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  • 1
    Electronic Resource
    Electronic Resource
    On the Composition of the Solar Interior Rapporteur Paper I (1998)
    Springer
    Space science reviews 85 (1998), S. 141-158 
    Details
    ISSN: 1572-9672
    Keywords: equation of state ; opacity ; helium abundance ; lithium abundance ; tachocline ; solar neutrinos ; helioseismology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Standard solar models, although they are free from the influence of much of the fluid motion that is bound to be present in the Sun, have been shown by helioseismology to represent the spherically averaged structure of the Sun amazingly well. This state of affairs has come about after painstaking refinements by a great many people of the pertinent microphysics, including that which controls the equation of state, the opacity, the nuclear reaction rates and the diffusion that inhibits gravitational segregation of chemical elements. It has instilled confidence in the modellers in being able to predict the composition of the solar interior. But there are consequences of the flow, related particularly to redistribution of chemical species, that can be difficult to identify observationally, yet which may degrade any inferences we might make. Their potential presence must at least be acknowledged by anyone who tries to asses the reliability of the models. This report summarizes the discussions in the preceding pages of this volume of the current theoretical and observational status of the subject, pointing to many of the caveats that have been raised, and attempting at the same time to put them into a seemingly coherent discourse in the context of our present understanding of the workings of the solar interior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005105224272
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  • 2
    Electronic Resource
    Electronic Resource
    Application of the thermodynamics of curved boundary layers to the scaled particle theory of hard-sphere fluids (1973)
    Springer
    Journal of statistical physics 8 (1973), S. 299-307 
    Details
    ISSN: 1572-9613
    Keywords: Statistical thermodynamics of curved boundary layers ; scaled particle theory ; equation of state ; cycle equation ; fluid-solid phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamics of curved boundary layers, with the assumption that the distance between the surface of a fluid cavity and its surface of tension is a quadratic function of the cavity radius, is applied to the exact thermo-dynamic expression forG, the central function of scaled particle theory. The coefficients in the quadratic representation are determined so as to satisfyall five of the known exact conditions onG valid for cavity radii between one-half and one molecular diameter. The results of the calculation are displayed as the hard-sphere equation of state, the boundary tension associated with the surface of tension, and the distance between the cavity surface and the surface of tension. Although the hard-sphere equation of state obtained by this method using all five conditions onG is more accurate than in the case where only two or three conditions are used, the original scaled particle theory, in whichG itself was represented simply by a quadratic function of inverse powers of cavity radius, still yields the more accurate equation of state. Nevertheless, the present approach limits approximations to the distance between the cavity surface and the surface of tension, a small quantity in itself. The path to a still more improved theory remains well defined, contingent upon the discovery of additional exact conditions, and does not depend, as in the original scaled particle theory, on a form forG arrived at in a somewhat ad hoc manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020269
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  • 3
    Electronic Resource
    Electronic Resource
    The pressure of a hard sphere fluid on a curved surface (1986)
    Springer
    Journal of statistical physics 42 (1986), S. 509-521 
    Details
    ISSN: 1572-9613
    Keywords: Hard sphere fluid ; wall-atom distribution function ; wall contact values ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01127724
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  • 4
    Electronic Resource
    Electronic Resource
    The hard-sphere fluid: New exact results with applications (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 1389-1412 
    Details
    ISSN: 1572-9613
    Keywords: Bridge function ; tail function ; cavity functions ; hard-sphere fluids ; second zero-separation theorem ; self-consistent theory ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A theorem for convolution integrals is proved and then applied to extend the “second zero-separation theorem” to the bridge functionb(r) and direct-correlation tail functionsd(r). This theorem allows us to exactly relate∂b(r)/∂r and∂d(r)/∂ratr=0 for the hard-sphere fluid to the “contact value” of the radial distribution functiong(r) atr=σ +. From this we obtain immediately the exact values of ∂b(r)/∂r and ∂d(r)/∂r atr=0 through second order in number density ρ. Using our results to compare the exact and Percus-Yevick (PY) bridge function, we find that they differ significantly. After obtaining the bridge function and tail function and their derivatives atr=0 andr=σ through, we suggest new approximations forb(0) andd(0) as well as an analytical integral-equation theory to improve the PY approximation in the pure hard-sphere fluid. The major deficiency of that approximation has been its poor assessment of the cavity function inside the hard-core region. Our theory remedies this defect in a way that yields ay(r) that is self-consistent with respct to the virial and compressibility relations and also the two zero-separation relations involvingy(r) and its spatial derivative atr=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011655
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  • 5
    Electronic Resource
    Electronic Resource
    A general approach to association using cluster partition functions (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1287-1306 
    Details
    ISSN: 1572-9613
    Keywords: Association ; phase equilibrium ; statistical mechanics ; partition function ; chemical engineering ; equation of state ; chemical equilibrium ; cluster distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181285
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  • 6
    Electronic Resource
    Electronic Resource
    Room-temperature compressibilities of MnO and CdO: further examination of the role of cation type in bulk modulus systematics (1999)
    Springer
    Physics and chemistry of minerals 26 (1999), S. 644-648 
    Details
    ISSN: 1432-2021
    Keywords: Key words MnO ; CdO ; rock-salt monoxides ; X-ray diffraction ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Room-temperature volume measurements up to 8.1 GPa reveal that rock-salt structured MnO and CdO have identical compressibility in the pressure range studied. In the plot of bulk modulus vs unit-cell volume, CdO plots well above the trend of the 3d transition metal monoxides, a behavior that deviates from empirical predictions of constant K 0 V 0. The present observations are in favor of our earlier suggestion that, for isostructural solids, the empirically predicted bulk modulus-volume relationship may be limited to their subsets that share the same valence electron character (i.e., s vs 3d vs 4d). For cations forming transition metal monoxides, variations of Pauling electronegativity with ionic radius show differences that are qualitatively similar to the observed trends of bulk modulus, suggesting that bond covalency differences may contribute to the different behaviors between the 3d and 4d transition metal monoxides.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002690050229
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  • 7
    Electronic Resource
    Electronic Resource
    The SiO2 polymorphs: The equations of state and thermodynamic properties of phase transformations (1987)
    Springer
    Physics and chemistry of minerals 14 (1987), S. 58-66 
    Details
    ISSN: 1432-2021
    Keywords: equation of state ; thermodynamic properties ; phase transformations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Thermal equations of state have been derived for polymorphic forms of SiO2 and values of $$\mathop \smallint \limits_0^P$$ V T dP have been tabulated. Available experimental data on the phase equilibria at high pressures and temperatures have been used with these equations to calculate the standard thermodynamic functions for the α-quartz-coesite and coesite-stishovite transformations. A study of sensitivity of calculated thermodynamical properties to uncertainties of phase equilibria data, initial data for elastic constants and equations of state has been carried out. The discrepancies between standard thermodynamic properties of these transformations calculated from phase equilibria data and solution calorimetry data still persist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311149
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  • 8
    Electronic Resource
    Electronic Resource
    Equation of state calculations for hot, dense matter at arbitrary densities and temperatures (1989)
    Springer
    Acta mechanica Sinica 5 (1989), S. 361-368 
    Details
    ISSN: 1614-3116
    Keywords: average atom model ; equation of state ; Dirac-Slater equation ; pressure ionization effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Within the approximations of spherical lattice cell, central-field, and relativistic Fermi statistics, an algorithm with average atom model is presented to calculate the electronic energy levels and equation of state for hot and dense matter at arbitrary densities and temperatures. Choosing Zink's analytical potential as initial potential, we have solved the Dirac-Slater equation which satisfies the Weigner-Seitz boundary condition. The electronic energy bands are not taken into account. Taking energy level degeneracy as a continuous function of density, we have considered the pressure ionization effects for highly dense matter. Results for13Al atom are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02488009
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  • 9
    Electronic Resource
    Electronic Resource
    The salinity of hypersaline brines: Concepts and misconceptions (1999)
    Springer
    International journal of salt lake research 8 (1999), S. 55-70 
    Details
    ISSN: 1573-8590
    Keywords: Dead Sea ; equation of state ; pycnometry ; salinity ; saturation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geography
    Notes: Abstract Some widespread misconceptions about salinity are pointed out, explained and commented on. Definitions, units, and methods of salinity determination recommended for brines of moderate salinities may become unsuitable for highly saline brines. Various salinity units are examined and commented on, and density at a precisely monitored temperature is chosen as the preferable “substitute parameter” for salinity determination of hypersaline brines. It is shown that ambient air density during pycnometric measurements must be known as accurately as required of the brine's density, and that its value must be added to the direct pycnometric measurement. Variations of atmospheric pressure at the time of pycnometry must be taken into account if greater than 15 mB. For a salinity accuracy of ±0.02 per mille, as required for some physical and chemical studies, the temperature of the sample during salinity measurement must be monitored with an accuracy of at least 0.04°C. A definite curve in the ρ-S plane, corresponding to the conversion of salinity to density at a fixed temperature, andvice-versa, does not exist if the brine is saturated in one of its salts. Non-linearity in the equation of state is shown to affect the surface level drop due to evaporation; the effect is negligible at low salinities, but a 10 per cent correction is already required at the salinity found in the northern Red Sea (41 per mille). Reliable reference points for the conversion of absolute salinity to density of highly saline brines are not known, at present, as accurately as desirable; pending the accurate determination of such reference points, a substantial dilution of hypersaline brines (for the purpose of adapting them to conductivity measurements) would multiply the error range by more than a hundred fold. On the other hand, a minute dilution of hypersaline brine samples to prevent salt crystal formation is possible and would not bring about any major increase of the error range in their density (salinity) determination.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02442137
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  • 10
    Electronic Resource
    Electronic Resource
    The salinity of hypersaline brines: Concepts and misconceptions (1999)
    Springer
    International journal of salt lake research 8 (1999), S. 55-70 
    Details
    ISSN: 1573-8590
    Keywords: Dead Sea ; equation of state ; pycnometry ; salinity ; saturation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geography
    Notes: Abstract Some widespread misconceptions about salinity are pointed out, explained and commented on. Definitions, units, and methods of salinity determination recommended for brines of moderate salinities may become unsuitable for highly saline brines. Various salinity units are examined and commented on, and density at a precisely monitored temperature is chosen as the preferable “substitute parameter” for salinity determination of hypersaline brines. It is shown that ambient air density during pycnometric measurements must be known as accurately as required of the brine's density, and that its value must be added to the direct pycnometric measurement. Variations of atmospheric pressure at the time of pycnometry must be taken into account if greater than 15 mB. For a salinity accuracy of ±0.02 per mille, as required for some physical and chemical studies, the temperature of the sample during salinity measurement must be monitored with an accuracy of at least 0.04°C. A definite curve in the ρ-S plane, corresponding to the conversion of salinity to density at a fixed temperature, and vice-versa, does not exist if the brine is saturated in one of its salts. Non-linearity in the equation of state is shown to affect the surface level drop due to evaporation; the effect is negligible at low salinities, but a 10 per cent correction is already required at the salinity found in the northern Red Sea (41 per mille). Reliable reference points for the conversion of absolute salinity to density of highly saline brines are not known, at present, as accurately as desirable; pending the accurate determination of such reference points, a substantial dilution of hypersaline brines (for the purpose of adapting them to conductivity measurements) would multiply the error range by more than a hundred fold. On the other hand, a minute dilution of hypersaline brine samples to prevent salt crystal formation is possible and would not bring about any major increase of the error range in their density (salinity) determination.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009059827435
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  • 11
    Electronic Resource
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    Thermal expansivity of particulate composites: Interlayer versus molecular model (1989)
    Springer
    Rheologica acta 28 (1989), S. 302-310 
    Details
    ISSN: 1435-1528
    Keywords: Composite ; thermalexpansivity ; interlayer model ; lattice model ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract We continue the comparison of the results of an interlayer model, based on the theory of elastic continua, and a molecular model, derived from a theory of mixtures, previously presented in terms of bulk moduli K. We now derive expressions for the dependence of the thermal expansivityα c on the volume fractionφ f of the filler, at low and elevated values ofφ f . Correspondencies between the characteristic parameters, viz. adhesion and repulsion ratios on the one hand, and interlayer content and thermal properties of matrix, filler, and layer, on the other, are examined. Since in the molecular theory bothα andK are derived from an equation of state, the identical set of parameters determines both functions and suggests correlations between them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01329339
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  • 12
    Electronic Resource
    Electronic Resource
    Bulk modulus of particulate composites: A comparison between a statistical and micro-mechanical approach (1986)
    Springer
    Rheologica acta 25 (1986), S. 161-165 
    Details
    ISSN: 1435-1528
    Keywords: Filled composite ; bulk modulus ; lattice model ; equation of state ; interlayer model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Two models are compared. One is based on the theory of elastic continua, and describes the interaction between filler and matrix in terms of an interfacial layer of varying volume fraction and elastic properties. The other derives from an equation of state for the constituents and the composite, based on molecular considerations. The filler-matrix interaction is then expressed in terms of segmental attractions and repulsions. We examine the dependence of the bulk modulusK c (ϕ f ) on the volume fractionϕ f of filler and then show the correspondence between the two theories in terms of the infinite dilution limit of the ratio [K c (ϕ f ) −K m ]/(K m ϕ f ) where the indexm refers to the matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01332134
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  • 13
    Electronic Resource
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    Microphysics: Equation of State (1998)
    Springer
    Space science reviews 85 (1998), S. 49-60 
    Details
    ISSN: 1572-9672
    Keywords: helioseismology ; equation of state ; helium abundance ; excited states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The equation of state is one of the three fundamental ingredients used to construct stellar models. The plasma of the interiors of stars such as the Sun is only slightly non-ideal. However, the extraordinary accuracy of the helioseismological data requires refined equations of state. It turned out to be necessary to include a Coulomb correction, commonly evaluated in the Debye-Hückel approximation. Higher-order non-ideal effects have implications as well, both for plasma physics and for solar physics. As a typical example, the recently studied thermodynamic consequence of excited states in compound particles is discussed. This effect is of considerable relevance in the helioseismic determination of the helium abundance in the solar convection zone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005176317912
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  • 14
    Electronic Resource
    Electronic Resource
    High-pressure equation of state for solid krypton from interatomic potentials (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 1359-1365 
    Details
    ISSN: 1572-9613
    Keywords: High pressure ; equation of state ; krypton ; interatomic potential ; solid krypton ; many-body interactions ; Monte Carlo method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The pressure-volume isotherm for krypton at 300 K is evaluated by the Monte Carlo method using pair and three-body potentials. The pair potentials used are that of Aziz and Slaman and a slightly modified version of their potential which gives better agreement with high-energy scattering data. The three-body potentials considered are the Axilrod-Teller interaction and the first-order three-body exchange interaction as parametrized by Loubeyre. The results are compared with recent measurements at pressures up to 300 kbar and the implications of the comparison are discussed. The best agreement with experiment is found using the Axilrod-Teller interaction as the only many-body interaction, indicating that the three-body exchange interaction is to a large extent canceled by higher many-body interactions, at least in the highly symmetrical environment of the crystal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011653
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  • 15
    Electronic Resource
    Electronic Resource
    Further application of the statistical thermodynamics of curved surfaces to scaled particle theory (1973)
    Springer
    Journal of statistical physics 7 (1973), S. 143-159 
    Details
    ISSN: 1572-9613
    Keywords: Statistical thermodynamics of curved boundary layers ; scaledparticle theory ; equation of state ; cycle equation ; fluid-solid phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamics of curved boundary layers is combined with scaled particle theory to determine the rigid-sphere equation of state. In particular, the boundary analog of the Gibbs-Tolman-Koenig-Buff equation is solved for a rigid-sphere fluid, using the approximation that the distance between the surface of a cavity and its surface of tension is a function of the density only (the first-order approximation). This, in conjunction with several exact conditions onG, the central function of scaled particle theory, leads to an approximate rigid-sphere fluid equation of state and a qualitatively correct rigid-sphere solid equation of state. The fluid isotherm compares favorably with previous results (2.9 % error in the fourth virial coefficient), but due to the inaccuracy of the solid isotherm, no phase transition is obtained. The theory described here is to be contrasted with previous approaches in that a less arbitrary functional form forG is assumed, and the surface of tension and cavity surface are not assumed to be coincident. The “cycle equation” of Reiss and Tully-Smith is rederived by a simpler route and shown to be correct to all orders of cavity curvature, rather than only first order as was originally thought. A new exact condition, obtained from the compressibility equation of state, is used as a boundary condition for the “cycle equation” to determine the location of the equimolecular surface. This molecular calculation compares favorably (discrepancy of 〈2 %) with a thermodynamic calculation based on the boundary analog of the Gibbs adsorption equation and indicates the accuracy and consistency of the first-order approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01024212
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  • 16
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    Coulomb Systems at Low Density: A Review (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 1163-1330 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb ; plasma ; Saha ; screening ; Debye–Hückel ; virial ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004600603161
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  • 17
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    Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 101-110 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; R 134a ; refrigerants ; simulated annealing ; stepwise regression ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438961
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  • 18
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    Equations of state for the thermodynamic properties of R32 (difluoromethane) and R125 (pentafluoroethane) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 79-89 
    Details
    ISSN: 1572-9567
    Keywords: difluoromethane (R32) ; equation of state ; pentafluoroethane (R125) ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Thermodynamic properties of difluoromethane (R32) and pentafluoroethane (R125) are expressed in terms of 32-term modified Benedict-Webb-Rubin (MBWR) equations of state. For each refrigerant, coefficients are reported for the MBWR equation and for ancillary equations used to fit the ideal-gas heat capacity and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined with a multiproperty fit that used the following types of experimental data: PVT: isochoric, isobaric, and saturated-liquid heal capacities; second virial coefficients; and properties at coexistence. The respective equations of stale accurately represent experimental data from 160 to 393 K and pressures to 35 MPa for R32 and from 174 to 448 K and pressures to 68 MPa for R125 with the exception of the critical regions. Both equations give reasonable results upon extrapolation to 500 K and 60 MPa. Comparisons between predicted and experimental values are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438959
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  • 19
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    A fundamental equation of state for 1,1-difluoroethane (HFC-152a) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 91-100 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; Helmholtz free energy ; HFC-152a ; refrigeranis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438960
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  • 20
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    Determination of thermodynamic properties from the speed of sound (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 663-673 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; speed of sound ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We describe methods by which all of the observable thermodynamic properties of a compressed gas, including the compressibility factor and the isochoric heat capacity, may be determined from sound speed data by numerical integration of a pair of partial differential equations. The technique may be employed over a wide range of conditions. Initial values are required. but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of analytic and numerical results. The results indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.
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    URL: http://dx.doi.org/10.1007/BF01438851
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    Molecular simulation and theory of associating chain molecules (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 705-713 
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    ISSN: 1572-9567
    Keywords: associating fluids ; chain fluids ; computer simulations ; equation of state ; hydrogen bonding ; Lennard-Jones ; Monte Carlo
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A closed-form statistical mechanical based equation of state for associating chain fluids is presented. A Lennard-Jones chain is used as a reference to account for the repulsive, dispersive and anisotropic (size) contributions, while the short-range directional attraction is treated as a perturbation expansion based on Wertheim's first-order theory of associating fluids. A model fluid composed of a chain of tangently bonded Lennard-Jones spheres with an associating square-well site at one of the end spheres is studied. Isobaric-isothermal Monte Carlo simulations were performed for this model at subcritical and supercritical temperatures at a association strength typical of hydrogen-bonding systems. The theory is seen accurately to predict the simulation results subject to the limitations of the equation of state of the reference fluid. The system studied has some of the main complexities found in associating chain molecules such as organic acids, alkanols, and primary amines.
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    The ISM Equation of State Applied to Refrigerants (1999)
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    International journal of thermophysics 20 (1999), S. 1547-1555 
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    ISSN: 1572-9567
    Keywords: cohesive energy ; equation of state ; non-polar fluids ; refrigerants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this work, we apply an equation of state based on statistical–mechanical perturbation theory to liquid refrigerants and their mixtures. Three temperature-dependent parameters are needed to use the equation of state: the second virial coefficient, B 2(T), an effective van der Waals covolume, b(T), and a scaling factor, α(T). The second virial coefficients are calculated from a correlation based on the heat of vaporization, ΔH vap, and the liquid density at the freezing point, ρfp. α(T) and b(T) can also be calculated from the second virial coefficient by a scaling rule. Based on the theory, these two temperature-dependent parameters depend only on the repulsive branch of the potential function, and therefore, by our procedure, can be found from ΔH vap and ρfp. The theory has considerable predictive power, since it permits the construction of the p–v–T surface from the heat of vaporization plus the triple-point density. The equation of state is tested for pure, two- and three-component liquid refrigerant mixtures.
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    URL: http://dx.doi.org/10.1023/A:1021401407904
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    Equation of State for Molten Alkali Metal Alloys (1999)
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    International journal of thermophysics 20 (1999), S. 1575-1585 
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    ISSN: 1572-9567
    Keywords: alkali metal alloys ; cohesive energy ; equation of state ; statistical mechanics ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Calculated results of the liquid density of binary molten alloys of Na–K and K–Cs over the whole range of concentrations and that of a ternary molten eutectic of Na–K–Cs from the freezing point up to several hundred degrees above the boiling point are presented. The calculations were performed with the analytical equation of state proposed by Ihm, Song, and Mason, which is based on statistical-mechanical perturbation theory. The second virial coefficients were calculated from the corresponding-states correlation of Mehdipour and Boushehri. Calculation of the other two temperature-dependent parameters was carried out by scaling. The calculated results cover a much wider range of temperatures and are more accurate than those presented in our previous work.
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    Compressibilities of ternary mixtures C1-nC16-CO2 under pressure from ultrasonic measurements of sound speed (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 851-871 
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    ISSN: 1572-9567
    Keywords: compressibility ; equation of state ; high pressure ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Speed of sound measurements have been performed on three mixtures of the ternary system methane + carbon dioxide + normal hexadecane. The systems have been investigated from 12 to 70 MPa in the temperature range from 313 to 393 K. Furthermore, these measurements have allowed the evaluation of the isothermal and the isentropic compressibilities up to 70 MPa from low pressure (〈40-MPa) density data.
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    URL: http://dx.doi.org/10.1007/BF01439193
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    Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 909-944 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; ethane ; methane ; plait point ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.
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    Equation of state for compressed liquids from surface tension (1996)
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    International journal of thermophysics 17 (1996), S. 945-957 
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    ISSN: 1572-9567
    Keywords: compressed liquids ; corresponding states ; equation of state ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A method for predicting an analytical equation of state for liquids from the surface tension and the liquid density at the freezing temperature (γ 1,ϱ 1) as scaling constants is presented. The reference temperature. Tref. is introduced and the product (T ref T 1 1 2 ) is shown to be an advantageous corresponding temperature for the second virial coeflicienls. B2(T). of spherical and molecular fluids. Thus, B2(T) follows a promising corresponding states principle and then calculations forα(T) andb(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, (γ 1,ϱ 1) are sufficient for the determination of thermophysical properties of fluids from the freezing line up to the critical temperature. The present procedure has the advantage that it can also be used in cases whereT c andP c are not known or the vapor pressure is too small to allow accurate measurements. We applied the procedure to predict the density of Lennard-Jones liquids over an extensive range of temperatures and pressures. The results for liquids with a wide range of acentric factor values are within 5%.
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    Thermodynamic Properties of Sulfur Hexafluoride (2000)
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    International journal of thermophysics 21 (2000), S. 739-765 
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    ISSN: 1572-9567
    Keywords: Burnett measurements ; equation of state ; heat capacity ; intermolecular potential ; speed of sound ; sulfur hexafluoride ; SF6 ; thermodynamic properties ; vapor pressure ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present new vapor phase speed-of-sound data u(P, T), new Burnett density–pressure–temperature data ρ(P, T), and a few vapor pressure measurements for sulfur hexafluoride (SF6). The speed-of-sound data spanned the temperature range 230 K≤T≤460 K and reached maximum pressures that were the lesser of 1.5 MPa or 80% of the vapor pressure of SF6. The Burnett ρ(P, T) data were obtained on isochores spanning the density range 137 mol·m−3≤ρ≤4380 mol·m−3 and the temperature range 283 K≤T≤393 K. (The corresponding pressure range is 0.3 MPa≤P≤9.0 MPa.) The u(P, T) data below 1.5 MPa were correlated using a model hard-core, Lennard–Jones intermolecular potential for the second and third virial coefficients and a polynomial for the perfect gas heat capacity. The resulting equation of state has very high accuracy at low densities; it is useful for calibrating mass flow controllers and may be extrapolated to 1000 K. The new u(P, T) data and the new ρ(P, T) data were simultaneously correlated with a virial equation of state containing four terms with the temperature dependences of model square-well potentials. This correlation extends nearly to the critical density and may help resolve contradictions among data sets from the literature.
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    URL: http://dx.doi.org/10.1023/A:1006697620523
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    A thermodynamic property formulation for nitrogen from the freezing line to 2000 K at pressures to 1000 MPa (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 503-511 
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    ISSN: 1572-9567
    Keywords: equation of state ; nitrogen ; saturation properties ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new fundamental equation explicit in Helmholtz energy for thermodynamic properties of nitrogen from the freezing line to 2000 K at pressures to 1000 MPa is presented. A new vapor pressure equation and equations for the saturated liquid and vapor densities as functions of temperature are also included. The techniques used for development of the fundamental equation are those reported in a companion paper for ethylene. 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 also included in that paper. The property formulation using the fundamental equation reported here may generally be used to calculate pressures and densities with an uncertainty of ±0.1%, heat capacities within ± 2%, and velocity of sound values within ±2%. The fundamental equation is not intended for use near the critical point.
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    Statistical mechanical description of supercritical fluid extraction and retrograde condensation (1987)
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    International journal of thermophysics 8 (1987), S. 449-471 
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    Keywords: conformal solution theory ; equation of state ; mixing rules ; mixtures ; retrograde condensation ; statistical mechanics ; supercritical fluid extraction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The phenomena of supercritical fluid extraction (SFE) and its reverse effect, which is known as retrograde condensation (RC), have found new and important applications in industrial separation of chemical compounds and recovery and processing of natural products and fossil fuels. Full-scale industrial utilization of SFE/RC processes requires knowledge about thermodynamic and transport characteristics of the asymmetric mixtures involved and the development of predictive modeling and correlation techniques for performance of the SFE/RC system under consideration. In this report, through the application of statistical mechanical techniques, the reasons for the lack of accuracy of existing predictive approaches are described and they are improved. It is demonstrated that these techniques also allow us to study the effect of mixed supercritical solvents on the solubility of heavy solutes (solids) at different compositions of the solvents, pressures, and temperatures. Fluid phase equilibrium algorithms based on the conformal solution van der Waals mixing rules and different equations of state are presented for the prediction of solubilities of heavy liquid in supercritical gases. It is shown that the Peng-Robinson equation of state based on conformal solution theory can predict solubilites of heavy liquid in supercritical gases more accurately than the van der Waals and Redlich-Kwong equations of state.
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    Chempak: Physical-Properties Database Structure and Development (1998)
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    International journal of thermophysics 19 (1998), S. 771-779 
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    ISSN: 1572-9567
    Keywords: databases ; equation of state ; thermodynamic properties ; transport properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    Thermodynamic properties of methane in the critical region (1988)
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    International journal of thermophysics 9 (1988), S. 73-84 
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    Keywords: critical parameters ; critical phenomena ; equation of state ; methane ; sound velocity ; specific heat ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A scaled fundamental equation is presented for the thermodynamic properties of methane in the critical region. The equation supplements the international formulation for the thermodynamic properties of methane issued by IUPAC.
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    The prediction of high-density thermodynamic states using molecular shape factors (1988)
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    International journal of thermophysics 9 (1988), S. 975-983 
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    ISSN: 1572-9567
    Keywords: corresponding states ; equation of state ; molecular shape factor ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new extended corresponding-states method for the prediction of high-density states for pure fluids is presented. The method incorporates the use of molecular shape factors. This approach requires accurate equations for the saturated-liquid density and the vapor pressure for the fluid in question. In addition, an equation of state for the vapor phase is also required. With this information, the molecular shape factors are calculated on the saturated-liquid line of the fluid being predicted, and they are assumed to be constant in the high-density, single-phase region along isotherms. This property prediction method is well suited for application to any fluid that has an equation of state valid in the vapor phase. Modern equations of state for nitrogen and oxygen were used to define properties of reference fluids in the development and testing of this new method. Experimental data for liquid ethylene were used to verify the accuracy of the new prediction method. Tests have shown that this approach predicts high-density data accurately to approximately six times the critical pressure and up to 85 % of the critical temperature. The results of these tests are presented and discussed.
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    Isochoric pvT measurements of SF6 in the density range 100 to 1200 kg · m−3 (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 791-802 
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    Keywords: adsorption isotherm ; compressibility factor ; equation of state ; isochoric measurement ; SF6
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The pvT properties of SF6 were determined by an isochoric method. The pressure p and the temperature T were measured in the pressure range 1.5 MPa ⩽ p ⩽ 9.0 MPa and in the temperature range 293 K ⩽ T ⩽ 340 K. The results are compared with data in the literature. The adsorption of SF6 on glass and iron surfaces and its influence on the pvT measurements are also briefly discussed.
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    Selected equation of state in the acentric factor system (1988)
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    International journal of thermophysics 9 (1988), S. 965-974 
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    Keywords: acentric factor ; corresponding states ; equation of state ; virial coefficient
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    Notes: Abstract A new equation of state in the acentric factor system is developed on the basis of high-precision data. The region inT r,ρ r space where there is good agreement is identified, as well as the regions of significant departures. The equation fits very well in the critical region.
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    Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 217-228 
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    Keywords: air ; equation of state ; fundamental equation ; high pressure ; high temperature ; thermodynamic properties
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    Notes: Abstract A thermodynamic property formulation for standard dry air based upon experimental P–ρ–T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.
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    Evaluation of the thermodynamic properties of tungsten (1985)
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    International journal of thermophysics 6 (1985), S. 395-409 
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    Keywords: enthalpy ; equation of state ; heat capacity ; high pressure ; high temperature ; thermodynamic properties ; tungsten
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    Notes: Abstract A new evaluation of the thermodynamic properties of tungsten has been made. A set of parameters describing the Gibbs energy of each individual phase as a function of temperature and pressure is given. The experimental information on the P, T phase diagram and the thermodynamic data are compared with calculations made using the presented set of parameters.
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    Prediction of transport properties of dense gases and liquids by the Peng-Robinson (PR) equation of state (1989)
    Springer
    International journal of thermophysics 10 (1989), S. 133-144 
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    Keywords: Enskog theory ; equation of state ; fluids (dense) ; thermal conductivity ; viscosity
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    Notes: Abstract An attempt is made in this work to combine the Enskog theory of transport properties with the simple cubic Peng-Robinson (PR) equation of state. The PR equation of state provides the density dependence of the equilibrium radial distribution function. A slight empirical modification of the Enskog equation is proposed to improve the accuracy of correlation of thermal conductivity and viscosity coefficient for dense gases and liquids. Extensive comparisons with experimental data of pure fluids are made for a wide range of fluid states with temperatures from 90 to 500 K and pressures from 1 to 740 atm. The total average absolute deviations are 2.67% and 2.02% for viscosity and thermal conductivity predictions, respectively. The proposed procedure for predicting viscosity and thermal conductivity is simple and straightforward. It requires only critical parameters and acentric factors for the fluids.
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    A new nonrandom lattice fluid model and its simplification by two-liquid theory for phase equilibria of complex mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 723-731 
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    Keywords: complex mixtures ; equation of state ; multiphase equilibria ; nonrandom lattice theory ; polymer solutions ; supercritical fluids
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A new riogorous equation of state (EOS) and its simplified version have been proposed by the present authors based on the full Guggenheim combinatorics ] of the nonrandom lattice hole theory. The simplified EOS. with the introduction of the concept of local composition, becomes similar to the density-dependent UNIQUAC model. However, im the present approach we have a volumetric EOS instead of the excess Gibbs function. Both EOSs were tested for their applicability in correlating the phase equilibria behavior of pure components and complex mixtures. Comparison of both models with experiment includes such systems as nonpolar nonpolar, nonpolar polar, and polar polar hydrocarbons, supercritical systems, and polymer solutions. With two parameters for each pure component and one binary interaction energy parameter, results obtained to date demonstrate that both formulations are quantitatively applicable to complex systems oer a wide range of temperatures, pressures, and concentrations.
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    Thermodynamic properties of the generalized Murnaghan equation of state of solids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1009-1026 
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    Keywords: Anderson-Grüneisen ; bulk modulus ; equation of state ; expansivity ; high pressure ; Murnaghan equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In the Murnaghan approximation, an isothermal relation between pressure (P) and volume (V) for solids is derived from the assumption that the isothermal bulk modulus (B) is a linear function ofP. This paper presents a thermodynamic analysis of a generalized form of the equation, based on treating all its various parameters [viz., V, B, and (∂B/∂P) T atP=0] as functions of temperature. Extending a previous study, the effect ofT upon (∂B/∂P) T is accounted for by using a dimensionless parameter introduced by us, which is used in formulating general expressions for the volume dependence of various thermophysical quantities,viz., the thermal expansion coefficient (α), the productαB, and the Grüneisen and Anderson-Grüneisen parameters. Some combinations of these parameters are identified, which show a simple dependence uponP. The new expressions are used in analyzing current approximations and the behavior of the solid in the low-compression range. In particular, an expression forα at highP is reported which generalizes the Anderson equation and previous results by us.
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    Application of nonlinear regression in the development of a wide range formulation for HCFC-22 (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1155-1164 
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    Keywords: chlorodifluoromethane ; equation of state ; HCFC-22 ; nonlinear fitting ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract 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-ρ-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.
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    Vapor-liquid equilibrium, coexistence curve, and critical locus for binary HFC-32/HFC-134a mixture (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1175-1184 
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    Keywords: binary interaction parameter ; critical density ; critical temperature ; equation of state ; R-32/134a mixture ; vapor-liquid coexistence curve ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Two kinds of equilibrium measurements of binary R-32/134a mixtures were carried out. The vapor-liquid equilibria were measured by the static method in the temperature range between 283 and 313 K. On the basis of the present experimental data, the temperature dependence of the binary interaction parameterk 12 for two equations of state, namely, the Soave-Redlich-Kwong equation and Carnahan-Starling-De Santis equation, was discussed. The vapor-liquid coexistence curve near the critical point was also measured by the observation of meniscus disappearance. The critical temperatures and critical densities of 30 and 70 wt% R-32 mixtures were determined on the basis of the saturation densities along the coexistence curve in the critical region. In addition, a correlation of the critical locus for this mixture is proposed as a function of composition.
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    The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1165-1174 
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    Keywords: activity coefficient ; equation of state ; MHV-2 ; refrigerants ; R32 ; R134a ; R125 ; vapor-liquid equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper reports on the development and application of a thermodynamic model based on the second-order Modified Huron Vidal equation of state (MHV-2) to predict the properties of ternary mixtures of the refrigerants R32, R125, and R134a. The mixing rules of this equation of state have been used to incorporate directly an activity-coefficient model for the excess Gibbs free energy. The parameters for the activity-coefficient model have been derived from experimental VLE data for binary mixtures. This methodology has enabled the production of a thermodynamically consistent model which can be used to predict the phase equilibria of R32/R125/R134a mixtures. The input data used in the model are presented in the paper and the predictions of the model are compared with available experimental data. The model has been used to predict the behavior of ternary refrigerant blends of R32/R125/R134a in fractionation scenarios, such as liquid charging and vapor leakage, which are of direct interest to the refrigeration industry. Details of these applications and comparisons with experimental data are discussed, along with other general uses of the thermodynamic model.
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    URL: http://dx.doi.org/10.1007/BF02081284
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    Prediction of multiphase equilibria in associating fluids by a contact-site quasichemical equation of state (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1287-1297 
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    ISSN: 1572-9567
    Keywords: associating fluids ; contact-site model ; equation of state ; group contribution ; monomer fraction ; multiphase equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A contact-site quasichemical equation of state has been used Tor the modeling of different kinds of fluid phase equilibria (between a gas phase and one or more liquids) over a wide range of conditions. Among the systems of interest are the ternary mixtures water + alkanols + hydrocarbons (alkanes or alkynes), water + alkanols (or acetone)+ CO2, water + polyoxyethyleneglycol ethers + heavy alkanes. The model has been applied to describing the thermodynamic properties of the binary subsystems and to predict the phase behavior of the ternary systems. For longer-chain alkanols and hydrocarbons a group-contribution approach is implemented, which allows the modeling when no experimental data are available. The model gives reasonable predictions of phase behavior and the correct trends in the calculated phase diagrams in most cases. The concentrations of associates in liquid and gas phases are estimated by the model and compared with some experimental and computer simulation data. The predictive abilities of the model, its limitations, and possible ways of its improvement are discussed.
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    URL: http://dx.doi.org/10.1007/BF02081296
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    A New equation of state for square-well molecules (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1277-1286 
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    ISSN: 1572-9567
    Keywords: equation of state ; molecular simulation ; perturbation theory ; second virial coefficient ; square-well molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents a new equation of state for the square-well fluid based on perturbation theory. This equation has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and accurately interpolates between the two limits. Monte Carlo simulations were performed to evaluate the limiting behavior of the theory in the dilute-gas regime. Comparison of the theory with the simulation results shows excellent agreement between the equation-of-state predictions and the data.
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    Ideal-gas thermodynamic properties for natural-gas applications (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1381-1392 
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    ISSN: 1572-9567
    Keywords: caloric properties ; equation of state ; ideal gas ; isobaric heat capacity ; natural gas ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Calculating caloric properties from a thermal equation of state requires information such as isobaric heat capacities in the ideal-gas state as a function of temperature. In this work, values for the parameters of thec p 0 correlation proposed by Aly and Lee were newly determined for 21 pure gases which are compounds of natural gas mixtures. The values of the parameters were adjusted to selectedc p 0 data calculated from spectroscopic data for temperatures ranging from 10 to 1000 K. The data sources used are discussed and compared with literature data deduced from theoretic models and caloric measurements. The parameters presented will be applied in a current GERG project for evaluating equations of state (e.g., the AGA 8 equation) for their suitability for calculating caloric properties.
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    An analytical method of predicting Lee-Kesler-Plöcker equation-of-state binary interaction coefficients (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1393-1411 
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    ISSN: 1572-9567
    Keywords: computer algorithm ; binary interaction coefficient ; equation of state ; mixture ; nonpolar and polar substances ; thermodynamic properties ; reduced properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An analytical method is proposed for finding numerical values of binary interaction coefficients for the Lee-Kesler-Plöcker (LKP) equation of state. The method is based on solving simultaneous equations from Plöcker's mixing rules for pseudocritical parameters of a mixture and the Lee-Kesler equation for the saturation line. For mixtures of hydrocarbons containing from two to nine carbon atoms, the divergence between calculated and experimentally based interaction coefficients (ICs) is no more than ±0.4%. The method is extended to mixtures of polar substances. For polar mixtures, aneffective molar composition concept is introduced which takes into account the impact of dipole moments on the process of molecular associations. Formulas for finding the effective molar composition of mixtures containing polar and/or nonpolar constituents and the binary interaction coefficient (κ ij) based on this effective composition and pure component properties are shown. Calculatedκ ij values for 12 binary mixtures of polar substances differ by 0.4 % or less from correspondingκ ij values obtained by processing experimental data on saturated pressure (P s) and saturated temperature (T s) lines for these same mixtures. A simplified alternativeκ ij approximation method with an error (2–5 %) is also given for mixtures of polar substances.
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    A corresponding-states principle for the equation of state of linear homonuclear fused-hard-sphere fluids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1413-1419 
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    ISSN: 1572-9567
    Keywords: equation of state ; corresponding states ; fused-hard-sphere fluids ; hard spheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A theoretically based corresponding-states principle previously developed for the equation of state of hard-convex-body fluids is extended to rigid linear homonuclear fused-hard-sphere fluids. Effective volumes and shapes are introduced in order to account for the nonconvexity of the molecules. The excess compressibility factor, reduced by means of a parameter which can be determined analytically, is a common function of the effective packing fraction. The analytical expression for the function can be obtained from the equation of state of the hard-sphere fluid. Existing simulation data for diatomics, triatomics and tetraatomics show excellent agreement with the corresponding-states principle.
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    URL: http://dx.doi.org/10.1007/BF02083549
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    An analytical equation of state for molten alkali metals (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1429-1438 
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    ISSN: 1572-9567
    Keywords: cohesive energy ; equation of state ; molten alkali metals ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper brings the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range. As for normal fluids, the latent heat of vaporization and density at freezing temperature are the only inputs (scaling factors). The correspondingstates correlation of normal fluids is used to calculate the second virial coefficient,B 2(T), of alkali metals, which is scarce experimentally and its calculation is complicated by dimer formation. Calculations of the other two temperature-dependent constants,α(T) andb(T), follow by scaling. The virial coefficients of alkali metals cannot be expected to obey a law of corresponding states for normal fluids. The fact that two potentials are involved may be the reason for this. Thus, alkali metals have the characteristics of interacting through singlet and triple potentials so that the treatment by a single potential here is fortuitous. The adjustable parameter of the equation of state,γ, compensates for the uncertainties inB 2(T). The procedure used to calculate the density of liquids Li through Cs from the freezing line up to several hundred degrees above the boiling temperatures. The results are within 5 %.
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    Solubilities of long-chain hydrocarbons in carbon dioxide (1996)
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    International journal of thermophysics 17 (1996), S. 23-33 
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    ISSN: 1572-9567
    Keywords: equation of state ; heavy hydrocarbons ; natural gas ; supercritical carbon dioxide ; wax deposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Heavy hydrocarbons are becoming an increasingly important problem for the natural gas industry as it develops more costly gas reserves, such as those in the deep Gulf of Mexico. The waxy substances precipiate during natural gas processing, causing blockage of transmission pipelines. Knowledge of the solubility behavior of these hydrocarbon solids is therefore necessary to develop solutions to the solid deposition problem. This work reports solid-supercritical fluid equilibrum data for long-chain n-alkanes in carbon dioxide, a component of natural gas, over a range of temperatures and pressures that are typical of natural gas processing. A flow apparatus was used to measure the solubility, and the data were correlated by the Patel-Teja equation of state. Satisfactory agreement was obtained between calculated and experimental values, so the equation of state may be used to estimate the conditions for solid deposition and the amounts of solids formed at typical processing conditions.
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    An accurate Van der Waals-type equation of state for the Lennard-Jones fluid (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 391-404 
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    ISSN: 1572-9567
    Keywords: coexistence curve ; equation of state ; Lennard Jones fluid ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract A new equation of state (EOS) is proposed for the Helmholtz energyF of the Lennard Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation.F =F u +F v. WhereF u is a hard body contribution andF A an anttractive dispersion force contribution. The expression forF H is closely related to the hybrid Barker Henderson pertubation theory. The construction ofF A is accomplished with the Setzmann Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS of Johnson et al. shows improvement in the description of the vapor liquid coexistence properties, thepvT data. and in peculiar, of the calorie properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still by about 30%.
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    Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 455-484 
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    ISSN: 1572-9567
    Keywords: CF4 ; C2F6 ; equation of state ; hexafluoroethane ; speed of sound ; tetrafluoromethane ; thermodynamic properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A cylindrical resonator was employed to measure the sound speeds in gaseous CF4 and C2F6. The CF4 measurements span the temperature range 300 to 475 K, while the C2F6 measurements range from 210 to 475 K. For both gases, the pressure range was 0.1 MPa to the lesser of 1.5 MPa or 80% of the sample’s vapor pressure. Typically, the speeds of sound have a relative uncertainty of less than 0.01 % and the ideal-gas heat capacities derived from them have a relative uncertainty of less than 0.1%. The heat capacities agree with those determined from spectroscopic data. The sound speeds were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two models for the virial coefficients were employed, one based on square-well potentials and the second based on a Kihara spherical-core potential. The resulting virial equations reproduce the sound-speed measurements to within 0.005 % and yield densities with relative uncertainties of 0.1% or less. The viscosity calculated from the Kihara potential is 2 to 11% less than the measured viscosity.
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    URL: http://dx.doi.org/10.1007/s10765-005-0001-6
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    Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1629-1638 
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    ISSN: 1572-9567
    Keywords: equation of state ; mixtures ; R-32 ; R-125 ; R-134a ; R-152a ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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%.
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    An Equation of State for 1,1,1-Trifluoroethane (R-143a) (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1639-1651 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; Helmholtz energy ; R-143a ; 1,1,1-trifluoroethane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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–ρ–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.
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    Determination of Second Virial Coefficients and Virial Equations of R-32 (Difluoromethane) and R-125 (Pentafluoroethane) Based on Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1677-1688 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; hydrofluorocarbon ; R-32 ; R-125 ; second virial coefficient ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The second virial coefficients, B, for difluoromethane (R-32, CH2F2) and pentafluoroethane (R-125, CF3CHF2) are derived from speed-of-sound data measured at temperatures from 273 to 343 K with an experimental uncertainty of ±0.0072%. Equations for the second virial coefficients were established, which are valid in the extensive temperature ranges from 200 to 400 K and from 240 to 440 K for R-32 and R-125, respectively. The equations were compared with theoretically derived second virial coefficient values by Yokozeki. A truncated virial equation of state was developed using the determined equation for the virial coefficients. The virial equation of state represents our speed-of-sound data and most of the vapor PρT data measured by deVries and Tillner-Roth within ±0.01 and ±0.1%, respectively.
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    Application of New, Modified BWR Equations of State to the Corresponding-States Prediction of Natural Gas Properties (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1721-1735 
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    ISSN: 1572-9567
    Keywords: corresponding states ; density ; equation of state ; Lee–Kesler ; natural gas mixtures ; n-heptane ; n-pentane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The accurate description of mixtures includes both single-phase (bulk) properties and the location of phase equilibrium boundaries, e.g., properties that depend upon partial molar properties. In order to estimate these properties, many variants of corresponding-states theory have been developed, especially for nonpolar mixtures such as those found in natural gas systems, In this work we have developed two new, modified BWR equations of state for two natural gas components (n-pentane and n-heptane) and used these equations in a reformulated (Teja-like) Lee–Kesler model. The reformulated model has been tested on bulk-phase properties of hydrocarbon systems, in both the pure and the mixed states. Results have been obtained using the original Lee–Kesler model, the extended corresponding-states theory, and the multifluid corresponding-states principle using several combinations of reference fluids chosen from this and previous equation of state studies. Details of the new equations of state and theoretical comparisons are reported.
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    Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1557-1574 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical properties ; critical volume ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.
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    Speed of Sound in the Liquid Phase of the R134a/152a Refrigerant Blend (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1689-1697 
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    ISSN: 1572-9567
    Keywords: equation of state ; experimental method ; phase equilibrium parameters ; refrigerant ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in the liquid phase of the binary blend of R134a and R152a and its components has been studied. The speed of sound was measured by means of the impulse method at a frequency of 2.1 MHz. The temperature range was 230 to 350 K at pressures up to 16 MPa. The values of speed of sound were measured with a standard error of not more than 0.25%. The results obtained for both components of the blend are represented with expressions based on a physical model. The standard deviation (versus the model) of the measured data is 0.09%, On the basis of the results obtained, the Redlich–Kister correlation has been used over the entire ranges of composition, temperature, and pressure to determine the speed of sound in the liquid phase and at the bubble point of the blend investigated.
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    Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 805-829 
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    ISSN: 1572-9567
    Keywords: BCl3 ; boron trichloride ; equation of state ; HBr ; hydrogen bromide ; speed of sound ; thermodynamic properties ; transport properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in gaseous hydrogen bromide (HBr) and boron trichloride (BCl3) was measured using a highly precise acoustic resonance technique. The HBr speed-of-sound measurements span the temperature range 230 to 440 K and the pressure range from 0.05 to 1.5 MPa. The BCl3 speed-of-sound measurements span the temperature range 290 to 460 K and the pressure range from 0.05 MPa to 0.40 MPa. The pressure range in each fluid was limited to 80% of the sample vapor pressure at each temperature. The speed-of-sound data have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacities as a function of temperature with a relative standard uncertainty of 0.1%. The heat capacities agree with those calculated from spectroscopic data within their combined uncertainties. The speeds of sound were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on the hard-core square-well intermolecular potential model and the second based on the hard-core Lennard–Jones intermolecular potential model. The resulting virial equations of state reproduced the speed-of-sound measurements to 0.01% and can be expected to calculate vapor densities with a relative standard uncertainty of 0.1%. Transport properties calculated from the hard-core Lennard–Jones potential model should have a relative standard uncertainty of 10% or less.
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    Thermodynamic Properties of Sutherland Fluids from an Analytical Perturbation Theory (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 899-908 
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    ISSN: 1572-9567
    Keywords: Barker–Henderson perturbation theory ; equation of state ; hard-sphere fluid ; radial distribution function ; Sutherland potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Analytical expressions are obtained for the thermodynamic properties of fluids with potentials consisting of a spherical hard core plus an attractive tail of the form 1/r γ (Sutherland fluids). To this end, use is made of the Barker–Henderson perturbation theory together with an analytical expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid. This expression was derived previously on the basis of the analytical solution of the Percus–Yevick integral equation theory. The results are compared with available simulation data for a wide range of densities, temperatures, and values of the potential parameter γ. The overall agreement is good, and the accuracy is similar to that obtained using more accurate solutions for the radial distribution function of the hard-sphere fluid leading to nonanalytical expressions for the thermodynamic properties of the fluid considered.
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    Vapor–Liquid Equilibria for the 1,1,1-Trifluoroethane (HFC-143a)+1,1,1,2-Tetrafluoroethane (HFC-134a) System (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 871-881 
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    ISSN: 1572-9567
    Keywords: binary interaction parameters ; equation of state ; HFC-134a ; HFC-143a ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor–liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-143a+HFC-134a system. Fifty-four equilibrium data are obtained for the HFC-143a+HFC-134a system over the temperature range from 263.15 to 313.15 K at 10 K intervals. The experimental data were correlated with the Carnahan–Starling–De Santis (CSD) and Peng–Robinson (PR) equations of state. Based upon the present data, the binary interaction parameters for the CSD and PR equations of state were calculated for six isotherms for the HFC-143a+HFC-134a system. The binary interaction parameters for both equations of state were fitted by a linear equation as a function of temperature. The present data were in good agreement with the calculated results from the CSD equation of state, and the deviations were less than 1.0% with the exception of two points.
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    Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1373-1405 
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    ISSN: 1572-9567
    Keywords: associating fluids, critical state ; crossover theory ; equation of state ; enthalpies ; heat capacities ; n-alkanols ; thermodynamic properties ; speed of sound ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    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) (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1097-1121 
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    ISSN: 1572-9567
    Keywords: calorimeter ; chlorotrifluoromethane ; density ; equation of state ; heat capacity ; isochoric ; liquid ; R13 ; vapor ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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, ρ, 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, ρ, 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(ρ, 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%.
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    A scaled equation of state for real fluids in the critical region (1985)
    Springer
    International journal of thermophysics 6 (1985), S. 465-481 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; scaling laws ; steam ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65⩽(θ/θ c)⩽1.4 and for reduced temperatures (T/T c)⩽1.2, the equation represents P-V-T data for steam within the experimental accuracy.
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    Aqueous Electrolytes at Near-Critical and Supercritical Temperatures (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 355-366 
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    ISSN: 1572-9567
    Keywords: aqueous electrolytes ; calcium chloride ; equation of state ; near-critical properties ; phase-diagram type ; potassium chloride ; sodium chloride ; supercritical properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The aqueous electrolyte systems $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O, KCl}}{\kern 1pt} {\text{ - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O and CaCl}}{\kern 1pt} {\text{ - H}}_{\text{2}} {\text{O}}$$ are of great interest both geologically and industrially. Equations of state were developed recently for these systems; they are based on theoretical modeling for mixtures of hard spheres with appropriate diameters and dipole moments for H2O, NaCl, and KCl and with a quadrupole moment for CaCl2. Empirical terms are added as required to fit the available experimental data. The fit to the compositions and densities at equilibrium of the saturated vapor and liquid constitutes a severe test, in addition to properties in the single-phase regions. Temperatures range upward from 300°C for NaCl and KCl and from 250°C for CaCl2 for these equations. Complications from hydrolysis and alternate equations valid at lower temperatures are discussed briefly. In addition, there is a very important theoretical aspect relating to the general phase diagrams. With the high ratio of critical temperatures of the salts to that of water, complex diagrams involving liquid–liquid phase separation near the critical point of water are expected. But no such effect is observed experimentally; instead, one finds simple type I phase diagrams. This is particularly clear in the case of $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O}}$$ , where the database is very accurate and extends above 1000 K.
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    Compressibility and sound velocity measurements on N2 up to 1 GPa (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 103-116 
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    ISSN: 1572-9567
    Keywords: adiabatic compressibility ; equation of state ; density ; high pressure ; isothermal compressibility ; nitrogen ; pVT ; sound velocity ; ultrasonics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A gas expansion technique has been used to determine the pVT properties of N2 up to 1 GPa at 298.15 K, with an accuracy of 0.08% in density, 1 mK in temperature, and 0.05%+0.2 MPa in pressure. The sound velocity has been measured by a phase-comparison pulse-echo technique between 123 and 298 K at intervals of 25 K and at pressures up to 1 GPa, with an accuracy of better than 0.02% in sound velocity, 10 mK in temperature, and 0.05%+0.2 MPa in pressure. An equation of state is presented that correlates the density data over the wide pressure range of 36–1000 MPa with maximum deviations between the calculated and the experimental densities of less than 0.05%.
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    On the use of Grüneisen parameters in the treatment of shock-wave data (1987)
    Springer
    International journal of thermophysics 8 (1987), S. 751-761 
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    ISSN: 1572-9567
    Keywords: equation of state ; Grüneisen parameter ; shock-wave ; solidstate physics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The relations between the thermodynamic Grüneisen parameter, γ, the parameter defined by the Mie-Grüneisen equation of state of solids, γ e, and the average quantity γ involved in the energy-pressure equation which is used in the so-called reduction of shock-wave data are examined. General expressions connecting these quantities are reported, and the approximations of γ made in the reduction of shock-wave data are considered. The results of a very recent treatment of the shock-wave data for zirconium are considered. This treatment does not involve approximations of γ. The validity of the usual approximation γ/ V = constant is examined in the light of these results.
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    Mixing Rules for van der Waals-Type Equations of State Based on Activity-Coefficient Models (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 1429-1445 
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    ISSN: 1572-9567
    Keywords: activity coefficient models ; equation of state ; excess functions ; mixing rules
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    Topics: Physics
    Notes: Abstract A new approach for incorporation of the excess free energy from an activity coefficient model (ACM) into an equation of state (EOS) has been proposed. The approach is based on a concept that any ACM is valid at a low but finite value of compressibility factor. This condition allows us to analyze the “infinite pressure” approximation in a general way. It is shown that the “infinite pressure” approach neglects the contribution of the repulsive term of the EOS to the excess free energy of a mixture. This, in turn, introduces inconsistency which results in the difference in the calculated excess free energy of the EOS and the base ACM. The new approach defines parameter a of the EOS as an implicit function of compositions and temperature, thus requiring an iterative procedure using the “infinite pressure limit” as a starting point. The new approach can be modified to provide the correct composition dependence of a mixture second virial coefficient. Applicability of the new method has been tested for binary systems under vapor–liquid and liquid–liquid equilibrium conditions.
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    Thermodynamic Properties for R-404A (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 129-140 
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    ISSN: 1572-9567
    Keywords: correlation ; equation of state ; R-125 ; R-134a ; R-143a ; R-404A ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    Equation of state for fluid alkali metals: Binodal (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 533-543 
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    ISSN: 1572-9567
    Keywords: alkali metals ; binodal ; corresponding states ; equation of state ; fluid metals ; rectilinear diameter ; thermodynamic similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    A thermodynamic property formulation for cyclohexane (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 519-531 
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    ISSN: 1572-9567
    Keywords: cyclohexane ; equation of state ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract 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.
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    Vapor–Liquid Equilibrium of HFC-32/134a And HFC-125/134a Systems (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 519-530 
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    ISSN: 1572-9567
    Keywords: activity coefficients ; binary interaction parameters ; equation of state ; fugacity coefficients ; HFC-32/134a mixture ; HFC-125/134a mixture ; thermodynamic consistency ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor-liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-32/134a and HFC-125/134a systems. Twenty-two equilibrium data are obtained for the HFC-32/134a system over the temperature range from 258.15 to 283.15 K at 5 K intervals and the composition range from 0.2 to 0.8 liquid mole fraction. Twenty-five equilibrium data are obtained for the HFC-125/134a system over the temperature range from 263.15 to 303.15 K at 10 K intervals and the composition range from 0.18 to 0.81 liquid mole friction. These data have been tested and found to be thermodynamically consistent. Based upon the present data, the binary interaction parameters of the Carnahan-Starling-De Santis (CSD) and Redlich–Kwong–Soave (RKS) equations of state are calculated for five isotherms for the HFC-125/134a mixture and six isotherms for the HFC-32/134a mixture. The calculated results from the CSD equation are compared with data in the open literature.
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    Equation of State for Complex Liquid Mixtures from Surface Tension (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 601-610 
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    ISSN: 1572-9567
    Keywords: complex liquid mixtures ; corresponding states ; equation of state ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The present work shows a successful extension of previous studies to molecular liquids for which the second virial coefficients are not known. Recent advances in the statistical mechanical theory of equilibrium fluids can be used to obtain an equation of state (EOS) for compressed normal liquids and molten alkali metals. Three temperature-dependent quantities are needed to use the EOS: the second virial coefficient, B(T), an effective van der Waals covolume, b(T), and a scaling factor, α(T). The second virial coefficients are calculated from a correlation that uses the surface tension, γtr, and the liquid density at the triple point. Calculation of α(T) and b(T) follows by scaling. Thus, thermodynamic consistency is achieved by use of two scaling parameters (γtr, ρtr). The correlations embrace the temperature range T tr〈T〈T c and can be used in a predictive mode. The remaining constant parameter is best found empirically from ρtr data for pure dense liquids. The equation of state is tested on 42 liquid mixtures The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T tr to T c.
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    A Generalized Model for the Thermodynamic Properties of Mixtures (1999)
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    International journal of thermophysics 20 (1999), S. 825-835 
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    ISSN: 1572-9567
    Keywords: cryogens ; equation of state ; hydrocarbons ; mixtures ; refrigerants ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. 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 generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.
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    Thermophysical Properties of Gaseous Tungsten Hexafluoride from Speed-of-Sound Measurements (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 185-206 
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    ISSN: 1572-9567
    Keywords: equation of state ; intermolecular potential ; speed-of-sound ; thermodynamic properties ; transport properties ; tungsten hexafluoride ; virial coefficients ; viscosity ; WF6
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound was measured in gaseous WF6 using a highly precise acoustic resonance technique. The data span the temperature range from 290 to 420 K and the pressure range from 50 kPa to the lesser of 300 kPa or 80% of the sample's vapor pressure. At 360 K and higher temperatures, the data were corrected for a slow chemical reaction of the WF6 within the apparatus. The speed-of-sound data have a relative standard uncertainty of 0.005%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. These heat capacities are in reasonable agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound-speed data to within ±0.005% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less. The hard-core Lennard–Jones potential was used to estimate the viscosity and the thermal conductivity of dilute WF6. The predicted viscosities agree with published data to within 5% and can be extrapolated reliably to higher temperatures.
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    Prediction of Critical Properties of Binary Mixtures Using the PRSV-2 Equation of State (1998)
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    International journal of thermophysics 19 (1998), S. 239-258 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical properties ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The aim of this work is to test the value of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for predicting the critical behavior of binary mixtures. A procedure adopted by Heidemann and Khalil, based on the Helmholtz free energy, has been followed. The resulting two complex nonlinear equations have been solved simultaneously for the critical temperature and volume, while the critical pressure is calculated from the PRSV-2 equation of state itself. Three forms of binary-interaction parameters have been tried: the zero-type, conventional one-parameter type, and Margules two-parameter type. The optimum values of the binary interaction parameters, based on minimizing the sum of the squares of the relative errors between predicted and experimental critical temperatures, have been calculated for 20 polar and nonpolar systems. The Margules two-parameter type gives the best results, but its mathematical derivation is cumbersome and it requires more computation time. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperatures and pressures agree well with the experimental results, and are always better than those predicted by the group-contribution method. The deviations in the predicted critical volumes using any of the tested binary-interaction parameter types are relatively large compared to those using the group-contribution method.
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    A crossover description for the thermodynamic properties of fluids in the critical region (1986)
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    International journal of thermophysics 7 (1986), S. 75-85 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; renormalization-group theory ; specific heat ; thermodynamic properties ; van der Waals equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We have developed a “crossover” formalism that reconciles the singular asymptotic critical behavior of the thermodynamic properties of fluids with the classical behavior of these properties well away from the critical point. The proposed formalism is based on theoretical predictions for the crossover behavior suggested by the renormalization-group theory of critical phenomena. We demonstrate the formalism for a fluid whose classical behavior away from the critical point is represented by the equation of state of van der Waals.
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    A thermodynamic property formulation for ethylene from the freezing line to 450 K at pressures to 260 MPa (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 491-501 
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    ISSN: 1572-9567
    Keywords: equation of state ; ethylene ; saturation properties ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new thermodynamic property formulation based upon a fundamental equation explicit in Helmholtz energy of the form A=A(ρ, 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-ρ-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.
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    Experimental study of the ultrasonic velocity in liquid cesium at high temperatures and pressures (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 821-828 
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    ISSN: 1572-9567
    Keywords: cesium ; equation of state ; heat capacity ; high temperature ; pulse method ; sound velocity ; ultrasonic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The sound velocity in liquid cesium under pressures up to 60 MPa and temperatures to 1500 K is measured using a modified-pulses phase-sensitive technique. The sound velocity (at frequency 10 MHz) is determined by means of the pulse propagation time measurement through the cesium sample. The experimental error is 0.2%. The results obtained are discussed.
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    Application of critical-region scaling to pure-component equations of state (1986)
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    International journal of thermophysics 7 (1986), S. 911-922 
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    ISSN: 1572-9567
    Keywords: carbon dioxide ; critical region ; equation of state ; hydrocarbons ; scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A critical scaling method for equations of state developed by Fox at the National Bureau of Standards has been extended to predict thermodynamic properties and all of the first and second derivatives of the chemical potential and density. This is done by using a new damping function and developing expressions which avoid all numerical evaluations of the derivatives needed in calculating thermodynamic properties. Using this procedure, an analytical 32-constant equation of state was scaled in the critical region for pure light hydrocarbons and for carbon dioxide. The BWRS equation was scaled for heavier hydrocarbons. Calculations of the saturated vapor and liquid densities of methane in the region from 175 K to the critical temperature of 190.5 K were improved, and the mean absolute error decreased from 0.153 without scaling to 0.031 with scaling. Other derivative properties were also improved in the critical region for several of the lighter pure hydrocarbons.
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    Importance of thermophysical data in process simulation (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 987-1002 
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    ISSN: 1572-9567
    Keywords: activity coefficient ; equation of state ; heat of vaporization ; Henry constant ; phase equilibria ; predictive methods ; process simulation ; ternary interactions ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The need for thermophysical properties of components and their mixtures has grown as computer simulation of processes has developed and expanded. Although equations of state require fewer input data, they are not yet generally applicable to all types of systems. Accordingly, in many cases, the liquid activity models are still very much required. A long-time disadvantage of the liquid activity method, for systems containing supercritical components, is overcome if the Henry constant is utilized. A van Laar-type interpolative equation provides the Henry constant in liquid mixtures from the values in the pure liquid components. The addition of a ternary interaction in addition to the usual binary ones provides improved MVL prediction of phase equilibria, espcially VLLE involving three phases. Examination of the consistency of thermal properties is made feasible with the aid of a generalized reduced Frost-Kalkwarf vapor pressure equation. It is useful also for extending and supplementing sparse data and for predicting properties from the structure and boiling point. Possible trends in properties needed and their availability to simulators are discussed in view of available computer facilities.
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    Improved tables for the calculation of nonspherical contributions to second virial coefficients (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 1115-1133 
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    ISSN: 1572-9567
    Keywords: equation of state ; molecular gases ; nonspherical interactions ; second virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A set of improved numerical tables is given for use in calculating the effects of nonspherical molecular interactions on the second virial coefficients of simple molecular gases. The second virial coefficients are given as a spherical-core contribution (not discussed in this paper) plus a series of nonspherical perturbation terms. The tables give easy-to-interpolate auxiliary functions that occur in the perturbation terms. These functions depend on the form assumed for the spherical-core part of the interaction potential, but only in a relatively insensitive way, so that the tables should be adequate for almost all calculations that are likely to occur in this connection. The auxiliary functions J nT are tabulated for n from 6 to 30 and T from 0.5 to 10, where T* = kT/ɛe 0 and ɛe 0 is the well depth of the spherical-core potential. Explicit formulas are given for the simple cases of axially symmetric molecules, but the tabulated functions can also be used for more complex cases.
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    Thermodynamic properties of 1-chloro-1,2,2,2-tetrafluoroethane (R124) (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 85-101 
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    ISSN: 1572-9567
    Keywords: Benedict-Webb-Rubin (BWR) equation ; 1-chloro-1,2,2,2-tetrafluoroethane ; compressibility factor ; critical pressure ; critical temperature ; equation of state ; R124 ; specific volume ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    URL: http://dx.doi.org/10.1007/BF00504002
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    Measurement of the compressibility and sound velocity of neon up to 1 GPa (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 803-812 
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    ISSN: 1572-9567
    Keywords: compressibility ; equation of state ; high pressure ; neon ; pVT ; sound velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The density of neon has been determined at 298.15 K as a function of pressure from 80 MPa to 1 GPa. The precision of the measurements is 0.03%, while the estimated absolute accuracy is between 0.05 and 0.09%. The sound velocity has been measured between 98 and 298 K with intervals of 25 K and at pressures up to 1 GPa, with an accuracy generally better than 0.06%. The adiabatic compressibility and the ratio of the specific heats are calculated by combining pVT with velocity-of-sound data at 298 K. Several equations of state are fitted to the density data at 298.15 K.
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    URL: http://dx.doi.org/10.1007/BF00503246
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    Thermodynamic properties of n-hexane (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 439-452 
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    ISSN: 1572-9567
    Keywords: critical region ; equation of state ; n-hexane ; sound velocity ; specific heat ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
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    URL: http://dx.doi.org/10.1007/BF00513082
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    Equations of state for hard-sphere fluids (1988)
    Springer
    International journal of thermophysics 9 (1988), S. 953-963 
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    ISSN: 1572-9567
    Keywords: contact value of radial distributions ; equation of state ; hard-sphere fluids ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Equations of state and contact values of hard-sphere radial distribution functions (rdf's) which are given by a linear combination of the Percus— Yevick and scaled-particle virial expressions are considered. In the one-component case the mixing coefficientθ(η) is, in general, a function of the volume fractionη. In mixtures the coefficientθ(η i ,d i ), in general, depends upon the volume fractionη i , and diameterd i , of each species,i andj. For the contact valuesY ij of the rdf's, the mixing coefficientsΘ ij (η k ) also depend on speciesi andj. Density expansions for the exactθ for the one-component hard-sphere fluid are obtained and compared with several approximations made in earlier works and in our own work, as well as with simulations. For a mixture, it turns out that one cannot obtain the exact fourth virial coefficient by using a linear combination of the Percus-Yevick and scaled-particle virial expressions forY ij unless one allowsΘ ij to depend on mole fractionsx i even at the zeroth order of its density expansion. We also find thatΘ ij must depend on particle speciesi andj in order to satisfy the exact limits obtained earlier by Sung and Stell. A new equation of state for the binary hard-sphere mixture which satisfies all the exact limits we have considered is suggested.
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    Equation of State for Nonpolar Fluids: Prediction from Boiling Point Constants (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1123-1137 
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    ISSN: 1572-9567
    Keywords: compressed liquids ; corresponding states ; equation of state ; gases ; second virial coefficient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new corresponding states correlation for the second virial coefficient of nonpolar fluids in terms of the boiling point constants is presented. The scaling constants are the normal boiling point temperature, T bp, which is used to form a dimensionless temperature and the liquid density at the normal boiling point, ρ bp, which is used to form a dimensionless second virial coefficient. The procedure has been examined for a large number of substances including noble gases, diatomic molecules, saturated hydrocarbons up to C8, and a number of aliphatic, aromatic, and cyclic hydrocarbons. The resulting correlation has been applied to predict the equation of state of fluids over the range from the vapor-pressure curve to the freezing curve at various temperatures from the triple point up to the nonanalytical critical region. The equation of state has been applied to reproduce the liquid density of a great number of compounds both in the saturation and compressed states, at temperatures up to 2000 K and pressures up to 10000 bar, within an accuracy of a few percent. In particular we have shown that knowledge of two readily measurable constants is sufficient to determine the pvT surface of pure normal fluids having a variety of structural complexities.
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    URL: http://dx.doi.org/10.1023/A:1026498021221
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    Equation of state for liquid helium from 1.4 to 4 K and asymptotic limits at the lamda line (1985)
    Springer
    International journal of thermophysics 6 (1985), S. 63-82 
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    ISSN: 1572-9567
    Keywords: equation of state ; helium ; lamda line ; logarithmic singularity ; low temperature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A liquid helium state equation has been constructed for the range 1.4 to 4 K for pressures up to 25×105 Pa consistent with the known asymptotic behavior of state properties at the lamda line. It utilizes a slightly different form of state equation than used in previous studies at the lamba line, resulting in simpler expressions for all thermodynamic variables while retaining good agreement with experimental data. The amplitude ratio, A/A′, of the logarithmic term is found to be 1.14±0.03, independent of pressure, in contrast to earlier work which indicated that this ratio was pressure dependent above 15×105 Pa. The state equation can also be used to show that the entropy variation along the lama line is independent of A or A′ and to predict a finite value of Cv at the lamda line.
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    URL: http://dx.doi.org/10.1007/BF00505792
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    Extended corresponding states as a tool for the prediction of the thermodynamic properties of mixtures (1986)
    Springer
    International journal of thermophysics 7 (1986), S. 901-910 
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    ISSN: 1572-9567
    Keywords: equation of state ; ethane ; extended corresponding states ; methane ; mixtures ; nitrogen ; P-V-T-x
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The principle of corresponding states, with one of its many extensions, is used to predict the thermodynamic properties of the binary mixtures N2-CH4 and CH4-C2H6. Comparisons of the predicted properties with experimental data are given to illustrate some of the powers and problems associated with the method. Problems encountered in modeling mixtures, which are not necessarily associated with the mathematical model of the equation of state, are also discussed. Wide-range equations of state for the two binary systems mentioned above are presented.
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    A new method for optimizing the structure of thermodynamic correlation equations (1989)
    Springer
    International journal of thermophysics 10 (1989), S. 1103-1126 
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    ISSN: 1572-9567
    Keywords: correlation equation ; equation of state ; least-squares principle ; optimization method ; search method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An optimization strategy is presented for optimizing the structure of empirical thermodynamic correlation equations. Based on a comprehensive functional expression for the physical dependence considered, which is called a “bank of terms,” the new procedure optimizes the structure and the length of the equation as well. The application of this method results in an equation which meets the quality wanted for representing the experimental data with the lowest number of fitted coefficients. The procedure can be used for the determination of the structure of any equation where the method of the linear least squares is applicable. A detailed description of the algorithm is given which includes values for the control parameters for different applications in the field of thermodynamics (vapor pressure equations, equations of state, etc.) and also for applications in other fields. The optimization steps are described using an equation which represents a relationship between variables in a general form. It is demonstrated how even the complex problem of the optimization of a fundamental equation for the Heimholtz energy can be written in terms of this general equation.
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    URL: http://dx.doi.org/10.1007/BF00500566
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    Equilibrium in multiphase polydisperse fuids (1989)
    Springer
    International journal of thermophysics 10 (1989), S. 1181-1204 
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    ISSN: 1572-9567
    Keywords: continuous thermodynamics ; distribution function ; equation of state ; Gibbs phase equilibrium ; polydisperse mixtures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Based on the principle of Gibbs phase equilibrium, three different algorithms are developed for phase equilibrium calculations of polydisperse mixtures. These algorithms are based on (i) the equality of the chemical potentials of components in each phase, (ii) the minimization of the total Gibbs free energy of the system with respect to all the system variables, and (iii) the equilibrium ratios constraint between the phases. All three algorithms demonstrate applicability to mixtures with different mole fraction distribution functions and different equations of state. The results of calculations using the three phase algorithms are compared with the simulated multicomponent hydrocarbon mixture data, and the results are in good agreement.
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    Describing vapor-liquid equilibria in methanol +n-alkane systems by means of an equation of state with association (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 227-236 
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    ISSN: 1572-9567
    Keywords: association ; equation of state ; false liquid-liquid split ; methanol +n-alkane systems ; mixing rule ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The ability of an equation of state incorporating association to describe vapor-liquid equilibrium of methanol +n-alkane systems has been tested. An equation of state with association is divided into “physical” and “chemical” parts, where the Patel-Teja cubic equation of state is used for the description of the physical part and an association tenn forms the chemical part. Five two- and threeparameter mixing rules were tested and compared with an equation of state without association. On the average for the first eight n-alkanes, the improvement in fit of pressure using association was 30–50 % and the calculated vapor compositions were also much improved. In addition, there were lewer points with unstable liquid phase (false liquid-liquid split). Both with and without association, density-dependent mixing rules based on a local-composition concept gave the best result.
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    The selection of international standards for the thermodynamic properties of HFC-134a and HCFC-123 (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 781-790 
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    ISSN: 1572-9567
    Keywords: environmentally acceptable refrigerants ; equation of state ; thermodynamic properties ; international standards
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The objectives and activities of the International Energy Agency-Annex 18 are summarized. One of the goals of the Annex was to determine the formulations that best represent the thermodynamic properties of HFC-134a and HCFC-123. The formulations selected were those which accurately represented the experimental data and simultaneously exhibited thermodynamic consistency. Methods of comparison include analysis of the experimental data, statistical comparisons of values calculated from the property formulations to experimental values, and graphical analyses of the thermodynamic surface. The analytical methods used are summarized in this paper. The equations of state reviewed in these comparisons represented the most accurate formulations available in December 1992. Four equations of state were reviewed for HFC-I34a and three equations of state were considered for HCFC-123. These equations represented the work of independent researchers in Germany, Japan, and the United States. The formulations selected as international standards are presented.
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    Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 563-588 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical region ; D2O ; equation of state ; H2O ; phase behavior ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A parametric crossover model is adapted to represent the thermodynamic properties of pure D2O in the extended critical region. The crossover equation of state for D2O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D2O + H2O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D2O and for the D2O + H2O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T c(x)≤T≤1.5T c(x) and densities 0.35ρc(x)≤ρ≤1.65ρc(x).
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    URL: http://dx.doi.org/10.1023/A:1022609205399
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    The Equation of State of Song and Mason Applied to Fluorine (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 611-629 
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    ISSN: 1572-9567
    Keywords: equation of state ; fluorine ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An analytical equation of state is applied to calculate the compressed and saturation thermodynamic properties of fluorine. The equation of state is that of Song and Mason. It is based on a statistical–mechanical perturbation theory of hard convex bodies and is a fifth-order polynomial in the density. There exist three temperature-dependent parameters: 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-dependent parameters can be calculated if the intermolecular pair potential is known. However, the equation is usable with much less input than the full intermolecular potential, since the scaling factor and effective volume are nearly universal functions when expressed in suitable reduced units. The equation of state has been applied to calculate thermodynamic parameters including the critical constants, the vapor pressure curve, the compressibility factor, the fugacity coefficient, the enthalpy, the entropy, the heat capacity at constant pressure, the ratio of heat capacities, the Joule–Thomson coefficient, the Joule–Thomson inversion curve, and the speed of sound for fluorine. The agreement with experiment is good.
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    URL: http://dx.doi.org/10.1023/A:1022665323146
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    Thermodynamic Properties of Trifluoroiodomethane (CF13I)1 (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 393-404 
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    ISSN: 1572-9567
    Keywords: critical parameters ; equation of state ; ideal-gas heat capacity ; PVT ; speed of sound ; surface tension ; trifluoroiodomethane ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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 β 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.
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    URL: http://dx.doi.org/10.1023/A:1006683529436
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    A Thermodynamic Property Model for Fluid-Phase Propane (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1045-1072 
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    ISSN: 1572-9567
    Keywords: equation of state ; Helmholtz free energy ; hydrocarbon ; natural working fluid ; propane ; R-290 ; refrigerant ; thermodynamic property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A fundamental equation of state for propane (R-290), formulated in terms of the non-dimensional Helmholtz free energy, is presented. It was developed based on selected reliable measurements for pressure-volume-temperature (PVT), isochoric and isobaric heat capacities, speed of sound, and the saturation properties which were all converted to ITS-90. Supplementary input data calculated from a virial equation for the vapor-phase PVT properties at lower temperatures and other correlations for the saturated vapor pressures and saturated vapor- and liquid-densities have also been used. The present equation of state includes 19 terms in the residual part and represents most of the reliable experimental data accurately in the range of validity from 85.48 K (the triple point temperature) to 623 K, at pressures to 103 MPa, and at densities to 741 kg·m−3. The smooth behavior of the derived thermodynamic properties in the entire fluid phase is demonstrated. In addition, graphical and statistical comparisons between experimental data and the available thermodynamic models, including the present one, showed that the present model can provide a physically sound representation of all the thermodynamic properties of engineering importance.
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    URL: http://dx.doi.org/10.1023/A:1026441903474
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    Thermodynamic properties of gaseous argon at temperatures between 110 and 450 K and densities up to 6.8 mol · dm−3 determined from the speed of sound (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 1325-1347 
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    ISSN: 1572-9567
    Keywords: argon ; compression factor ; equation of state ; heat capacity ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Thermodynamic properties of gaseous argon have been determined from our recent highly accurate measurements of the speed of sound by means of a numerical integration of the differential equations which link the speed of sound and the equation of state. Compression factosr and both isochoric and isobaric heat capacities at temperatures between 110 and 450 K at densities up to either one-half of the critical (T ⩾ 150 K ) or 74 percent of the saturated-vapor density (T 〈 150 K ) are reported. To perform the integration, initial conditions were required along an isotherm close to the critical temperature. The method of integration is described in detail and the results are compared withpVT and calorimetric data from the literature.
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    Critical evaluation of the thermodynamic properties of molybdenum (1985)
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    International journal of thermophysics 6 (1985), S. 367-393 
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    ISSN: 1572-9567
    Keywords: enthalpy ; equation of state ; heat capacity ; high pressure ; high temperature ; molybdenum ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamic properties and the pressure-temperature phase diagram of pure Mo have been evaluated from experimental information using thermodynamic models for the Gibbs energy of the individual phases. A set of parameters describing the Gibbs energy of the various phases as a function of temperature and pressure is presented. The agreement between experimental data and calculated values is satisfactory.
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    Linear Isotherm for Compressed Molten Alkali Metals (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 317-330 
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    ISSN: 1572-9567
    Keywords: alkali metals ; density ; equation of state ; linear regularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Molten alkali metals are shown to be in the domain of the newly developed linear regularity that is valid for pure compressed liquids and liquid mixtures. It holds in the range of melting to boiling temperature and shows deviations as the critical temperature is approached. The agreement with experimental data is better than 1.4% when it is used to predict the density of molten Li, Na, K, Rb, and Cs metals. A reasonable conformity with the ISM statistical mechanical equation of state is manifested.
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    Equation of State for Molten Alkali Metals from Surface Tension. Part II (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 331-340 
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    ISSN: 1572-9567
    Keywords: alkali metals ; corresponding states ; equation of state ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This work presents a new method for predicting the equation of state for molten alkali metals, based on statistical–mechanical perturbation theory from two scaling constants that are available from measurements at ordinary pressures and temperatures. The scaling constants are the surface tension and the liquid density at the boiling temperature (γb, ρb). Also, a reference temperature, T Ref, is presented at which the product (T Ref T b 1/2 ) is an advantageous corresponding temperature for the second virial coefficient, B 2(T). The virial coefficient of alkali metals cannot be expected to obey a law of corresponding states for normal fluids, because two singlet and triplet potentials are involved. The free parameter of the Ihm–Song–Mason equation of state compensates for the uncertainties in B 2(T). The vapor pressure of molten alkali metals at low temperatures is very low and the experimental data for B 2(T) of these metals are scarce. Therefore, an equation of state for alkali metals from the surface tension and liquid density at boiling temperature (γb, ρb) is a suitable choice. The results, the density of Li through Cs from the melting point up to several hundred degrees above the boiling temperature, are within 5%.
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    URL: http://dx.doi.org/10.1023/A:1021475808271
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