Gas Imperfection. II. Thermodynamic Quantities for Some Unsaturated Aliphatic Hydrocarbons Derived from the Equations of State.

1941 ◽  
Vol 45 (2) ◽  
pp. 321-328
Author(s):  
Edwin E. Roper
Keyword(s):  
Equations Of State ◽  
Aliphatic Hydrocarbons ◽  
Thermodynamic Quantities

scholarly journals A Comparative Study of Hydrogen Equations of State

1994 ◽  
Vol 147 ◽  
pp. 306-329 ◽  
Author(s):  
D. Saumon
Keyword(s):  
State Physics ◽  
Equation Of State ◽  
Comparative Study ◽  
Equations Of State ◽  
Point Of View ◽  
Thermodynamic Quantities ◽  
Careful Evaluation ◽  
Black Boxes ◽  
Critical Issues

AbstractThe numerous complexities underlying large tables of thermodynamic quantities act as a deterrent to a careful evaluation of their reliability. As a consequence, equations of state are often used as black boxes. To clarify this situation, some of the more critical issues of equation of state physics are discussed from the point of view of the user. They are illustrated by a comparison of four equations of state for hydrogen. The flaws and disagreements thus brought into light are explained and evaluated with simple physical arguments.

scholarly journals Heat kernel approach for confined quantum gas

2020 ◽  
Vol 35 (13) ◽  
pp. 2050100
Author(s):  
Ping Zhang ◽  
Tong Liu
Keyword(s):  
Heat Kernel ◽  
Equations Of State ◽  
Dimensional Space ◽  
Quantum Gases ◽  
Thermodynamic Quantities ◽  
Quantum Gas ◽  
Confined Space ◽  
Kernel Approach ◽  
Ideal Quantum ◽  
The One

In this paper, based on the heat kernel technique, we calculate equations of state and thermodynamic quantities for ideal quantum gases in confined space with external potential. Concretely, we provide expressions for equations of state and thermodynamic quantities by means of heat kernel coefficients for ideal quantum gases. Especially, using an analytic continuation treatment, we discuss the application of the heat kernel technique to Fermi gases in which the expansion diverges when the fugacity [Formula: see text]. In order to calculate the modification of heat kernel coefficients caused by external potentials, we suggest an approach for calculating the expansion of the global heat kernel of the operator [Formula: see text] based on an approximate method of the calculation of spectrum in quantum mechanics. We discuss the properties of quantum gases under the condition of weak and complete degeneration, respectively. Moreover, we give an expansion of the one-loop effective action in D-dimensional space.

scholarly journals Hyperons in hot dense matter: what do the constraints tell us for equation of state?

2018 ◽  
Vol 35 ◽  
Author(s):  
M. Fortin ◽  
M. Oertel ◽  
C. Providência
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Symmetry Energy ◽  
Nuclear Physics ◽  
Equations Of State ◽  
Dense Matter ◽  
Baryon Octet ◽  
Thermodynamic Quantities ◽  
Binary Neutron Star ◽  
Hot Matter

AbstractFor core-collapse and neutron star merger simulations, it is important to have adequate equations of state which describe dense and hot matter as realistically as possible. We present two newly constructed equations of state including the entire baryon octet, compatible with the main constraints coming from nuclear physics, both experimental and theoretical. One of the equations of state describes cold β-equilibrated neutron stars with a maximum mass of 2 Msun. Results obtained with the new equations of state are compared with the ones of DD2Y, the only existing equation of state containing the baryon octet and satisfying the above constraints. The main difference between our new equations of state and DD2Y is the harder symmetry energy of the latter. We show that the density dependence of the symmetry energy has a direct influence on the amount of strangeness inside hot and dense matter and, consequently, on thermodynamic quantities. We expect that these differences affect the evolution of a proto-neutron star or binary neutron star mergers. We propose also several parameterisations based on the DD2 and SFHo models calibrated to Lambda hypernuclei that satisfy the different constraints.

Thermodynamic properties of modified hairy and BTZ black holes

2021 ◽  
pp. 2150068
Author(s):  
Muhammad Yasir ◽  
Kazuharu Bamba ◽  
Abdul Jawad
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Equations Of State ◽  
Massive Gravity ◽  
Black Hole Thermodynamics ◽  
Thermodynamic Quantities ◽  
Btz Black Hole ◽  
Yang Mills ◽  
First Order

We consider the Hairy black hole of dimensionally continued gravity with power-Yang–Mills magnetic source and Lorentz symmetry violating Bañados, Teitelboim and Zanelli (BTZ) black hole in massive gravity. We utilize the general form of first law of black hole thermodynamics and compute different thermodynamic quantities. Keeping in mind the importance of negative cosmological constant [Formula: see text], we derive corresponding equations of state and discuss the phase transitions which is comparable with chemical Van der Waals fluid. We also find out the critical points and observe that system exhibits first-order small as well as large black holes phase transitions.

scholarly journals The role of the critical compressibility factor in the equation of state for the critical fluid

2021 ◽  
pp. 26-36
Author(s):  
A.D. Alekhin ◽  
O.I. Bilous ◽  
Ye.G. Rudnikov
Keyword(s):  
Critical Point ◽  
Linear Model ◽  
Thermodynamic Potential ◽  
Equations Of State ◽  
Compressibility Factor ◽  
Fluctuation Theory ◽  
Thermodynamic Quantities ◽  
Phase Boundaries ◽  
Critical Isochore ◽  
Critical Isotherm

Based on the literature data of PVT measurements, the amplitudes of the equations of the critical isotherm D0(Zk), the critical isochore Г0(Zk), the phase boundaries В0(Zk) are expressed in terms of the critical factor of compressibility of the substance Zk=PkVk/RTk  in the entire fluctuation region near the critical point. By doing so, a phenomenological method has been used for calculating the values of the critical exponents of the fluctuation theory of phase transitions based on the introduction of small parameters into the equations of the fluctuation theory. It has been shown that, within the limits of the PVT measurement errors, these dependences D0(Zk) and В0(Zk) on the compressibility factor are linear, and Г0  practically does not depend  on the compressibility factor Zk. The relationship of these amplitudes with the amplitudes a and k of the linear model of the system of parametric scale equations of state of substance near the critical point has been established. It has been shown that the dependences k(Zk) and а(Zk) are also linear in the entire fluctuation region near the critical point. The obtained dependences k(Zk) and а(Zk) agree with the known relationship between the amplitudes of the critical isotherm D0(Zk), critical isochore Г0(Zk), phase boundaries В0(Zk) Aerospace Institute of the National Academy of Sciences of Ukrainewithin the framework of the system of parametric scaling equations. The relations а(Zk), k(Zk)  make it possible, on the basis of a linear model of the system of parametric scale equations of state of substance, to determine such important characteristics of the critical fluid as the temperature and field dependences of the correlation length Rc(T,m)  and the fluctuation part of the thermodynamic potential Ф(T,m)  in the entire fluctuation region near the critical point. Then, based on the form of the fluctuation part of the thermodynamic potential Ф(T,m)~Rc(T,m)-3, the results obtained allow one to calculate the field and temperature dependences of the thermodynamic quantities for a wide class of molecular liquids in the close vicinity of the critical point (DP<10-3, Dr<10-2, t<10-4), where precision experiments are significantly complicated, and its can also be used when choosing the conditions for the most effective practical application of the unique properties of the critical fluid in the newest technologies.

scholarly journals Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 295
Author(s):  
Abdel Nasser Tawfik ◽  
Carsten Greiner
Keyword(s):  
Differential Equations ◽  
Cosmological Constant ◽  
Early Universe ◽  
Bulk Viscosity ◽  
Analytical Solutions ◽  
Large Scale ◽  
Equations Of State ◽  
Cosmic Time ◽  
Thermodynamic Quantities ◽  
Road Maps

Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, H(a(t)), where H(t) is the Hubble parameter and a(t) is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular H(t) and a(t) are obtained, where H(t) diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of H(a(t)) is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing H(a(t)) with increasing a(t) varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure.

scholarly journals Thermal fluctuations to the thermodynamics of a non-rotating BTZ black hole

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Nadeem-ul-islam ◽  
Prince A Ganai ◽  
Sudhaker Upadhyay
Keyword(s):  
Black Hole ◽  
Free Energy ◽  
Isothermal Compressibility ◽  
Equations Of State ◽  
Thermal Fluctuations ◽  
Thermodynamic Quantities ◽  
Leading Order ◽  
Btz Black Hole ◽  
Horizon Radius ◽  
First Order

Abstract We discuss the effect of small statistical thermal fluctuations around the equilibrium of the thermodynamics of a small non-rotating BTZ black hole. This is done by evaluating the leading-order corrections to the thermodynamical equations of state, namely entropy, free energy, internal energy, pressure, enthalpy, Gibbs free energy, and specific heat, quantitatively. In order to analyze the effects of perturbations on the thermodynamics, we plot various graphs and compare corrected and non-corrected thermodynamic quantities with respect to the event horizon radius of a non-rotating BTZ black hole. We also derive the first-order corrections to isothermal compressibility.

scholarly journals AQUA: a collection of H2O equations of state for planetary models

2020 ◽  
Vol 643 ◽  
pp. A105 ◽  
Author(s):  
Jonas Haldemann ◽  
Yann Alibert ◽  
Christoph Mordasini ◽  
Willy Benz
Keyword(s):  
Equation Of State ◽  
Internal Energy ◽  
High Pressures ◽  
Equations Of State ◽  
Chemical Elements ◽  
Thermodynamic Quantities ◽  
Calculated Density ◽  
Temperature Range ◽  
Wide Range ◽  
The Impact

Context. Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state often only cover parts of the pressure-temperature space needed in planetary modelling. Aims. We aim to construct an equation of state of H2O spanning a very wide range, from 0.1 Pa to 400 TPa and 150 to 105 K, which can be used to model the interior of planets. Methods. We combined equations of state valid in localised regions to form a continuous equation of state spanning over the above-mentioned pressure and temperature range. Results. We provide tabulated values for the most important thermodynamic quantities: the density, adiabatic temperature gradient, entropy, internal energy, and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density-temperature and density-internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equations of state like ANEOS and QEOS. Conclusions. AQUA is a combination of existing equations of state useful for planetary models. We show that, in most regions, AQUA is a thermodynamic consistent description of water. At pressures above 10 GPa, AQUA predicts systematic larger densities than ANEOS or QEOS. This is a feature that was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equations of state and regarding experimental data of water at high pressures.

scholarly journals On the Influence of the Treatment of Heavy Elements in the Equation of State on the Resulting Values of the Adiabatic Exponent Γ1

1993 ◽  
Vol 137 ◽  
pp. 304-306 ◽  
Author(s):  
W. Däppen ◽  
D.O. Gough ◽  
A.G. Kosovichev ◽  
E.J. Rhodes
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Thermodynamic Quantity ◽  
Forthcoming Paper ◽  
Heavy Elements ◽  
Element Abundance ◽  
Thermodynamic Quantities ◽  
Helium Abundance ◽  
Solar Convection ◽  
Solar Composition

Helioseismology and asteroseismology put high demands on the accuracy and consistent numerical realization of the equation of state (for a review see Däppen, these proceedings). This is explicitly illustrated by the helioseismic determination of the helium abundance of the solar convection zone in a recent investigation by Kosovichev et al. (1992). In that work it was observed that details of the treatment of the heavy elements matter more than is intuitively expected. Naively, one would expect an uncertainty of less than 10−4 in the key thermodynamic quantity, the adiabatic gradient Γ1. This is because in material of solar composition the heavy-element abundance is less than about 1.5 × 10−3 by number, and under solar conditions the dominant nontrivial contributions to the seismically relevant thermodynamic quantities predicted by modern equations of state agree to a few per cent, even for the much more abundant hydrogen and helium. However, Kosovichev et al. (1992) found that uncertainties in the treatment of the heavy elements translate into discrepancies in Γ1 of the order of 10−3, which is enough to disturb the helioseismic helium-abundance determination significantly. We briefly present the reason below. A forthcoming paper will show more detailed results, though some further information can already be found in papers by Kosovichev et al. (1992) and Christensen–Dalsgaard & Däppen (1992).

scholarly journals Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1366
Author(s):  
Mara Murri ◽  
Mauro Prencipe
Keyword(s):  
Phase Transition ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Ambient Pressure ◽  
Beta Phase ◽  
Thermodynamic Quantities ◽  
Anharmonic Effects ◽  
Displacive Phase Transition ◽  
Intrinsic Anharmonicity ◽  
Good Agreement

The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach.

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