PρT parameterization of SAFT equation of state: developing a new parameterization method for equations of state

2021 ◽  
pp. 113024
Author(s):  
Arash Pakravesh ◽  
Fatemeh Zarei ◽  
Hosseinali Zarei
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Parameterization Method

SITE-SPECIFIC EQUATIONS OF STATE FOR COASTAL SEA AREAS AND INLAND WATER BODIES

2017 ◽  
Author(s):  
Natalia Andrulionis ◽  
Natalia Andrulionis ◽  
Ivan Zavialov ◽  
Ivan Zavialov ◽  
Elena Kovaleva ◽  
...  
Keyword(s):  
Equation Of State ◽  
Black Sea ◽  
Water Samples ◽  
Equations Of State ◽  
Sea Water ◽  
Ionic Composition ◽  
Water Bodies ◽  
Aral Sea ◽  
The Black Sea ◽  
Coastal Sea

This article presents a new method of laboratory density determination and construction equations of state for marine waters with various ionic compositions and salinities was developed. The validation of the method was performed using the Ocean Standard Seawater and the UNESCO thermodynamic equation of state (EOS-80). Density measurements of water samples from the Aral Sea, the Black Sea and the Issyk-Kul Lake were performed using a high-precision laboratory density meter. The obtained results were compared with the density values calculated for the considered water samples by the EOS-80 equation. It was shown that difference in ionic composition between Standard Seawater and the considered water bodies results in significant inaccuracies in determination of water density using the EOS-80 equation. Basing on the laboratory measurements of density under various salinity and temperature values we constructed a new equation of state for the Aral Sea and the Black Sea water samples and estimated errors for their coefficients.

Application of the Redlich-Kwong-Soave equation of state to the solubility of water in compressed gases

1984 ◽  
Vol 49 (5) ◽  
pp. 1116-1121
Author(s):  
Josef P. Novák ◽  
Jaroslav Matouš ◽  
Petr Pick ◽  
Jiří Pick
Keyword(s):  
Equation Of State ◽  
Binary Systems ◽  
Equations Of State ◽  
Published Data ◽  
Interaction Coefficients

Published data on the solubility of water in compressed gases were employed for calculating the interaction coefficients kij in the Redlich-Kwong-Soave equations of state for binary systems of water with argon, nitrogen, CO2, N2O, CH4, C2H6, or C2H4. With these coefficients, the estimate of the solubility of water in these gases has been improved by more than one order.

scholarly journals Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Boussinesq Equations ◽  
Climate Science ◽  
Rational Functions ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Primitive Equations ◽  
Well Posedness ◽  
Nonlinear Thermodynamics

AbstractWe consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space $${{\mathcal {H}}^{1}}$$ H 1 . The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

scholarly journals Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
J. Lütgert ◽  
J. Vorberger ◽  
N. J. Hartley ◽  
K. Voigt ◽  
M. Rödel ◽  
...  
Keyword(s):  
Equation Of State ◽  
Polyethylene Terephthalate ◽  
Density Functional ◽  
Equations Of State ◽  
Md Simulations ◽  
X Ray Diffraction ◽  
Functional Theory ◽  
Shock Hugoniot ◽  
Highly Correlated

AbstractWe present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, $$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$ ( C 10 H 8 O 4 ) n , also called mylar) shock-compressed to ($$155 \pm 20$$ 155 ± 20 ) GPa and ($$6000 \pm 1000$$ 6000 ± 1000 ) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

Thermodynamic properties of liquid mixtures: Selection of the pure liquid parameter

1974 ◽  
Vol 27 (3) ◽  
pp. 647 ◽  
Author(s):  
DV Fenby ◽  
NF Pasco
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Liquid Mixtures ◽  
Pure Liquid ◽  
Excess Thermodynamic Properties ◽  
Pure Fluids ◽  
Liquid Parameter ◽  
Selection Of

There has recently been a revival of interest in theories of liquid mixtures based on analytic equations of state for pure fluids. We have shown that the method used to determine the parameters of the pure-liquid equation of state has a significant effect on the excess thermodynamic properties obtained from such theories.

The theory of rubber elasticity

1976 ◽  
Vol 351 (1666) ◽  
pp. 397-406 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Rubber Elasticity ◽  
Elastic Behaviour ◽  
Excluded Volume ◽  
Simple Pattern ◽  
Dynamical Approach ◽  
Equilibrium Approach ◽  
The Future

It is argued that since statistical mechanics has developed in two ways, the dynamical approach of Boltzmann and the equilibrium approach of Gibbs, both should be valuable in rubber elasticity. It is shown that this is indeed the case, and the generality of these approaches allows one to study the problem in greater depth than hitherto. In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of state. It is noticeable that although the calculated equations of state are quite complex, they do not fit into a simple pattern of invariants. The future for these developments is briefly discussed.

A Mechanical Equation of State for Inelastic Deformation of Iron: An Analytic Description

1977 ◽  
Vol 99 (1) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Rohde ◽  
J. C. Swearengen
Keyword(s):  
Equation Of State ◽  
Stress Relaxation ◽  
Power Law ◽  
Reaction Rate ◽  
Equations Of State ◽  
Analytic Description ◽  
Rate Theory ◽  
Predictive Capability ◽  
Reaction Rate Theory ◽  
The Relationship

The applicability of two familiar analytic descriptions of micromechanical deformation as equations of state for polycrystalline iron is discussed. These equations are the power law and the relationship based on reaction rate theory. It is shown that the reaction rate description fails to describe adequately individual stress relaxation events without invoking undue complexity from use of adjustable parameters. Moreover, even in that case, this formulation lacks the predictive capability required in an equation of state. Conversely, the power law is found not only to describe stress relaxation data properly but also to provide the capability of predicting stress relaxation following initial deformation by different loading paths. It thus appears to represent an equation of state for the material.

scholarly journals Fundamental physics and the absence of sub-millisecond pulsars

2018 ◽  
Vol 620 ◽  
pp. A69 ◽  
Author(s):  
B. Haskell ◽  
J. L. Zdunik ◽  
M. Fortin ◽  
M. Bejger ◽  
R. Wijnands ◽  
...  
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Gravitational Wave ◽  
Equations Of State ◽  
Rotation Frequency ◽  
Hadronic Matter ◽  
Spin Distribution ◽  
Test Models ◽  
State Of Matter

Context. Rapidly rotating neutron stars are an ideal laboratory to test models of matter at high densities. In particular, the maximum rotation frequency of a neutron star depends on the equation of state and can be used to test models of the interior. However, observations of the spin distribution of rapidly rotating neutron stars show evidence for a lack of stars spinning at frequencies higher than f ≈ 700 Hz, well below the predictions of theoretical equations of state. This has generally been taken as evidence of an additional spin-down torque operating in these systems, and it has been suggested that gravitational wave torques may be operating and be linked to a potentially observable signal. Aims. We aim to determine whether additional spin-down torques (possibly due to gravitational wave emission) are necessary, or if the observed limit of f ≈ 700 Hz could correspond to the Keplerian (mass-shedding) break-up frequency for the observed systems, and is simply a consequence of the currently unknown state of matter at high densities. Methods. Given our ignorance with regard to the true equation of state of matter above nuclear saturation densities, we make a minimal physical assumption and only demand causality, that is, that the speed of sound in the interior of the neutron star should be lower than or equal to the speed of light c. We then connected our causally limited equation of state to a realistic microphysical crustal equation of state for densities below nuclear saturation density. This produced a limiting model that gave the lowest possible maximum frequency, which we compared to observational constraints on neutron star masses and frequencies. We also compared our findings with the constraints on the tidal deformability obtained in the observations of the GW170817 event. Results. We rule out centrifugal breakup as the mechanism preventing pulsars from spinning faster than f ≈ 700 Hz, as the lowest breakup frequency allowed by our causal equation of state is f ≈ 1200 Hz. A low-frequency cutoff, around f ≈ 800 Hz could only be possible when we assume that these systems do not contain neutron stars with masses above M ≈ 2 M⊙. This would have to be due either to selection effects, or possibly to a phase transition in the interior of the neutron star that leads to softening at high densities and a collapse to either a black hole or a hybrid star above M ≈ 2 M⊙. Such a scenario would, however, require a somewhat unrealistically stiff equation of state for hadronic matter, in tension with recent constraints obtained from gravitational wave observations of a neutron star merger.

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