Functions for the Calculation of Entropy, Enthalpy, and Internal Energy for Real Fluids Using Equations of State and Specific Heats

1964 ◽  
pp. 227-233 ◽  
Author(s):  
J. G. Hust ◽  
A. L. Gosman
Keyword(s):  
Internal Energy ◽  
Equations Of State ◽  
Specific Heats ◽  
Real Fluids

scholarly journals Variability of the adiabatic parameter in monoatomic thermal and non-thermal plasmas

2018 ◽  
Vol 616 ◽  
pp. A58 ◽  
Author(s):  
Miguel A. de Avillez ◽  
Gervásio J. Anela ◽  
Dieter Breitschwerdt
Keyword(s):  
Internal Energy ◽  
Impact Ionization ◽  
Thermal Evolution ◽  
Numerical Models ◽  
Linear Equations ◽  
Thermal Plasmas ◽  
Specific Heats ◽  
Partial Pivoting ◽  
Electron Distributions ◽  
Collisional Ionization

Context. Numerical models of the evolution of interstellar and integalactic plasmas often assume that the adiabatic parameter γ (the ratio of the specific heats) is constant (5/3 in monoatomic plasmas). However, γ is determined by the total internal energy of the plasma, which depends on the ionic and excitation state of the plasma. Hence, the adiabatic parameter may not be constant across the range of temperatures available in the interstellar medium. Aims. We aim to carry out detailed simulations of the thermal evolution of plasmas with Maxwell–Boltzmann and non-thermal (κ and n) electron distributions in order to determine the temperature variability of the total internal energy and of the adiabatic parameter. Methods. The plasma, composed of H, He, C, N, O, Ne, Mg, Si, S, and Fe atoms and ions, evolves under collisional ionization equilibrium conditions, from an initial temperature of 109 K. The calculations include electron impact ionization, radiative and dielectronic recombinations and line excitation. The ionization structure was calculated solving a system of 112 linear equations using the Gauss elimination method with scaled partial pivoting. Numerical integrations used in the calculation of ionization and excitation rates are carried out using the double-exponential over a semi-finite interval method. In both methods a precision of 10−15 is adopted. Results. The total internal energy of the plasma is mainly dominated by the ionization energy for temperatures lower than 8 × 104 K with the excitation energy having a contribution of less than one percent. In thermal and non-thermal plasmas composed of H, He, and metals, the adiabatic parameter evolution is determined by the H and He ionizations leading to a profile in general having three transitions. However, for κ distributed plasmas these three transitions are not observed for κ < 15 and for κ < 5 there are no transitions. In general, γ varies from 1.01 to 5/3. Lookup tables of the γ parameter are presented as supplementary material.

Equations of state for fluids based on hard sphere repulsion

2015 ◽  
Vol 29 (13) ◽  
pp. 1550089 ◽  
Author(s):  
Minhui Shan ◽  
Jianxiang Tian
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Equations Of State ◽  
The Past ◽  
Complex Interactions ◽  
Structures And Properties ◽  
The One ◽  
Real Fluids

As is well-known, the structures and thermodynamic properties of fluids are determined by the complex interactions, i.e., the repulsive one and the attractive one, among particles. The simplest equation-of-state (EOS) model maybe the one of hard sphere repulsion plus or multiplying some attraction. Followed by the rapid promotion of the accuracy of hard sphere EOS in the past dozens of years, one question rises as whether more accurate hard sphere repulsion derives better prediction of the structures and properties of fluids with a special attraction. In this work, we used two repulsions with clearly different accuracy and some attractions to construct series equations of state (EOSs) for real fluids, and then we discussed the saturated properties at liquid–gas equilibrium. We found that the answer to the question aforementioned is not definitely standing.

Transonic nozzle flow of dense gases

1993 ◽  
Vol 247 ◽  
pp. 661-688 ◽  
Author(s):  
A. Kluwick
Keyword(s):  
Stokes Equations ◽  
Equations Of State ◽  
Weak Shock ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Perturbation Equation ◽  
Navier Stokes Equations ◽  
Sonic Point ◽  
Specific Heats ◽  
Dense Gases

The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Navier–Stokes equations supplemented with realistic equations of state for gases which have relatively large specific heats a novel form of the viscous transonic small-perturbation equation is derived. Evaluation of the inviscid limit of this equation shows that three sonic points rather than a single sonic point may occur during isentropic expansion of such media, in contrast to the case of perfect gases. As a consequence, a shock-free transition from subsonic to supersonic speeds cannot, in general, be achieved by means of a conventional converging–diverging nozzle. Nozzles leading to shock-free flow fields must have an unusual shape consisting of two throats and an intervening antithroat. Additional new results include the computation of the internal thermoviscous structure of weak shock waves and a phenomenon referred to as impending shock splitting. Finally, the relevance of these results to the description of external transonic flows is discussed briefly.

ON THE THERMODYNAMICS OF AN ANHARMONIC CRYSTAL WITH HIGH ANISOTROPY

1995 ◽  
Vol 09 (04n05) ◽  
pp. 585-597 ◽  
Author(s):  
V.I. ZUBOV ◽  
M.P. LOBO ◽  
J.N.T. RABELO
Keyword(s):  
Equations Of State ◽  
Quantum Corrections ◽  
Anharmonic Crystal ◽  
Cubic Crystal ◽  
Specific Heats ◽  
Atomic Displacements ◽  
High Anisotropy ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Strong Anharmonicity

The correlative method of the unsymmetrized self-consistent field is used to study the atomic properties of a simple model of an anharmonic crystal with strong anisotropy, namely, a crystal with primitive hexagonal (PH) lattice. The self-consistent potential, Helmholtz free energy and mean-square atomic displacements are obtained in the case of weak anharmonicity. Equations of state are derived and solved. The internal energy and specific heats are calculated. The first quantum corrections are expressed in terms of the de Boer parameter included. An influence of anharmonicity is analyzed. The thermal expansion of the model considered is very anisotropic but the quantum corrections to the lattice parameters are isotropic. The results of calculations are compared with those for one- and two-dimensional models and for the isotropic crystal with the same coordination number as in the PH lattice, i.e. a body-centered cubic crystal. Other things being equal, the coefficient of volume expansion and specific heats of anisotropic crystals are greater than those of isotropic ones. A possibility of studying the strong anharmonicity in anisotropic crystals is discussed.

scholarly journals VII. On the ratio of the specific heats of the paraffins and their monohalogen derivatives

1894 ◽  
Vol 54 (326-330) ◽  
pp. 101-105
Keyword(s):  
Internal Energy ◽  
Specific Heats ◽  
Organic Gases

The experiments were undertaken to find whether the internal energy of the molecules of organic gases, as deduced from the ratio of the specific heats, showed any regularities corresponding to the chemical resemblances symbolised by the graphic formulæ. The paraffins and their monohalogen derivatives are very suitable for the purpose, as their chemical relations to each other are simple, they are easily volatile, and are stable enough to be unaffected by ordinary purifying agents.

scholarly journals INTERACTING CONSTITUENTS IN COSMOLOGY

2008 ◽  
Vol 17 (06) ◽  
pp. 857-879 ◽  
Author(s):  
R. ALDROVANDI ◽  
R. R. CUZINATTO ◽  
L. G. MEDEIROS
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Source Terms ◽  
Systematic Method ◽  
Usual Approach ◽  
Interaction Terms ◽  
Real Fluids ◽  
Universe Evolution ◽  
Source Fluid

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

scholarly journals A MultiScale Gibbs-Helmholtz Constrained Cubic Equation of State

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Angelo Lucia
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Internal Energy ◽  
Equations Of State ◽  
Energy Parameter ◽  
New Approach ◽  
Cubic Equation Of State ◽  
Cubic Equation ◽  
Dynamics Simulations

This paper presents a radically new approach to cubic equations of state (EOS) in which the Gibbs-Helmholtz equation is used to constrain the attraction or energy parameter, a. The resulting expressions for for pure components and for mixtures contain internal energy departure functions and completely avoid the need to use empirical expressions like the Soave alpha function. Our approach also provides a novel and thermodynamically rigorous mixing rule for . When the internal energy departure function is computed using Monte Carlo or molecular dynamics simulations as a function of current bulk phase conditions, the resulting EOS is a multiscale equation of state. The proposed new Gibbs-Helmholtz constrained (GHC) cubic equation of state is used to predict liquid densities at high pressure and validated using experimental data from literature. Numerical results clearly show that the GHC EOS provides fast and accurate computation of liquid densities at high pressure, which are needed in the determination of gas hydrate equilibria.

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