A general equation of state for high density matter from thermodynamic symmetry

Xue, Ti-Wei; Zhang, Guo

doi:10.1063/5.0077707

Cited by 7 publications

(12 citation statements)

References 38 publications

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“…The ideal gas EOS in P-S-T form is where is the specific heat at constant pressure and the subscript 0 denotes a given thermodynamic state. The ideal dense matter EOS in P–V-T form is 13 where is the specific work at constant temperature, defined as 14 …”

Section: Modelingmentioning

confidence: 99%

“…As we know, the ideal gas EOS, is a well-known low-density limiting model and all matter shares this simple relation at ultra-low densities 12 . Recently, it has been found that there is thermodynamic symmetry between the features of the two extremes of density, and thus an ideal dense matter EOS symmetric to the ideal gas EOS was presented 13 where is a constant, called the ideal dense matter constant. It is a high-density limiting model and all matter shares this simple relation at ultra-high densities 13 .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, it has been found that there is thermodynamic symmetry between the features of the two extremes of density, and thus an ideal dense matter EOS symmetric to the ideal gas EOS was presented 13 where is a constant, called the ideal dense matter constant. It is a high-density limiting model and all matter shares this simple relation at ultra-high densities 13 . Ideal gas and ideal dense matter are a pair of symmetric theoretical concepts.…”

Section: Introductionmentioning

confidence: 99%

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A global equation-of-state model from mathematical interpolation between low- and high-density limits

Xue

Guo

2022

Sci Rep

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The ideal gas equation of state (EOS) model is a well-known low-density limiting model. Recently, an ideal dense matter EOS model for the high-density limit symmetric to the ideal gas model has been developed. Here, by mathematically interpolating between the ideal gas and ideal dense matter limiting models, we establish a global model containing two EOS in the form of P-V-T and P-S-T for arbitrary ranges of densities. Different from empirical or semi-empirical EOS, the coefficients in the global EOS have a clear physical meaning and can be determined from a priori knowledge. The proposed global model is thermodynamically consistent and continuous. It reduces to the ideal gas model when approaching the low-density limit and to the ideal dense matter model when approaching the high-density limit. Verifications for 4He show that the global model reproduces the large-range behavior of matter well, along with providing important insight into the nature of the large-range behavior. Compared to the third-order virial EOS and the Benedict–Webb–Rubin EOS, the global P-V-T EOS has higher descriptive accuracy with fewer coefficients over a wide range of data for N2. The global model is shown to work well in extreme applied sciences. It predicts a linear, inverse relationship between entropy and volume when the temperature-to-pressure ratio is constant, which can explain the entropy-production behavior in shock-Hugoniots.

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Section: Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A global equation-of-state model from mathematical interpolation between low- and high-density limits

Xue

Guo

2022

Sci Rep

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“…However, the above view is now being challenged. Recent studies have found that the thermodynamic properties of matter, in themselves, have symmetry [8,9]. By contrast, the thermodynamic properties are directly dependent on the structure of the substance and the thermodynamic state it is in.…”

Section: Introductionmentioning

confidence: 99%

Correspondence of the Symmetry of Thermodynamic Properties of Matter with the Symmetry of Equations of State

Xue,

Guo

2023

Entropy

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Thermodynamics contains rich symmetries. These symmetries are usually considered independent of the structure of matter or the thermodynamic state where matter is located and, thus, highly universal. As Callen stated, the connection between the symmetry of fundamental laws and the macroscopic properties of matter is not trivially evident. However, this view is now being challenged. Recently, with symmetry to the ideal gas equation of state (EOS), an ideal dense matter EOS has been proposed, which has been verified to be in good agreement with the thermodynamic properties of high-density substances. This indicates that there is a certain symmetry between the thermodynamic properties of substances in their high- and low-density limits. This paper focuses on the distinctive features and the significance of this symmetry. It is a new class of symmetry that is dependent on the thermodynamic state of matter and can be incorporated into the existing symmetrical theoretical system of thermodynamics. A potential path for developing the EOS theory arising from this symmetry is discussed. EOS at high densities could be developed by correcting or extrapolating the ideal dense matter EOS based on this symmetry, which might fundamentally solve the difficulty of constructing EOS at high densities.

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“…Note also that its modification 13 leads also to the Murnaghan equation initially derived for highly compressive isotropic solids. Recently, there were some attempts to address Tait's parameters from general thermodynamic points of view considering the ultra-high pressure range 14 and its interpolating to the low-pressure limiting state 15 as well as from the theory thermodynamic fluctuations 16 that allows building the Tait-like shaped Fluctuations Theory-based Equation of State (FT-EOS), which extrapolates data obtained at ambient pressure to the elevated one up to some hundred Megapascals for a wide range of liquid's classes, including polar, and ionic liquids and liquid mixtures [17][18][19] . However, the latter fails when the pressure tends to GPa range; this has been argued as the transition of liquid's bulk modulus to the behaviour typical for isotropic solids (Murnaghan's equation) 20 .…”

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confidence: 99%

Combining the Tait equation with the phonon theory allows predicting the density of liquids up to the Gigapascal range

Postnikov

Belenkov

Chorążewski

2023

Sci Rep

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Predicting the density of liquids at ultrahigh pressures in the case when only the data measured at ambient pressure are available is a long-standing challenge for thermodynamic research. In this work, we archived this goal for molecular liquids by applying the half-sum of the Tait equation and the Murnagnan equation in the form coordinated with Tait’s at low pressure for predicting the density of molecular liquids up to the pressures more than 1 GPa with uncertainty comparable with the experimental one. It is shown that the control parameter, which is needed in addition to the initial density and the isothermal compressibility can be found using the speed of sound and the density at ambient pressure and has a clear physical interpretation in terms of the characteristic frequency of intermolecular oscillation mimicking the limiting frequency of Debye’s theory of heat conductivity of solids. This fact is discussed as arguing in favour of the modern phonon theory of liquid thermodynamics and expands it range of applicability to the volumetric properties of liquids at temperatures far below the critical one. The validity of the model is illustrated with the case study of classic Bridgman’s dataset as well as with some examples of ultrahigh-pressure data obtained by the diamond anvil cell and shock wave compression methods.

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A general equation of state for high density matter from thermodynamic symmetry

Cited by 7 publications

References 38 publications

A global equation-of-state model from mathematical interpolation between low- and high-density limits

A global equation-of-state model from mathematical interpolation between low- and high-density limits

Correspondence of the Symmetry of Thermodynamic Properties of Matter with the Symmetry of Equations of State

Combining the Tait equation with the phonon theory allows predicting the density of liquids up to the Gigapascal range

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