New Equation Of State Research Articles

An approximate nonrandom lattice theory of fluids: General derivation and application to pure fluids

A new equation of state was derived based on the nonrandom lattice fluid theory. By expanding the Helmholtz free energy from the full Guggenheim combinatory with vacant sites around the reference athermal sólution an approximate and explicit form was obtained. The model was tested for it's applicability and parameters for 211 pure fluids were presented. It was found that the model describes quantitatively the P-σ-T property above critical point the saturated density, the vapor pressure, and the heat of vaporization of various molecularly complex fluids with only two temperature dependent molecular parameters for each pure fluid. The structure of the formalism for pure fluids can be readily extended to multicomponent mixtures.

Equation of state for mixtures of hard-sphere chains including copolymers

Chiew's equation of state for mixtures of hard-sphere chains is generalized through the Carnahan-Starling radial distribution function for hard-sphere mixtures at contact for both the bonding and nonbonding terms. When compared with computer simulations of hard-sphere-chain mixtures, the new equation of state gives better agreement than the original equation of state. The new equation of state indicates the simplifying physical assumptions which are required to obtain the well-known Flory-Huggins a thermal entropy of mixing. The generalization presented here is applied to mixtures of hard-sphere-chain copolymers, where the spherical segments of a given chain may have different diameters. Illustrative calculations are presented for three types of copolymers (alternating, block, and random).

Generalized quartic equation of state for pure nonpolar fluids

AbstractA generalized quartic equation of state has been developed for pure nonpolar fluids. The equation of state contains four parameters which depend on three properties of the fluid—critical temperature, critical volume, and acentric factor. A mathematical approximation based on previously reported hard‐sphere molecular dynamics simulations has been used to model repulsive contributions to the pressure. Attractive forces were modeled using an empirical term. While the quartic equation yields four roots, one root is always negative and hence physically meaningless, and three roots behave like three roots of a cubic equation. Thus, the new equation of state has the advantages of a cubic, simplicity and unequivocal identification of the roots, while correctly modeling the attractive and repulsive contributions to the pressure. The new equation of state is more accurate than either the Peng‐Robinson or a previously proposed quartic equation of state. Accuracy in the supercritical and compressed liquid regions is improved substantially.

Equation of state for mixtures containing polar compounds

The new equation of state proposed by Brandani has been extended to mixtures, and appropriate mixing rules have been used for the parameters. Three adjustable binary parameters have been used to fit the experimental data of 13 binary mixtures containing at least one polar compound, with the exception of the system carbon dioxide— n-butane. The results of the fitting are satisfactory. When applied to a ternary mixture, predicted and experimental compositions of the liquid and vapor phase agree very well.

Viscous shear in general-relativistic astrophysical flows

Introducing the concept of general co-moving frames (gcmf) in [4] we have argued that it may become useful in a number of hydrodynamical and mhd applications. In [5] using thegcmf technique we have constructed a fully covariant, general-relativistic theory of strongly magnetized collisionless plasma. The approach proved itself to be highly convenient-it allowed us to find new equations of state for such a medium. In the present paper we have considered viscous shear in generalrelativistic astrophysical flows as an another example of the effective usage of orthonormal tetrads method. Namely, we have specified general corotating frames (gcrf)-subclass ofgcmf corresponding to the flows being in purely rotational motion. By means of gcrf we have been able to find expressions for nonzero components of shear tensor and turbulent viscosity tensor for the innermost region of a black hole accretion disc. We think that the method may be useful when considering analogous problems with astrophysical flows of more complicated geometry and/or dynamics. In particular, the method may become efficient for jets in active galactic nuclei (agn) and quasars [13], general-relativistic winds of compact objects [14] and the innermost regions of candidates for galactic black hole accretion discs [15]. To be sure, in some of these problems we have to use a more general set ofgcmf instead ofgcrf. Such problems, however, are beyond the scope of this paper, where we have only outlined the main background of the method and demonstrated its productivity in a simple case of quasi-keplerian accretion flow in a general-relativistic standard accretion disc.

Comparison between a noncubic equation of state particularly suitable for polar fluids and the Soave equation of state

Recently, Brandani et al. (1992) have presented a new equation of state based on theoretical results of a system of hard spheres with dipoles and on the computer simulation data for n-butane. This new equation of state was applied to the correlation of thermodynamic properties for 10 pure polar and nonpolar fluids. In the communication, the new equation of state has been tested using a data base constituted by the vapor pressures of 59 pure polar and nonpolar fluids. The aim was to find a correlation for the two adjustable parameters of the equation as a function of the acentric factor. The results were compared with those obtained using the equation of state of Soave (1972), which is widely used by chemical engineers for VLE calculations, even for polar substances (Bazua, 1983; Joffe et al., 1983)

Special Equations of State for Methane, Argon, and Nitrogen for the Temperature Range from 270 to 350 K at Pressures up to 30 MPa

In order to describe the thermodynamic behavior of methane, argon, and nitrogen in the so-called “natural-gas region,” namely, from 270 to 350 K at pressures up to 30 MPa as accurate as possible with equations of a very simple form, new equations of state for these three substances have been developed. These equations are in the form of a fundamental equation in the dimensionless Helmholtz energy; for calculating the pressure or the density, the corresponding equations explicit in pressure are also given. The residual parts of the Helmholtz function representing the behavior of the real gas contain 12 fitted coefficients for methane, 8 for argon, and 7 for nitrogen. The thermodynamic relations between the Helmholtz energy and the most important thermodynamic properties and the needed derivatives of the equations are explicitly given; to assist the user there is also a table with values for computer-program verification. The uncertainties when calculating the density ρ, the speed of sound w, the isobaric specific heat capacity cp, and the isochoric specific heat capacity cv are estimated as follows. For all three substances it is Δρ/ρ≤±0.02 % for p≤ 12 MPa and Δρ/ρ ≤ ±0.05% for higher pressures. For methane it is Δw/w≤±0.02% for p≤10 MPa and Δw/w≤+-0.1% for higher pressures; for argon it is Δw/w≲-0.1 % for p≤ 7 MPa, Δw/w≤±0.3 % for 7 <p≤30 MPa; and for nitrogen it is Δw/w≤±0.1% for p≤1.5 MPa and Δw/w±0.5% for higher pressures. For all three substances it is Δcp/cp≤±1 % and ΔCv/Cv≤±1 % in the entire range.

Thermodynamic properties of hard-chain molecules

The density and molecular size dependence of the equation of state for molecules that consist of freely jointed, tangent hard spheres is investigated. It is shown that the properties of hard-chain molecules can be accurately described using the properties of spherical molecules and a function c which varies approximately linearly with the reduced density. Monte Carlo and molecular dynamics simulation data for hard chains were used to develop the expression for c. The new equation of state is simple in form and more accurate for the calculation of compressibility factors for hard-chain molecules than either Wertheim’s first-order thermodynamic perturbation theory or the generalized Flory dimer theory (GFD). Further, this new equation reduces to the correct second virial coefficient limit as the density approaches zero.

Hadrons yielded by plasma

We consider nonequilibrium phase transitions of a quark-gluon plasma into hadrons proceeding via deflagration and supersonic condensation. The possible existence of a third phase, i.e. plasma of constitutent quarks is taken into account. New equations of state for hadronic gas are used, which include the proper volume of particles in a thermodynamically consistent way. The yields of hadrons are calculated for various values of the baryon density of the quark-gluon plasma.

Representation of excess properties of electrolyte solutions using a new equation of state

AbstractA new equation of state for electrolyte solutions has been developed from an expression of the Helmholtz free energy containing a nonelectrolyte part and a part relative to ions. The nonelectrolyte part is taken from the equations of state (EOS) of Schwartzentruber et al. (1989). The ionic part is composed of an MSA long‐range term to account for electrostatic interactions and a short‐range interaction term specific to ions. Using correlations between parameters and experimental ionic diameters, the model reduce to a one‐parameter model. It has been applied to numerous strong electrolyte systems and extended to ternary systems to test its predictability without mixing parameters for ions. Its results compare well to the results reported for other one‐parameter models (electrolyte EOS). Furthermore, it was found that the cation‐anion interaction parameter could also be correlated to experimental ionic diameters. Then, the osmotic coefficients of 28 alkaline and alkaline‐earth halide systems may be represented with a root mean square relative deviation of 2.9% using only six correlation parameters. This result has been extended to other systems, with the conclusion that the model with all parameters correlated may also be applied to systems other than halide solutions. The resulting model is predictive. The quality of the prediction was tested by determining osmotic coefficients relative to six systems without any parameter adjustment. The deviations of the predicted values range from 2.0 to 5.4%. The quality of the representation of mixed salts systems without mixing parameters was evaluated using experimental osmotic coefficients of 30 ternary systems.

The Lennard-Jones fluid revisited: new thermodynamic data and new equation of state

Abstract The Lennard-Jones fluid appeared as a natural benchmark during the work on the project aimed at utilizing the rigorous statistical mechanical results for practical equation of state calculations for real fluids. As already reported, however, the so far available molecular simulation data and analytical equations of state were found unsatisfactory for the purpose. Hence a new highly accurate set of data on pressure (-volume-temperature) and internal energy by the Monte-Carlo and molecular dynamics methods and on the chemical potential by Monte Carlo with the new version of the insertion particle method was generated. The data has been used to develop and test a new accurate perturbed hard body equation of state for the Lennard-Jones fluid. The performance of the equation of state on pseudoexperimental data is documented and possible applications of the equation of state for calculating the thermodynamic properties of real fluids are discussed.

A new equation of state for chlorodifluoromethane (R22) covering the entire fluid region from 116 K to 550 K at pressures up to 200 MPa

A new equation of state in the form of a fundamental equation explicit in the dimensionless Helmholtz free energy has been developed for chlorodifluoromethane (R 22). This equation, which contains 22 fitted coefficients, covers the entire fluid region from 116 K (triple point temperature) to 550 K at pressures up to 200 MPa. The mathematical form of the equation was determined with the help of a new method to optimize its structure. New pressure-density-temperature data in the liquid region and especially new vapour pressures and saturated liquid densities, as well as speed of sound data have been incorporated to extend the range of validity and to improve the accuracy of properties calculated with this equation beyond that of previous formulations. Independent equations are also included for the vapour pressure as well as for the saturated liquid and vapour densities. The uncertainty of the new wide-range equation of state can roughly be given as follows: ⩽ ± 0.1% in density (with the exception of the critical region), ⩽ ± 1% in heat capacity, ⩽ ± 0.5% in speed of sound in the liquid and ⩽ 0.1% in speed of sound in the gas phase. The new equation of state corresponds to the International Temperature Scale of 1990 (ITS-90).

Computer simulation and equation of state study of the Boyle and inversion temperature of simple fluids

A new equilibrium molecular dynamics procedure is proposed and tested for determining directly the Joule—Thompson inversion curve of model simulation fluids. This method has the advantage that the Joule—Thompson inversion temperature envelope does not need to come from a predetermined equation of state. We test the new simulation procedure for the Lennard-Jones (LJ) fluid and make comparisons with the predictions of a range of equations of state, both specific to the LJ fluid and also those of the van der Waals type. In particular, we test a new equation of state developed from the Redlich—Kwong equation of state but having a number of advantages, especially for the Joule—Thompson inversion curve. The simulation method is particularly effective in the dense fluid regime, having distinct advantages over the equation of states route. We also consider the Boyle temperature from the equation of state.

A new cubic equation of state

Abstract Two-parameter cubic equations of state are analyzed and a new three-parameter cubic equation of state is proposed with the critical compressibility factor taken as substance dependent. An apparent critical compressibility factor is determined by optimizing the calculation of saturated liquid densities while the equality of fugacities along the saturation curve is imposed. The new cubic equation of state, combined with a previously proposed α function and mixing rule, proves to be a powerful equation for predicting properties of pure components and mixtures. The new equation not only improves volumetric property calculations relative to earlier efforts, but also achieves high degree of accuracy in the calculation of vapor-liquid equilibria for highly nonideal systems such as polar/nonpolar mixtures. Alcohol/hydrocarbon mixtures are used as an extreme test of the new equation of state.

A new equation of state for polar and nonpolar pure fluids

Abstract Based on theoretical results for hard-dipolar spheres and the computer simulation data for n-butane a new equation of state is applied to the correlation of thermodynamic properties for ten pure polar and nonpolar fluids: methane, ethane, n-butane, water, ammonia, carbon dioxide, acetonitrile, ethanol, methanol and acetone. The reference system has the same dependence on density as that given by the Carnahan-Starling equation, but the coefficients are function of temperature through the reduced dipole moment. The effect of attractive forces is taken into account through an empirical function which contains two universal constants whose values are fixed by fitting computer simulation data for n-butane. For polar fluids, the equation gives results significantly better than those obtained from conventional cubic equations of state, when using the same limited experimental data for determining equation of state parameters.

Calculation of Thermodynamic properties of Fluid Using a New Equation of State

Using the Lennard-Jones (12-6) potential, a new equation of state is obtained that can predict properties of both gases and liquids relatively well. This equation of state is given as (Z-a)V2=(A/V2)-B, where Z is the compressibility factor, A and B are constants, and a is an adjustable parameter that depends on the temperature, volume and the nature of the fluid, and its expressions depends upon the fluid status. In this paper, appropriate expressions for argon are given for a, in the liquid region when 0.6<Tr<1, and in the gaseous region when 1.1<Tr

Hadronic equation of state and the onset of kaon condensation

An equation of state is presented which takes the finite size of baryons and of mesons consistently into account and incorporates the contributions of both nonstrange and strange hadrons. All extensive quantities (energy, particle number, entropy) are modified by a factor taking into account the excluded volume due to baryon repulsion. Intensive quantities (pressure) are not modified. This is achieved by introducing a baryon chemical potential, μB, which is shifted from its point-like value, μ B 0 , by a term proportional to the finite volume of a hadron,V0, as follows: μB=μ B 0 + V0[P0(T, μ B 0 )−P0(T, 0)], whereP0 is the pressure for pointlike particles. The last term is necessary to conserve baryon number at the phase transition point. The differences between the new equation of state and those considered previously in the literature are discussed. It is shown that kaon condensation sets in only in the mixed phase of the transition, where hadrons, quarks and gluons are present simultaneously in thermodynamical equilibrium.

The molecular-metallic transition of hydrogen and the structure of Jupiter and Saturn

view Abstract Citations (152) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Molecular-Metallic Transition of Hydrogen and the Structure of Jupiter and Saturn Chabrier, Gilles ; Saumon, Didier ; Hubbard, William B. ; Lunine, Jonathan I. Abstract Recently, a new equation of state for hydrogen which predicts a molecular-metallic phase transition at finite temperature has become available. It is combined with a helium equation of state, and the resulting thermodynamic description of H/He mixtures is used to compute interior models of Jupiter and Saturn, subject to the constraints of the measured gravitational harmonics of both planets. The inferred heavy element abundance distribution in their interior and the possible consequences on their formation are discussed. In particular, the Z-element enhancement and smaller core in Saturn relative to Jupiter, a conclusion of this study, may indicate a depletion of water ice in the Jupiter formation zone. Publication: The Astrophysical Journal Pub Date: June 1992 DOI: 10.1086/171390 Bibcode: 1992ApJ...391..817C Keywords: Equations Of State; Helium Hydrogen Atmospheres; Jupiter (Planet); Metallic Hydrogen; Phase Transformations; Planetary Structure; Saturn (Planet); Abundance; Giant Stars; Lunar and Planetary Exploration; EQUATION OF STATE; MOLECULAR PROCESSES; PLANETS AND SATELLITES: INDIVIDUAL JUPITER; PLANETS AND SATELLITES: INDIVIDUAL SATURN full text sources ADS |

Pressure derivatives of the bulk modulus

Simple relations between the first (or second) pressure derivative of the bulk modulus and first (or second) thermal Grüneisen parameter γTh (or qTh) are derived from equations that relate KT(P) to vibrational frequencies Vi as a function of pressure for cubic structures or those that have only one nearest neighbor distance, by assuming that the mode Grüneisen parameters, γi = −∂ ln vi/∂ ln V, are approximately equal. The free volume equation results, which holds within experimental uncertainties for about 70% for solids meeting the symmetry requirements. Agreement is poor for compounds with the rutile structure, which have the largest range of γi observed. Another result is a three‐parameter equation of state, KoK″o = (5/3 ‐ K′o)2 ‐ (5/3 ‐ K′o)qTh(0) ‐ (K′o ‐ 1)2. All available experimental determinations of K″o are bracketed by the spectroscopic limits for qTh. Use of the average value of zero for qTh (or qTh calculated from other thermodynamic parameters) gives the proper sign for K″o and nearly the same values as experiment, suggesting that this approximate equation can be used predictively. The equations involving K″o and K′o are probably valid for any structure, if the γi are roughly equal, although this most likely occurs for solids that compress nearly isotropically. The new formula, with qTh of zero, give values similar to that obtained from the Vinet‐Ferrante‐Rose‐Smith equation at low K′o gives the same values as the Birch‐Murnaghan (third‐order finite strain) equation near K′o of 4, and gives nearly equal values as the Grover‐Getting‐Kennedy equation of state at high K′o. Physically reasonable positive values of K″o as K′o approaches zero are obtained only from the new equation of state and that of Vinet et al. Comparison of the new equation of state with third‐order finite strain suggests that the latter is also likely to be incorrect at high K′o and thus should be cautiously applied to V(P) for liquids.

A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa

This work reviews the data on thermodynamic properties of methane which were available up to the middle of 1991 and presents a new equation of state in the form of a fundamental equation explicit in the Helmholtz free energy. A new strategy for optimizing the structure of empirical thermodynamic correlation equations was used to determine the functional form of the equation. The Helmholtz function containing 40 fitted coefficients was fitted to selected experimental data of the following properties: (a) thermal properties of the single phase (pρT) and (b) of the liquid-vapor saturation curve (psρ′ρ″) including the Maxwell criterion, (c) speed of sound w, (d) isochoric heat capacity cv, (e) isobaric heat capacity cp, (f) difference of enthalpy Δh, and (g) second virial coefficient B. Independent equations are also included for the vapor pressure, the saturated liquid and vapor densities, the isobaric ideal gas heat capacity and the melting pressure as functions of temperature. Tables for the thermodynamic properties of methane from 90 K to 620 K for pressures up to 1000 MPa are presented. For the density, uncertainties of ±0.03% for pressures below 12 MPa and temperatures below 350 K and ±0.03% to ±0.15% for higher pressures and temperatures are estimated. For the speed of sound, the uncertainty ranges from ±0.03% to ±0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of ±1%. To verify the accuracy of the new formulation, the calculated property values are compared with selected experimental results and existing equations of state for methane. The new equation of state corresponds to the new International Temperature Scale of 1990 (ITS-90) and is extrapolable up to pressures of 20000 MPa.