Abstract
Some thermodynamic relations that follow from the van der Waals equation are considered. It is shown that they are applicable to real substances and model systems described by absolutely different equations of state. These relations are associated with definite geometric lines on the density–temperature plane. The data for the model systems that substantiate the derived regularities were calculated by numerical simulation methods. For real substances, the relevant databases constructed according to experiments were used. It has also been established by numerical simulation that the limitations of the regularities under investigation are related to the nature of attraction in the interparticle interaction potential.
Similar content being viewed by others
References
Van der Waals, J.D., PhD Thesis, Leiden, The Netherlands, 1873.
Smirnov, B.M., Usp. Fiz. Nauk, 2001, vol. 171, no. 12, p. 1291.
Cailletet, L.P. and Mathias, E.C., J. Phys. Théor. Appl., 1886, vol. 5, p. 549.
Timmemans, J., Physico-Chemical Constants of Pure Organic Compounds, Amsterdam: Elsevier, 1950.
Fillipov, L.P., High Temp., 1984, vol. 22, no. 4, p. 545.
Fillipov, L.P., High Temp., 1987, vol. 25, no. 6, p. 789.
Sanchez, I.C. and Biening, K.L., J. Phys. Chem. B, 2014, vol. 118, no. 42, p. 13704.
Novikov, I.I., High Temp., 1995, vol. 33, no. 1, p. 149.
Novikov, I.I., High Temp., 1997, vol. 35, no. 4, p. 659.
Batchinski, A., Ann. Phys., 1906, vol. 19, p. 307.
Holleran, E., Ind. Eng. Chem. Fundam., 1974, vol. 13, no. 3, p. 297.
Powels, J.G., J. Phys. C: Solid State Phys., 1983, vol. 16, p. 503.
Rabinovich, V.A., Vasserman, A.A., and Nedostup, V.I., Thermophysical Properties of Neon, Argon, Krypton, and Xenon, Berlin: Hemispere, 1988.
Kutney, M.C., Reagan, M.T., Smith, K.A., Tester, J.W., and Herschbach, D.R., J. Phys. Chem. B, 2000, vol. 104, p. 9513.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Phys. Chem. B, 2009, vol. 113, no. 11, p. 3521.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Phys. Chem., 2009, vol. 130, no. 21, p. 214111.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Phys. Chem. B, 2013, vol. 117, no. 25, p. 7750.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Phys. Chem. B, 2014, vol. 118, no. 42, p. 12239.
Nedostup, V.I., High Temp., 2013, vol. 51, no. 1, p. 72.
Wei, Q.R. and Herschbach, D.R., J. Phys. Chem. C, 2013, vol. 117, no. 43, p. 22438.
Kulinskii, V.L., J. Chem. Phys., 2014, vol. 141, no. 5, p. 054503.
Fillipov, L.P., Metody rascheta i prognozirovaniya svoistv veshchestv (Methods of Calculation and Prediction of Properties of Substances), Moscow: Mosk. Gos. Univ., 1988.
Brazhkin, V.V. and Ryzhov, V.N., J. Chem. Phys., 2011, vol. 135, no. 8, p. 084503.
Brazhkin, V.V., Lyapin, A.G., Ryzhov, V.N., Trachenko, K., Fomin, Yu.D., and Tsiok, E.N., Usp. Fiz. Nauk, 2012, vol. 182, no. 11, p. 1137.
Guggenheim, E.A., J. Chem. Phys., 1945, vol. 13, no. 7, p. 253.
Balescu, R., Equilibrium and Nonequilibrium Statistical Mechanics, New York: Wiley, 1975.
Mulero, A. and Parra, M.I., Phys. Chem. Liq., 2008, vol. 46, no. 3, p. 263.
Shah, P., Chakrabarti, P., and Chakravarty, C., Mol. Phys., 2001, vol. 99, no. 7, p. 573.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Chem. Phys., 2013, vol. 139, no. 4, p. 046101.
Burshtein, A.L., J. Mol. Liq., 1993, vol. 58, p. 1.
Kulinskii, V.L., J. Phys. Chem. B, 2010, vol. 114, no. 8, p. 2852.
Bulavin, L.A. and Kulinskii, V.L., J. Phys. Chem. B, 2011, vol. 115, no. 19, p. 6061.
Apfelbaum, E.M. and Vorob’ev, V.S., J. Phys. Chem. B, 2010, vol. 114, no. 30, p. 9820.
Vorob’ev, V.S., Chem. Phys. Lett., 2014, vols. 605–606, p. 47.
Lemmon, E.W., McLinden, W.M.O., and Friend, D.G., NIST Chemistry WebBook, NIST Standard Reference Database, Linstrom, P.J. and Mallard, M.G., Eds., no. 69 (online), Gaithersburg, MD, 2004. http://webbooknistgov/chemistry/f luid/.
Span, R., Lemmon, E.W., Jacobsen, R.T., Wagner, W., and Yokozeki, A.A., J. Phys. Chem. Ref. Data, 2000, vol. 29, no. 6, p. 1361.
Fokin, L.R. and Popov, V.N., High Temp., 2013, vol. 51, no. 4, p. 465.
Grilly, E.R. and Mills, R.L., Phys. Rev., 1957, vol. 105, no. 4, p. 1140.
Kozhevnikov, V.F., Zh. Eksp. Teor. Fiz., 1990, vol. 97, no. 2, p. 541.
Jungst, S., Knuth, B., and Hensel, F., Phys. Rev. Lett., 1985, vol. 55, no. 20, p. 2160.
Kikoin, I.K. and Senchenkov, A.P., Fiz. Met. Metalloved., 1967, vol. 24, no. 5, p. 843.
Fokin, L.R., Popov, V.N., and Naurzakov, S.P., High Temp., 2011, vol. 49, no. 6, p. 832.
Stankus, S.V., Khairulin, R.A., Martynets, V.G., and Bezverkhii, P.P., High Temp., 2013, vol. 51, no. 5, p. 695.
Gathers, G.R., Rep. Prog. Phys., 1986, vol. 49, no. 4, p. 341.
Korobenko, V.N. and Rakhel, A.D., J. Phys.: Condens. Matter, 2014, vol. 26, no. 4, p. 045701.
Fortov, V.E., Dremin, A.N., and Leont’ev, A.A., Teplofiz. Vys. Temp., 1975, vol. 13, no. 5, p. 1072.
Likalter, A.A., Phys. Rev. B: Condens. Matter Mater. Phys., 1996, vol. 53, no. 8, p. 4386.
Hess, H., Kloss, A., Rakhel, A., and Schneidenbach, H., Int. J. Thermophys., 1999, vol. 20, no. 4, p. 1279.
Beutl, M., Pottlacher, G., and Jaiger, H., Int. J. Thermophys., 1994, vol. 15, no. 6, p. 6.
Lomonosov, I.V., Doctoral (Phys.-Math.) Dissertation, Chernogolovka: Inst. Probl. Chem. Phys., Russ. Acad. Sci., 1999.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.S. Vorob’ev, E.M. Apfelbaum, 2016, published in Teplofizika Vysokikh Temperatur, 2016, Vol. 54, No. 2, pp. 186–196.
Based on the Proceedings of the XIV Russian Conference on the Thermophysical Properties of Substances (RCTP-14), Kazan, October 2014.
Rights and permissions
About this article
Cite this article
Vorob’ev, V.S., Apfelbaum, E.M. The generalized scaling laws based on some deductions from the van der Waals equation. High Temp 54, 175–185 (2016). https://doi.org/10.1134/S0018151X16020243
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0018151X16020243