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Chapter III The Molecular Density, the Definitions of Gross Fields, and the Equation of Evolution

Elsevier B.V.
DOI: 10.1016/s0079-8169(08)62259-x
  • Mathematics


Publisher Summary This chapter discusses the kinetic theory of Maxwell. It describes the kinetic theory of gases, which is a mathematical model in which a gas is envisaged as a collection of molecules, each tracing out in the course of time a trajectory in space determined by such forces as the molecule may experience. The basic variables that are used in discussing molecular motions are a time t, a place x, and a velocity v. The time t, the co-ordinates xm of the place x, and the components vk of the velocity v are assigned physical dimensions of time, length, and length/time, respectively. The chapter presents an assumptionthat positions and velocities of individual molecules are distributed randomly, according to a specific rule. This rule is described by means of a molecular density. The kinetic theory represents the interaction of molecules as having a significant effect only in intervals of time as short as to make molecules seem to appear or disappear instantly at (t, x, v) at a rate that depends in some specified way on molecular density. This rate is assumed determined by a collisions operator, which maps a given molecular density onto another function of t, x, and v.

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