Abstract
This chapter starts defining statistical ensembles and the relative partition functions which are the starting point to completely characterize the thermodynamic properties of a system. It must be noted that the partition functions can be determined in the framework of the classical or quantum theory, considering the proper statistics. In this book, we consider mainly nondegenerate plasmas, where the effects of Pauli exclusion principle (Bose/Einstein or Fermi/Dirac distributions) are not relevant, and the Boltzmann statistics can be used.
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Notes
- 1.
An exception to this assumption can be found in Chap. 5 for the ortho–para effect in the rotation of light diatomic molecules.
- 2.
If the particles have internal structure, as excited states or angular momentum, variables to consider internal states must be added.
- 3.
The Dirac function can be calculated as the limit for d → 0 of a square function of unitary surface and width d, i.e., \(\delta (x) = \left \{\begin{array}{ll} 0 & x\neq 0\\ \infty &x = 0 \end{array} \right..\)
- 4.
\({\sum }_{n=0}^{\infty }\frac{{x}^{n}} {n!} ={ \mathrm{e}}^{x}.\)
- 5.
In this theory, interaction potentials depend only on positions \(\left \{{\mathbf{r}}_{i}\right \}\) and not on the velocities \(\left \{{\mathbf{p}}_{i}\right \}\) as it can happen in the presence of magnetic fields.
- 6.
Considering forces which involve multi-particle interactions is possible but the theory becomes much more complicated.
- 7.
The potential here is considered spherical symmetric. The theory must be extended to consider potentials depending on the relative orientation of molecules. These effects can be important for large molecules.
- 8.
Even if the virial expansion can be applied for a generic multi-particle potential (Landau and Lifshitz 1986), a closed expression that relates the virial coefficients to the gas composition can be obtained only under the approximation of binary collisions.
- 9.
In principle, no completely repulsive state exists due to the presence of very small depth due to Van der Waals forces.
- 10.
Here, exact means that all the terms in the Debye–Hückel theory and infinite virial expansions are considered.
- 11.
The Debye–Hückel theory introduces the lowering of ionization potential and the correction to pressure and to all the thermodynamic functions. It results in a correlation between the configuration integral and the internal partition function.
References
Allen MP, Tildesley DJ (1989) Computer Simulation of Liquids. 2nd ed. Oxford University Press, USA
Biolsi L, Holland PM (1996) Thermodynamic properties of oxygen molecules at high temperatures. International Journal of Thermophysics 17(1):191–200
Capitelli M, Ficocelli E (1977) Thermodynamic properties of Ar − H 2. Revue Internationale des Hautes Temperatures et des Refractaires 14:195–200
Capitelli M, Lamanna UT (1976) Second virial coefficients of oxygen–oxygen and carbon–oxygen interactions in different electronic states. Chemical Physics 14:261–266
D’Angola A, Colonna G, Gorse C, Capitelli M (2008) Thermodynamic and transport properties in equilibrium air plasmas in a wide pressure and temperature range. European Physical Journal D 46:129–150
Fisher BB (1966) Calculation of the thermal properties of hydrogen. Tech. Rep. LA–3364, Los Alamos Scientific Laboratory
Frenkel D, Smit B (2002) Understanding molecular simulation : from algorithms to applications, 2nd edn. Academic Press
Guidotti C, Arrighini G, Capitelli M, Lamanna UT (1976) Second virial coefficients of ground state nitrogen atom. Zeitschrift für Naturforschung 31a:1722–1724
Hill TL (1955) Molecular clusters in imperfect gases. Journal Chemical Physics 23(4):617–623
Hilsenrath J, Klein M (1965) Tables of thermodynamic properties of air in chemical equilibrium including second virial corrections from 1500 K to 15000 K. Tech. Rep. AEDC–TR–65–58, AEDC
Hirschfelder JO, Curtiss CF, Bird RB (1966) Molecular Theory of Gases and Liquids, 2nd edn. Structure of Matter Series, John Wiley & Sons
Huang K (1987) Statistical Mechanics. John Wiley & Sons
Johnson JH, Panagiotopoulos AZ, Gubbins KE (1994) Reactive canonical Monte Carlo - a new simulation technique for reacting or associating fluids. Molecular Physics 81(3):717–733
Landau D, Lifshitz E (1986) Statistical Physics. Pergamon Press, Oxford
Lisal M, Smith W, Nezbeda I (2000) Computer simulation of the thermodynamic properties of high–temperature chemically–reacting plasmas. Journal of Chemical Physics 113(12): 4885–4895
Lisal M, Smith W, Bures M, Vacek V, Navratil J (2002) REMC computer simulations of the thermodynamic properties of argon and air plasmas. Molecular Physics 100:2487–2497
NIST (2009) URL http://www.nist.gov/srd/index.htm
Pagano D, Casavola A, Pietanza LD, Colonna G, Giordano D, Capitelli M (2008) Thermodynamic properties of high-temperature jupiter-atmosphere components. Journal of Thermophysics and Heat Transfer 22(3):8
Pagano D, Casavola A, Pietanza LD, Capitelli M, Colonna G, Giordano D, Marraffa L (2009) Internal partition functions and thermodynamic properties of high-temperature jupiter-atmosphere species from 50 K to 50,000 K. Tech. Rep. STR-257
Pirani F, Albertí M, Castro A, Teixidor MM, Cappelletti D (2004) Atom–bond pairwise additive representation for intermolecular potential energy surfaces. Chemical Physics Letters 394 (1–3):37–44
Ree FH (1983) Solubility of hydrogen-helium mixtures in fluid phases to 1 GPa. The Journal of Physical Chemistry 87(15):2846–2852
Smith W, Lisal M, Nezbeda I (2006) Molecular-level Monte Carlo simulation at fixed entropy. Chemical Physics Letters 426(4-6):436–440
Smith WR, Triska B (1994) The reaction ensemble method for the computer simulation of chemical and phase equilibria. i. theory and basic examples. The Journal of Chemical Physics 100(4):3019–3027
Turner H, Brennan J, Lisal M, Smith W, Johnson J, Gubbins K (2008) Simulation of chemical reaction equilibria by the reaction ensemble Monte Carlo method: a review. Molecular Simulation 34:119–146
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Capitelli, M., Colonna, G., D’Angola, A. (2012). Real Effects: II. Virial Corrections. In: Fundamental Aspects of Plasma Chemical Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8182-0_7
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