A perturbed Yukawa chain equation of state for refractory liquid metals

The perturbed Yukawa chain equation of state (EoS) has been employed to calculate the liquid density of refractory metals over a wide range of temperatures and pressures. The model uses three independent parameters: m-segment number, σ-segment size, and ε/k-segment energy. For pure components, parameters have been obtained by fitting the models to experimental data on liquid densities. Our calculations on the liquid density of tantalum, rhenium, molybdenum, titanium, zirconium, hafnium and niobium from undercooled temperatures up to several hundred degrees above the boiling point and pressures ranging from 0 to 200?MPa reproduces very accurately the experimental pVT data.     

A new equation of state for metal alloys

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model volumetric properties of molten metals and their alloys considering a trimer expression obtained from the statistical associating fluid theory. The van der Waals dispersion forces were applied as perturbation term. Two parameters appeared in the PHT EOS, reflecting the dispersive energy among trimers, ε and the hard-core diameter σ were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the saturated and isobaric densities of 16 molten metals including alkali metals, alkali earth and refractory metals over the temperature range within 234–7400 K and pressures up to 436 MPa. From 677 data points examined, the average absolute deviation (AAD) of the predicted densities from the experimental ones was found to be 1.60%. Furthermore, the estimated uncertainties of predicted densities of alloys were ±3.00%.     

Corresponding-states correlation for the compressed liquid density of metals

Applying the previous correlation for the saturated liquid density of metals, we have developed a corresponding-states correlation for the prediction of their compressed liquid densities. The correlation needs the values of the melting and boiling point parameters of metals plus an adjustable parameter, used to predict the saturated liquid densities. In this work, we have shown that by employing the Tait equation together with the previous correlation, for saturated liquid densities, it is possible to develop an accurate method for the prediction of the compressed liquid density of metals. The agreement of the predicted density values with the experimental ones for alkali metals, mercury, bismuth, tin, and lead over a wide range of temperatures, from melting point up to several hundred degrees above the boiling point, and pressures ranging from the vapor pressure up to 4000 bar, is quite good. From 821 data points examined for the aforementioned metals the average absolute deviation for the calculated densities compared with experiment is 0.72%. The correlation is also examined against a number of existing regularities for the liquid phase.     

A perturbed hard-sphere equation of state for alkali metals

A perturbed hard-sphere equation of state, employing a basic frame proposed by Eslami [H. Eslami, J. Nucl. Mater. 336 (2005) 135–139] has been developed for alkali metals. Following the approach introduced by Ihm et al. [G. Ihm, Y. Song, E.A. Mason, J. Chem. Phys. 94 (1991) 3839–3848], the temperature dependence of the parameters a and b has been fitted to liquid density data for potassium. The scaling parameters that are used to reduce the temperature are the temperature and density at normal boiling point. The important improvement is to omit the adjustable parameters, the well depth and the location of the minimum of pair potential, which are required to apply the earlier equation of state of Eslami. The present EoS, which can be used without fitting parameters, reproduces the volumetric behavior of liquid alkali metals with a very good accuracy. Six hundred and ninety four data points at different pressures and temperatures are examined and the average absolute deviation of predicted liquid density data compared to experiment is 1.41%.     

Equation of state for mercury: revisited

An analytical equation of state by Song and Mason is developed to calculate the PVT properties of mercury. The equation of state is based on the statistical-mechanical perturbation theory of hard convex bodies and can be written as a fifth-order polynomial in the density. There exists three temperature-dependent parameters in the equation of state; the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependant parameters have been calculated using corresponding-states correlations based on the surface tension and the liquid density at the normal boiling point. Employing the present equation of state, we have calculated the PVT properties of mercury over a wide range of temperatures and pressures. The average absolute deviation for the calculated density of mercury in the saturation and compressed states is 1.09%.     

Application of a new equation of state to liquid refrigerant mixtures

A new general equation of state recently reported for pure liquids has been developed to predict the volumetric and thermodynamic properties of six binary and two ternary liquid refrigerant mixtures (including HCs and HFCs mixtures) at different temperatures, pressures, and compositions. The results show this equation of state can be used to reproduce and predict different thermodynamic properties of liquid refrigerant mixtures within experimental errors. The composition dependence of the parameters of this equation of state has been assumed as quadratic functions of mole fraction. Using these mixing rules, the agreement between calculated and experimental densities is better than 0.6% for binary mixtures and 2.3% for ternary mixtures. To compare the performance of this new equation of state against other well-known methods such as the COSTALD method, the density of some refrigerant mixtures, for which the parameters of COSTALD were available, has been computed and compared with those of this new equation of state.     

An improved perturbed hard-sphere equation of state

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the Patel–Teja equation of state (PT) and the Peng–Robinson equation of state (PR) and the original CSPT model. The new CSPT combined with temperature-dependent functions was applied to the vapour–liquid equilibrium data available for 45 pure substances. The results indicate that the new CSPT model can accurately reproduce the experimental vapour–liquid equilibria in the whole temperature and pressure range. The successful calculations of the PVT in the critical region suggest the new CSPT has wide applicability. The new CSPT model is also superior to PR and the original CSPT for calculating the phase behaviour of binary mixtures.     

Densities and Apparent Molar Volumes of Aqueous H<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>BO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript> Solutions at Temperatures from 296 to 573 K and at Pressures up to 48 MPa

Densities of four aqueous H₃BO₃ solutions (0.062, 0.155, 0.315, and 0.529 mol-kg^–1) have been measured in the liquid phase with a constant volume piezometer immersed in a precisely controlled liquid thermostat. Measurements were made at temperatures between 296 and 573 K and pressures from 0.82 to 48 MPa. The total uncertainties of the density, pressure, temperature, and molality measurements were estimated to be less than 0.06%, 0.05%, 10 mK, and 0.0005 mol-kg^–1, respectively. The accuracy of the method was confirmed by PVT measurements on pure water for two isobars (30 and 39 MPa) at temperatures from 313 to 573 K. The experimental and calculated (IAPWS formulation) densities for pure water show excellent agreement which is within their experimental uncertainties (average absolute deviation, AAD=0.012%;). Apparent and partial molar volumes were derived using the measured densities for solutions and pure water, and these results were extrapolated to zero concentration to yield the partial molar volumes of the electrolyte (H₃BO₃) at infinite dilution. The temperature, pressure, and concentration dependencies of the apparent and partial molar volumes were studied. Small pressure and concentration effects on the apparent molar volumes were found at temperatures up to 500 K. The parameters of a polynomial type of equation of state for the specific volume V_sol(P, T, m) as a function of pressure, temperature, and molality were obtained with a least-squares method using the experimental data. The root-mean-square deviation between measured and calculated values from this polynomial equation of state is ±0.2 kg-m^–3 for density. Measured values of the solution densities and the apparent and partial molar volumes are compared with data reported in the literature.     

Modelling the volumetric properties of ionic liquids using a modified perturbed hard-sphere-chain equation of state

In this paper, a modified perturbed hard-sphere-chain equation of state (EOS) by Eslami [H. Eslami, Fluid Phase Equilib. 216 (2004) 21–26], is applied for modelling the thermodynamic properties of some ionic liquids (ILs). Two reliable scaling constants are used to determine two temperature-dependent parameters in the proposed EOS. The unique adjustable parameter that is reflecting the number of segments per molecule, r, compensates the uncertainties in the calculated temperature-dependent parameters. The reliability of the proposed EOS has been checked by comparing the results with 1561 experimental data points for 18 ILs over a broad range of pressures and temperatures. The overall average absolute deviation is 0.35%. A comparison of the predicted results, using the present EOS with the results of some previous models, indicates that the determined results of this EOS are in more accordance with experimental data than those.     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.     

Vapour–liquid equilibria, azeotropic data, excess enthalpies, activity coefficients at infinite dilution and solid–liquid equilibria for binary alcohol–ketone systems

Isothermal vapour–liquid equilibria (VLE), solid–liquid equilibria and excess enthalpies have been measured for the systems cyclohexanone + cyclohexanol and 2-octanone + 1-hexanol. Additionally in this paper binary azeotropic data at different pressures for 1-pentanol + 2-heptanone and 1-hexanol + 2-octanone have been determined with the help of a wire band column. Furthermore activity coefficients at infinite dilution for methanol, ethanol, 1-butanol and 1-propanol in 2-octanone at different temperatures have been measured with the help of the dilutor technique. These data together with literature data for alcohol–ketone systems were used to fit temperature-dependent group interaction parameters for the group contribution method modified UNIFAC (Dortmund) and the group contribution equation of state VTPR.     

Theoretical investigation of the viscosity of some liquid metals and alloys

The viscosities of some liquid metals and liquid binary alloys have been determined using the theoretical model developed by Morioka et al. (Z. Metallkd. 93, 4 (2002)). The model was applied successfully to the liquid mono-component metals Hg and Na and to the liquid binary alloys Hg–Na, Ag–Cu, Bi–Sn and Ag–Sb. The model successfully described the temperature dependence of viscosity for Hg and Na for a wide range of temperatures. The values of the adjustable parameters k and z were obtained for Hg and Na. For the liquid binary alloys, calculations were done at a particular temperature for each alloy and our results show that for Hg–Na and Ag–Cu there are both qualitative and quantitative agreements between calculated and experimental viscosity data. However, Bi–Sn and Ag–Sb manifested significant levels of quantitative discrepancies between calculated and experimental viscosity data.     

High-pressure phase behaviour of the binary system {CO2 + cis-decalin} from (292.75 to 373.75) K

The phase behaviour of the {CO₂ (1) + cis-decalin (2)} binary system has been experimentally studied at temperatures ranging from (292.75 to 373.75) K. Saturation pressures, ranging from (15.9 to 490.5) bar, were obtained using a variable volume high-pressure cell by visual observation of phase transitions at constant overall composition. For this system, no literature data are available and the results obtained in this study reveal the occurrence of vapor–liquid, liquid–liquid, and vapor–liquid–liquid phase transitions in the investigated temperature range. A total of 133 experimental points are reported including bubble points, dew points, liquid–liquid phase equilibria, and coordinates of the three-phase line. The experimental data can be reasonably predicted by the PPR78 model in which the temperature-dependent binary interaction parameter is calculated by a group contribution method.     

Surface tension of pure liquid lanthanide and early actinide metals

A systematic theoretical study of the surface tension of liquid rare earth metals and early actinides is performed. An equation, based on the theoretical considerations suggested by Eyring, enables one to calculate the surface tension of elementary substances in a wide temperature range from melting to boiling points. The results of temperature-dependent surface tension calculations of a pure liquid terbium (1629–1880?K) are fitted as γ?=?845?0.1 (T???T _m) (mJ?m²), where the surface tension decreases linearly with temperature. The surface tension was also calculated, at melting points, for all the liquid rare earth metals from La to Lu and for the first six metals of the actinide series from Ac to Pu. It is observed that the lanthanides may be divided into three groups in accordance with their electronic structure. Mostly, the calculated results agree well with available experimental data.     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

Phase behavior of binary mixtures of water,carbon dioxide and decane predicted with a lattice-gas model

The Kleintjens—Koningsveld lattice-gas model is used to predict the phase behavior of pure CO₂, water and decane, and of binary mixtures of CO₂ with water and decane. The model, with parameters fitted to experimental data, predicts very accurate vapor pressures and liquid—vapor coexistence densities for the pure fluids. For the binary mixtures, the model correctly predicts the qualitative patterns of phase behavior using two temperature-dependent mixture parameters fitted to simple polynomials over a small range of temperature. For quantitative predictions over wide temperature ranges, however, the temperature dependence of the mixture parameters must be fitted carefully over the same ranges of temperatures. The performance of the Kleintjens—Koningsveld model is compared to that of the Peng—Robinson model.     

Isothermal (vapour + liquid) equilibrium for binary mixtures of polyethylene glycol mono-4-nonylphenyl ether (PEGNPE) with methanol,ethanol, or 2-propanol

Saturated pressures of three binary systems of oligomeric polyethylene glycol mono-4-nonylphenyl ether (PEGNPE) with methanol, ethanol, and 2-propanol have been measured by using an autoclave (vapour + liquid) equilibrium (VLE) apparatus at temperatures ranging from (340 to 455) K and the oligomer content ranging from 0.100 to 0.400 in mole fraction. With a given feed composition, equilibrium pressures were measured at various temperatures to obtain VLE data. The experimental data were fitted to the Antoine equation and also correlated with activity coefficient models, the NRTL and the UNIQUAC. The correlation results showed good agreement between the calculated values and the experimental data. In general, the NRTL model yielded better results. Additionally, the solvent activities were evaluated from the experimental results and were compared with those from the NRTL and the UNIQUAC models.     

Analysis of thermoelastic properties and equation of state for cyclopentane,tetramethylsilane and 2,3-dimethylbutane

The thermoelastic properties and equation of state for liquids such as cyclopentane, tetramethylsilane and 2,3-dimethylbutane at high pressures and high temperatures have been analysed. The pressure dependences of thermal expansivity and isothermal compressibility have been determined for these liquids under pressure up to 100?MPa along different isotherms at selected temperatures in the range 208.0–298.15?K. We have formulated the pseudospinodal model for different liquids, along different isotherms for evaluating both thermal expansivity and isothermal compressibility with the change in pressure. It is found that the spinodal pressure is a characteristic property of the liquid depending only on temperature. The results obtained in this study are in good agreement with the experimental data reported in the literature. The plots between thermal expansivity versus pressure along different isotherms intersect each other for tetramethylsilane and 2,3-dimethylbutane. However, in the case of cyclopentane the plots do not intersect each other.     

Burnett—isochoric P—V—T measurements of a nominal 20 mol% hydrogen—80 mol% methane mixture at elevated temperatures and pressures

A new apparatus is described which has been developed to measure P—V—T relations for hydrogen—hdyrocarbon systems at elevated temperatures and pressures. The principal components are three heavy-walled spherical pressure cells with the same outer/internal diameter ratio, a fully submerged differential pressure cell, and measuring equipment including calibrated piston guages and a platinum resistance thermometer. This apparatus was used to measure densities of a 20.05±0.05 mol% hydrogen?79.95±0.05 mol% methane mixture from 273.15 to 600 K and pressures to 72 MPa. Two Burnett isotherms at 273.15 K established fluid densities without direct measurement of either mass or volume. Eight isochores, ranging in density from 1.62 to 14.91 mol dm^?3, were anchored to the Burnett isotherms at 273.15 K where their densities were firmly established. An analytic equation for the thermodynamic surface has been fitted to the resulting P—V—T data, giving a 0.01% root mean square deviation of calculated compressibility factors from experimental results.