The difluoromethane (HFC-32)+1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) and 1,1,1,2-tetrafluoroethane (HFC-134a)+1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) systems were studied at 298.15 and 312.65 K. The pressure and vapor and liquid compositions were measured at each temperature. The experimental data were correlated with the Peng–Robinson equation of state using the van der Waals one-fluid mixing rule. Calculated results show that this equation yields good agreement with the experimental data.     

Thermophysical properties of 1,1,1,2-tetrafluoroethane (R-134a)

The present hypothesis of depletion of the stratospheric ozone layer by some chlorofluorocarbons has prompted a lot of research and development of new stratospherically safe fluids in various uses such as refrigerants, blowing agents in foams, aerosol propellants, solvents, and many other uses. In the areas of certain refrigeration needs 1,1,1,2-tetrafluoroethane (R-134a) has been considered as a possible alternate to the use of dichloro-difluoromethane (R-12), the most commonly used refrigerant. R-12 is estimated to have a higher potential for ozone depletion. This will require a large number of thermophysical property data to help in designing equipment and also in manufacturing R-134a. This paper is intended to fill that need. The paper details the measurement and correlation of some of the important thermophysical properties such as vapor pressure, liquid density, and pressure-volume-temperature. The measured P-V-T data have been used to generate a Martin-Hou-type equation of state for this fluid over a wide range of temperature and pressure. Correlating equations are also developed for vapor pressure, liquid density, and ideal-gas specific heat. Ideal-gas specific heat has been estimated from measured spectroscopic data. The correlating equations can be used to generate the thermodynamic tables and charts. The critical temperature of R-134a has also been measured. Critical density and pressure have been estimated from measured data. The data and the correlations presented here are expected to be very useful to the refrigeration industry in the development of R-134a as a working fluid for refrigeration applications.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

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     

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.     

Equation of state for fluid alkali metals: Binodal

The three-parameter generalized van der Waals equation of state for liquids and gases is analyzed. This equation contains the generalized expressiona/V" for the molecular pressure: here the parametern takes into account the specificity of intermolecular attractive forces for various substances. The equation is presented in the reduced form, from which follows the single-parameter law of corresponding states with the thermodynamic similarity parametern. 11 is established that for alkali metals the value of the parameter it is the same and does not depend on temperature substantially. From the given generalized equation, the expressions for the binodal (equilibrium curve of the liquid and vapor phases) are obtained. For cesium. rubidium, and potassium, the temperature dependence of density is calculated over the temperature range from their melting point to the critical point: the results of the calculations agree with experimental data. It is established that for alkali metals, the law of rectilinear diameter breaks down in the vicinity of the critical point.Paper presented al the Twelfth Symposium on Thermophysical Properties. June 19 –24, 1994, Boulder, Colorado, U.S.A.     

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.     

Development of a New Alpha Function for the Peng–Robinson Equation of State: Comparative Study of Alpha Function Models for Pure Gases (Natural Gas Components) and Water-Gas Systems

Numerous modifications have been suggested for the temperature dependence of the attractive term of the Peng–Robinson equation of state (PR-EOS), through the alpha function. In this work, a new alpha function combining both exponential and polynomial forms is proposed. Pure-compound vapor pressures for different molecular species were fitted and compared using different alpha functions including the Mathias–Copeman and Trebble–Bishnoi alpha functions. The new alpha function allows significant improvements of pure compound vapor pressure predictions (about 1.2% absolute average percent deviations) for all the systems considered, starting from a reduced temperature of 0.4. In addition, a generalization of the classical Mathias–Copeman alpha function was proposed as a function of the acentric factor. These alpha functions were used for VLE calculations on water+various gases including gaseous hydrocarbons. A general procedure is presented to fit experimental VLE data. The corresponding thermodynamic approach is based on the Peng–Robinson equation of state with the above cited alpha functions. It includes the classical mixing rules for the vapor phase and a Henry's law approach to treat the aqueous phase.