Thisbookdealswith theclassicalkinetictheoryofgases.Itsaimisto present
the basic principles of this theory within an elementary framework and
from a more rigorous approach based on the Boltzmann equation. The
subjects are presented in a self-contained manner such that the readers
can und- stand and learn some methods used in the kinetic theory of
gases in order to investigate the Boltzmann equation. In Chapter 1, a
sketch on the evolution of the ideas of the kinetic theory is presented.
Afterwards, the basic principles of an elementary kinetic theory
areintroduced, which arebasedonthe concepts ofmean freepath, molecular
mean velocity and mean free time. The Maxwellian distribution function
is determinedfromstatisticalarguments, andthetransportcoe?cients ofshear
viscosity, thermal conductivity and self-di?usion are obtained from the
e- mentary theory. The most common interaction potentials used in the
kinetic theory of gases are also introduced in this chapter, and the
dynamics of a binary collision is analyzed. Chapter 2 is dedicated to
the study of the Boltzmann equation. First, the
BoltzmannequationisderivedandtheequationsoftheBBGKYhierarchyare
determined.Fromtheknowledgeofthetransferequation-whichfollowsfrom
theBoltzmannequation-themacroscopicbalanceequationsforthemoments
ofthedistributionfunctionarederived.Theequilibriumdistributionfunction
is determined from the Boltzmann equation and the equilibrium states of
a rare?ed gas are also analyzed. In this chapter, theH-theorem and the
paradoxes of Loschmidt and Zermelo are discussed. The chapter ends with
an analysis of the di?erent forms of the entropy which are used in
statistical mechanics to describe the canonical and microcanonical
ensembles.
