An Introduction to the Statistical Theory of Classical - download pdf or read online

By G.H. A. Cole

ISBN-10: 0080103979

ISBN-13: 9780080103976

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27a) Consequently, the grand partition function can be written in the form of a series : Ξ = 1 + z Z r ( l ) + z 2 Z r (2)+ . . 27b) This expansion is of considerable interest in the theory of imperfect gases. Thermodynamic functions follow from a knowledge of Ξ just as previously they followed from a knowledge of Z r . 28a) and the average number N of particles in the volume Vis given by N = z %- In Ξ(ζ, V, T). 28) by eliminating the fugacity z. 28). 28). 28a) the Gibbs free energy G is given by = ΜΤ\ηλ = Νμ.

The configuration and momentum space representations can be combined within the phase space structure by treating the components of position and of momentum collectively as relating to a set of six independent coordinate-momentum axes for each particle. The total phase of N particles at some time instant can then be represented as a distribution of a cloud of N points in a 6-dimensional hypothetical phase space. Such a space, showing the phase of each particle separately from the others, is called μ-space.

THE ROLE OF THE PARTITION FUNCTION The link between the microscopic statistical theory and macroscopic thermodynamics is made by considering the entropy, S. The microscopic phase function here is — k In f(iV) so that S= -Jfc>. 11) for f(JV) leads to the expression S = k\nZ^9 where (E) is the phase average of the Hamiltonian function. 19) 46 STATISTICAL THEORY OF CLASSICAL FLUIDS provided the Helmholtz free energy F is defined by F= -kTlnZ(V,T). 20) This relation between F a n d Z is basic to statistical thermodynamics.

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An Introduction to the Statistical Theory of Classical Simple Dense Fluids by G.H. A. Cole

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