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Journal articles on the topic 'Virial equation of state'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Singh, Vivek Kumar, and K. N. Khanna. "Virial coefficients from equation of state." Journal of Molecular Liquids 107, no. 1-3 (September 2003): 41–57. http://dx.doi.org/10.1016/s0167-7322(03)00139-9.

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2

Malijevský, Anatol, and Tomáš Hujo. "The Bender Equation of State and Virial Coefficients." Collection of Czechoslovak Chemical Communications 65, no. 9 (2000): 1464–70. http://dx.doi.org/10.1135/cccc20001464.

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The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

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3

Estela-Uribe, J. F., J. Jaramillo, M. A. Salazar, and J. P. M. Trusler. "Virial equation of state for natural gas systems." Fluid Phase Equilibria 204, no. 2 (February 2003): 169–82. http://dx.doi.org/10.1016/s0378-3812(02)00264-9.

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4

Galibin, N. S. "Exponential form of the virial equation of state." High Temperature 49, no. 2 (April 2011): 199–204. http://dx.doi.org/10.1134/s0018151x11020064.

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5

MAGANA, RUSLAN, HUA ZHENG, and ALDO BONASERA. "VIRIAL EXPANSION OF THE NUCLEAR EQUATION OF STATE." International Journal of Modern Physics E 21, no. 01 (January 2012): 1250006. http://dx.doi.org/10.1142/s0218301312500061.

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We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2, 3, …, N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second-order phase transition to the quark–gluon plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second-order phase transition we calculate the critical exponent δ by using Landau's theory of phase transition. We find δ = 3. Refining the properties of the EOS near the critical point gives δ = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures.

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6

Mattiello, S., and W. Cassing. "QCD equation of state in a virial expansion." Journal of Physics G: Nuclear and Particle Physics 36, no. 12 (October 23, 2009): 125003. http://dx.doi.org/10.1088/0954-3899/36/12/125003.

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7

Apfelbaum, E. M., and V. S. Vorob’ev. "Modified Virial Expansion and the Equation of State." Russian Journal of Mathematical Physics 28, no. 2 (April 2021): 147–55. http://dx.doi.org/10.1134/s1061920821020023.

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8

Young, J. B. "An Equation of State for Steam for Turbomachinery and Other Flow Calculations." Journal of Engineering for Gas Turbines and Power 110, no. 1 (January 1, 1988): 1–7. http://dx.doi.org/10.1115/1.3240080.

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Large-scale equations of state for steam used for generating tables are unsuitable for inclusion infinite difference flow calculation computer codes. Such codes, which are in common use in the turbomachinery industry, may require 106 property evaluations before convergence is achieved. This paper describes a simple equation of state for superheated and two-phase property calculations for use in these circumstances. Computational efficiency is excellent and accuracy over the range of application is comparable to that of the large-scale equations. Further advantages are that complete thermodynamic consistency is maintained and the equation can be differentiated analytically for direct substitution into the gas dynamic equations where required. A truncated virial form is used to represent superheated properties and a new empirical correlation for the third virial coefficient of steam is presented.

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9

Tian, Jianxiang, and Hua Jiang. "Equation of state for the hard tetrahedron fluid at stable state." International Journal of Modern Physics B 33, no. 14 (June 10, 2019): 1950136. http://dx.doi.org/10.1142/s0217979219501364.

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Based on the previous works [J. X. Tian, Y. X. Gui and A. Mulero, J. Phys. Chem. B 114, 13399 (2010); Phys. Chem. Chem. Phys. 12, 13597 (2010)], we constructed a new equation of state for the hard tetrahedron (HTH) fluid at stable state by using the recently published Monte Carlo simulation data [J. Kolafa and S. Labík, Mol. Phys. 113, 1119 (2015)]. It can reproduce the correct virial coefficients upto nine, which is the known highest order of virial coefficient for HTH fluid. It also describes the simulation data of the compressibility factor versus the packing fraction at stable state with high accuracy.

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10

Tian, Jianxiang, Yuanxing Gui, and A. Mulero. "New virial equation of state for hard-disk fluids." Physical Chemistry Chemical Physics 12, no. 41 (2010): 13597. http://dx.doi.org/10.1039/c0cp00476f.

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11

Tsonopoulos, C., and J. L. Heidman. "From the virial to the cubic equation of state." Fluid Phase Equilibria 57, no. 3 (January 1990): 261–76. http://dx.doi.org/10.1016/0378-3812(90)85126-u.

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12

VEGA, By CARLOS. "Virial coefficients and equation of state of hard ellipsoids." Molecular Physics 92, no. 4 (November 1997): 651–66. http://dx.doi.org/10.1080/002689797169934.

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13

Estela-Uribe, J. F., and J. Jaramillo. "Generalised virial equation of state for natural gas systems." Fluid Phase Equilibria 231, no. 1 (April 2005): 84–98. http://dx.doi.org/10.1016/j.fluid.2005.01.005.

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14

Bugaev, K. A., A. I. Ivanytskyi, V. V. Sagun, E. G. Nikonov, and G. M. Zinovjev. "Equation of State of Quantum Gases Beyond the Van der Waals Approximation." Ukrainian Journal of Physics 63, no. 10 (October 31, 2018): 863. http://dx.doi.org/10.15407/ujpe63.10.863.

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A recently suggested equation of state with the induced surface tension is generalized to the case of quantum gases with mean-field interaction. The self-consistency conditions of such a model and the conditions necessary for the Third Law of thermodynamics to be satisfied are found. The quantum virial expansion of the van der Waals models of such a type is analyzed, and its virial coefficients are given. In contrast to traditional beliefs, it is shown that an inclusion of the third and higher virial coefficients of a gas of hard spheres into the interaction pressure of the van der Waals models either breaks down the Third Law of thermodynamics or does not allow one to go beyond the van der Waals approximation at low temperatures. It is demonstrated that the generalized equation of state with the induced surface tension allows one to avoid such problems and to safely go beyond the van der Waals approximation. In addition, the effective virial expansion for the quantum version of the induced surface tension equation of state is established, and all corresponding virial coefficients are found exactly. The explicit expressions for the true quantum virial coefficients of an arbitrary order of this equation of state are given in the low-density approximation. A few basic constraints on such models which are necessary to describe the nuclear and hadronic matter properties are discussed.

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15

Reddy, M. Rami, and Seamus F. O'Shea. "The equation of state of the two-dimensional Lennard–Jones fluid." Canadian Journal of Physics 64, no. 6 (June 1, 1986): 677–84. http://dx.doi.org/10.1139/p86-125.

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By combining pressure and energy data from the virial equation of state, through fifth virial coefficients, with the second and third virial coefficients themselves and the results of computer-simulation calculations, we have constructed an equation of state for the two-dimensional Lennard–Jones fluid for 0.45 ≤ T* ≤ 5 and 0.01 ≤ ρ* ≤ 0.8. The fitted data include some in the metastable region, and, therefore, the equation of state also describes "van der Waals loops" including unstable regions. The form used is a modified Benedict–Webb–Rubin equation having 33 parameters including one nonlinear one. The fitting was done using a nonlinear least squares algorithm based on a Levenberg–Marquardt method. A total of 211 simulation points, 97 reported here for the first time, were used in the fitting, and the overall standard deviation is less than 2% for both energy and pressure. Second and third virial coefficients derived from the fit in the supercritical region are in excellent agreement with exact values. The critical constants derived from the fit are in reasonable agreement with published estimates.

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16

TIAN, JIANXIANG. "INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS." International Journal of Modern Physics B 25, no. 19 (July 30, 2011): 2593–600. http://dx.doi.org/10.1142/s0217979211100734.

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In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

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17

Horowitz, C. J., and A. Schwenk. "The virial equation of state of low-density neutron matter." Physics Letters B 638, no. 2-3 (July 2006): 153–59. http://dx.doi.org/10.1016/j.physletb.2006.05.055.

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18

Boublı́k, Tomáš. "Virial coefficients and equation of state of hard chain molecules." Journal of Chemical Physics 119, no. 14 (October 8, 2003): 7512–18. http://dx.doi.org/10.1063/1.1607913.

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19

Bondarev, V. N. "The virial equation of fluid state and non-classical criticality." European Physical Journal B 84, no. 1 (October 26, 2011): 121–29. http://dx.doi.org/10.1140/epjb/e2011-20391-7.

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20

JOSLIN, C. G., C. G. GRAY, S. GOLDMAN, B. TOMBERLI, and W. LI. "Solubilities in supercritical fluids from the virial equation of state." Molecular Physics 89, no. 2 (October 1996): 489–503. http://dx.doi.org/10.1080/002689796173859.

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21

Vega, Carlos, Santiago Lago, and Benito Garzón. "Linear hard sphere models Virial coefficients and equation of state." Molecular Physics 82, no. 6 (August 20, 1994): 1233–47. http://dx.doi.org/10.1080/00268979400100874.

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22

Tian, Jianxiang, Yuanxing Gui, and Angel Mulero. "New Closed Virial Equation of State for Hard-Sphere Fluids." Journal of Physical Chemistry B 114, no. 42 (October 28, 2010): 13399–402. http://dx.doi.org/10.1021/jp106502x.

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23

Vega, C., S. Lago, and B. Garzón. "Virial coefficients and equation of state of hard alkane models." Journal of Chemical Physics 100, no. 3 (February 1994): 2182–90. http://dx.doi.org/10.1063/1.466515.

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24

López De Haro, Mariano, Anatol Malijevský, and Stanislav Labík. "Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location." Collection of Czechoslovak Chemical Communications 75, no. 3 (2010): 359–69. http://dx.doi.org/10.1135/cccc2009510.

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Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

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25

Cibulka, Ivan, Lubomír Hnědkovský, and Květoslav Růžička. "Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene." Collection of Czechoslovak Chemical Communications 66, no. 6 (2001): 833–54. http://dx.doi.org/10.1135/cccc20010833.

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Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

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26

López de Haro, Mariano, Andrés Santos, and Santos B. Yuste. "Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures." Entropy 22, no. 4 (April 20, 2020): 469. http://dx.doi.org/10.3390/e22040469.

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New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

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27

Wang, Yu Fei, Xiao Peng Liu, and Xiao Gong Zhang. "Satellite Liquid Propellant Estimate Based on Virial Equation." Applied Mechanics and Materials 556-562 (May 2014): 2352–55. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.2352.

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The remaining liquid propellant of an on orbit satellite is an important factor to evaluate satellite’s performances and the method is generally used to estimate the volume of the remaining liquid propellant. However, the method has some errors that influence the estimation. This paper takes Virial equation to ameliorate method. By using on orbit data of two satellites, this method based on Virial Equation is validated. And the results indicate the estimation error is less, more close to the true state, and could be put into practical use.

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28

R-MONTEIRO, MARCO A., ITZHAK RODITI, and LIGIA M. C. S. RODRIGUES. "VIRIAL EXPANSION FOR AN ε-DEFORMED SYSTEM." Modern Physics Letters B 09, no. 10 (April 30, 1995): 607–10. http://dx.doi.org/10.1142/s0217984995000565.

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29

Schultz, Andrew J., Katherine R. S. Shaul, Shu Yang, and David A. Kofke. "Modeling solubility in supercritical fluids via the virial equation of state." Journal of Supercritical Fluids 55, no. 2 (December 2010): 479–84. http://dx.doi.org/10.1016/j.supflu.2010.10.042.

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30

Wheatley, Richard J. "Inverse Power Potentials: Virial Coefficients and a General Equation of State." Journal of Physical Chemistry B 109, no. 15 (April 2005): 7463–67. http://dx.doi.org/10.1021/jp040709i.

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31

Kim, Hye Min, Andrew J. Schultz, and David A. Kofke. "Virial Equation of State of Water Based on Wertheim’s Association Theory." Journal of Physical Chemistry B 116, no. 48 (November 28, 2012): 14078–88. http://dx.doi.org/10.1021/jp3067475.

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32

Bannerman, Marcus N., Leo Lue, and Leslie V. Woodcock. "Thermodynamic pressures for hard spheres and closed-virial equation-of-state." Journal of Chemical Physics 132, no. 8 (February 28, 2010): 084507. http://dx.doi.org/10.1063/1.3328823.

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33

Alastuey, A., and A. Perez. "Virial Expansion of the Equation of State of a Quantum Plasma." Europhysics Letters (EPL) 20, no. 1 (September 1, 1992): 19–24. http://dx.doi.org/10.1209/0295-5075/20/1/004.

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34

Tian, Jianxiang, Hua Jiang, Yuanxing Gui, and A. Mulero. "Equation of state for hard-sphere fluids offering accurate virial coefficients." Physical Chemistry Chemical Physics 11, no. 47 (2009): 11213. http://dx.doi.org/10.1039/b915002a.

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35

Viererblová, Linda, Jiří Kolafa, Stanislav Labík, and Anatol Malijevský. "Virial coefficients and equation of state of the penetrable sphere model." Phys. Chem. Chem. Phys. 12, no. 1 (2010): 254–62. http://dx.doi.org/10.1039/b917204a.

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36

Sperber, Daniel, Smita Srinivas, and Malgorzata Zielinska-Pfabé. "Nuclear Equation of State as Determined by the Quantum Virial Expansion." Australian Journal of Physics 44, no. 6 (1991): 639. http://dx.doi.org/10.1071/ph910639.

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The quantum virial expansion is used to investigate the properties of neutron matter in the temperature range 20 < kT < 60 MeV. The pressure as a function of temperature is determined for various densities of neutron matter. Also the stiffness, the energy and the coefficient of volume expansion all as a function of temperature and density are studied.

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37

Boublík, Tomáš. "Third virial coefficient and the hard convex body equation of state." Molecular Physics 83, no. 6 (December 20, 1994): 1285–97. http://dx.doi.org/10.1080/00268979400101951.

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38

ORBEY, HASAN, and NESE ORBEY. "AN EMPIRICAL VIRIAL-LIKE CUBIC EQUATION OF STATE FOR PHASE EQUILIBRIUM CALCULATIONS." Chemical Engineering Communications 90, no. 1 (April 1990): 35–45. http://dx.doi.org/10.1080/00986449008940575.

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39

Osondu Monago, Kenneth. "Fourth Order Virial Equation of State of a Nonadditive Lennard - Jones Fluid." International Journal of Computational and Theoretical Chemistry 3, no. 4 (2015): 28. http://dx.doi.org/10.11648/j.ijctc.20150304.11.

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40

Liang, Y. C., K. Mussack, and W. Däppen. "Low-temperature Extensions of the Virial Equation of State for Solar Modeling." Contributions to Plasma Physics 52, no. 2 (February 2012): 161–64. http://dx.doi.org/10.1002/ctpp.201100100.

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41

Kolafa, Jiří, and Stanislav Labík. "Virial coefficients and the equation of state of the hard tetrahedron fluid." Molecular Physics 113, no. 9-10 (January 13, 2015): 1119–23. http://dx.doi.org/10.1080/00268976.2014.996618.

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42

Silberring, L. "Residual properties of gases based on a complete virial equation of state." International Journal of Thermophysics 17, no. 6 (November 1996): 1387–422. http://dx.doi.org/10.1007/bf01438676.

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43

Wakefield, Charles B., and Constance Phillips. "Virial Coefficients Using Different Equations of State." Journal of Chemical Education 77, no. 10 (October 2000): 1371. http://dx.doi.org/10.1021/ed077p1371.

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44

Iguchi, Kazumoto. "Equation of State and Virial Coefficients of An Ideal Gas with Fractional Exclusion Statistics in Arbitrary Dimensions." Modern Physics Letters B 11, no. 18 (August 10, 1997): 765–72. http://dx.doi.org/10.1142/s0217984997000943.

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Equation of state and virial coefficients of an ideal gas with fractional exclusion (i.e. Haldane–Wu) statistics in arbitrary dimensions are derived herein, using the quantum statistical mechanics formulation for pressure and density of the system in terms of the D-dimensional momentum representation. The relationship between the convergence of the virial expansion and the existence of condensation is shown for this system.

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45

Kolobaev, iktor A., Sergey V. Rykov, Irina V. Kudryavtseva, Evgeniy E. Ustyuzhanin, Peter V. Popov, Vladimir A. Rykov, Aleksandr V. Sverdlov, and Alexander D. Kozlov. "Methodology for constructing the equation of state and thermodynamic tables for a new generation refrigerant." Izmeritel`naya Tekhnika, no. 2 (2021): 9–15. http://dx.doi.org/10.32446/0368-1025it.2021-2-9-15.

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A unified fundamental equation of state 2,3,3,3-tetrafluoropropene (R1234yf) has been developed, a fourth-generation ozone safe refrigerant, and a method for constructing the equation has been proposed. In the gas region, this equation transforms into the virial equation of state, and in the vicinity of the critical point it satisfies the requirements of the modern large-scale theory of critical phenomena and transforms into the Widom scale equation. On the basis of a single fundamental equation of state in accordance with GOST R 8.614-2018, standard reference data (GSSSD 380-2020) on the density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and sound velocity of R1234yf in the temperature range from 230 K to 420 K and pressures from 0.1 MPa to 20 MPa. A comparison of the calculated values of equilibrium properties with the most reliable experimental data obtained in the famous of the world, and tabular data obtained on the basis of the known fundamental equations of state R1234yf. Uncertainties of tabulated data for saturated vapor pressure, density, enthalpy, isobaric heat capacity, isochoric heat capacity, entropy and speed of sound of 2,3,3,3-tetrafluoropropene are estimated – standard relative uncertainties by type A, B, total standard relative and expanded uncertainties. The results obtained in the work show that the proposed unified fundamental equation of state adequately describes the equilibrium properties of R1234yf in the range of state parameters stated above.

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46

Shaul, Katherine R. S., Andrew J. Schultz, and David A. Kofke. "The effect of truncation and shift on virial coefficients of Lennard–Jones potentials." Collection of Czechoslovak Chemical Communications 75, no. 4 (2010): 447–62. http://dx.doi.org/10.1135/cccc2009113.

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We present virial coefficients of up to fifth order computed by Mayer-sampling Monte Carlo for several truncated-and-shifted Lennard–Jones potentials. We employ these coefficients within the virial equation of state to compute vapor-branch spinodals and critical points for each potential considered. We find that truncation distances of 5.0σ and higher yield values in significantly better agreement with those of the unmodified potential than those resulting from the more commonly used truncation distances of 2.5 and 3.0σ. We also employ these virial coefficients to examine the perturbed virial expansion method of Nezbeda and Smith for estimating the critical point. We find that the first-order perturbation performs well in characterizing the effect of potential truncation on the critical point for the truncation distances considered, with errors in critical temperatures ranging from –3 to +2% and errors in critical densities about constant at –22%. Addition of higher-order terms to the perturbation treatment brings it closer to the behavior given by the virial equation of state, which at fifth order underestimates the critical temperatures by 2 to 4% and the critical densities by 20 to 30%.

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47

El Hawary, Ahmed, Robert Hellmann, Karsten Meier, and Henner Busemann. "Eighth-order virial equation of state and speed-of-sound measurements for krypton." Journal of Chemical Physics 151, no. 15 (October 21, 2019): 154303. http://dx.doi.org/10.1063/1.5124550.

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48

Horowitz, C. J., and A. Schwenk. "Cluster formation and the virial equation of state of low-density nuclear matter." Nuclear Physics A 776, no. 1-2 (September 2006): 55–79. http://dx.doi.org/10.1016/j.nuclphysa.2006.05.009.

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49

Yang, Shu, Andrew J. Schultz, and David A. Kofke. "Thermodynamic Properties of Supercritical CO2/CH4 Mixtures from the Virial Equation of State." Journal of Chemical & Engineering Data 61, no. 12 (October 17, 2016): 4296–312. http://dx.doi.org/10.1021/acs.jced.6b00702.

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50

Chen, Ji-sheng, Jia-rong Li, Yan-ping Wang, and Xiang-jun Xia. "The virial equation of state for unitary fermion thermodynamics with non-Gaussian correlations." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 12 (December 15, 2008): P12008. http://dx.doi.org/10.1088/1742-5468/2008/12/p12008.

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