STATISTICAL MECHANICAL DERIVATION OF THE GENERALIZED BOLTZMANN EQUATION FOR A FLUID CONSISTING OF RIGID SPHERICAL MOLECULES

Journal Article · Wed Feb 01 04:00:00 EST 1961 · Physica

DOI:https://doi.org/10.1016/0031-8914(61)90044-1· OSTI ID:4068084

Sengers, J V; Cohen, E G.D.

An analysis is made as to whether the modified Boltzmann equation originally proposed by Enskog with intnitive arguments can be justified by a statistical mechanical derivation. In a preceding paper the theory of Bogolubov and the theory of Kirkwood as to the derivation of a generalized Boltzmann equation for a diluts gas were compared and it was proved the corrections to the ordinary Boltzmann equation due to the first order terms of an expansion in terms of a uniformity parameter mu are equal. In the presant paper both theories are applied to a dense system of rigid sperical molecules. It is shown that both theories give again a similar equation for the first distrioution function, leadlag under a number of assumptions to the Enskog equation. In sonae publications it was stated that the theory of Hirkwood would lead to an equation for the first distribution function essentiaily different from the Enskog equation and suggestions were raised elsewhere ths this disparity might be date to the integration procedure applied to the Liouville equation, which would not be legitimate for a discontinuous rigid sphere potential. On the contrary to this the present derivation shows that also in the theory of Kirkwood the Enskog equation can be obtained from the general (N-1) times integrated Liouville equation. (auth)

• Research Organization: Gemeente Universiteit, Amsterdam
• NSA Number: NSA-15-013520
• OSTI ID: 4068084
• Journal Information: Physica, Journal Name: Physica Vol. Vol: 27
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ATOMIC MODELS
BOLTZMANN EQUATION
DENSITY
DIFFERENTIAL EQUATIONS
DISTRIBUTION
FLUIDS
GASES
LIOUVILLE EQUATION
MECHANICS
MOLECULES
PHYSICS
SPHERES
STATISTICS
THERMODYNAMICS
TRANSPORT THEORY