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Margenau H, Murphy GM (1943) The Mathematics of Physics and Chemistry. D. Van Nostrand, New York 2 Putilov KA (1939) Lectures on Thermodynamics. Vses. Khim. , Moskva 3. Kittel C (1957) Introduction to Solid State Physics. Wiley, New York 4. Hodgman CD, Weast RC, Selby SM (eds) (1956) Handbook of Chemistry and Physics 38 edn. Chemical Rubber Publishing Co, Cleveland, OH 5. Tarasov V (1945) Dok!. Akad. Nauk 46: 22 6. Tarasov V (1947) Dok!. Akad. Nauk 58: 577 7. Tarasov V (1952) Zh. Fiz. 1 Gibbs' approach, or how to avoid molecular interactions Maxwell - Boltzmann statistics, with corrections for the quantum character of energy changes and the indistinguishable nature of molecules, works perfectly well when we consider systems of non-interacting molecules.

A function characterising the distribution of molecules over different energy layers is called the energy distribution function j(E). 11 ) in which df'(E) is the volume of the energy layer in phase space. 13) dE The actual form of the energy density of states can be found for a given model system. 14) The energy density of states is a sharply rising function of volume and energy as well as of the number of molecules. When a distribution law is known it is possible to calculate the mean over the ensemble value of any property U(p, q) at a given time t: (u{t)) = f fU{p,q)p(p,q,t)dp ...

6 Quantum statistics 31 statIstIcs approach classical (Maxwell - Boltzmann) statIstIcs when the exponential e-(~ - E)/kT is much higher than 1. 120) equals approximately 7,5 which is considerably higher than 1. Therefore the gas of He atoms at such temperature and pressure cannot be described by Maxwell- Boltzmann statistics and Bose - Einstein (for 4 He) or Fenni - Dirac (for 3 He) distribution laws must be used, All other molecular and mono-atomic gases are described by Maxwell- Boltzmann statistics, On the other hand, electrons (MHe!

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