Engineering Transactions, 3, 4, pp. 503-553, 1955

Równanie Boltzmanna i Jego Znaczenie w Teorii Gazów

Z. Szymański
Instytut Podstawowych Problemów Techniki PAN

Three ways of studying phenomena occurring in gases represented by
phenomenological hydrodynamics, kinetic theory and statistical mechanics are discussed as well as the relations between them. Next, fundamental notions and assumptions of the kinetic theory of gases are represented on the basis of the so called kinetic distribution function. Boltz-mann's equation is derived in an elementary way and its mathematical and physical sense is discussed.
The following section is devoted to the most simple solution of Boltzmann's equation represented by Max well's velocity. distribution law. On the basis of this solution the principles of molecular, aerodynamics are discussed. Next, the calculations of the theory of Enskog - Chapman - Burnett, leading to the determination of kinetic coefficients and to the so called equations of the third «approximation», are represented. In the next section the problem of irreversibility of the processes in gases is discussed. Boltzmann's «H» theorem is shown in an; abridged manner. The principal problem of irreversibility of equations of the kinetic theory of gases in connection with the reversibility of equations of mechanics is discussed. Further, Grad's method of solution:
of Boltzmann's equation by means of expansion in a series: of Hermite's three-dimensional polynomials is represented.
The next section is concerned with the application of Boltz- m an n's equation to shock wave investigation. Principal ways of treating the phenomenon of shock wave by means of the methods of the kinetic theory are examined.
The last section is devoted to the efforts to generalize Boltz-mann's equation and the kinetic theory. The problems of relations between the kinetic theory and statistical mechanics are also discussed. These efforts consist in a formal generalization extended to compressed gases and liquids. Three principal variants of the theory (due to Born-Green, Bogolubov-Gurov and Kirk wood) are discussed.

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