Read e-book online An Introduction to the Statistical Theory of Classical PDF

By G.H. A. Cole

ISBN-10: 0080103979

ISBN-13: 9780080103976

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Extra info for An Introduction to the Statistical Theory of Classical Simple Dense Fluids

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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. 31) dV T, N The full range of thermodynamic functions can then be related directly to the partition functions. F-V FLUID STATISTICAL THERMODYNAMICS 49 The importance of the grand canonical form as compared with the canonical form is that the former applies to open systems whereas the latter does not. The grand canonical form, therefore, is able to describe more general situations (like the simultaneous equilibrium between different phase of matter) than is the canonical form.

2) dp^ = Π dp,·, and dr^ = Π dr3-, 42 STATISTICAL THEORY OF CLASSICAL FLUIDS so that p ^ and rN can be regarded as vectors in a hypothetical 6iV-dimensional phase space. For the partial phase element to be associated with A(< N) particles we have the obvious notation Vh = (Pi, P2> Ps, · . Ρ/Λ rh = (r l5 r 2 , r3, . . 3) h dp*1 = Π dp,·, and drh = Π dr,·. j=l j=l (N) To distinguish the distribution f from the previous specific distribution / ( J V ) , f(iV) is often called the generic 7V-th order phase distribution since reference is not made to specific particles.

It determines the time evolution of f{N) according to the dictates of classical particle mechanics. The Liouville equation will form the basis of the arguments to follow. The phase distribution function f{N) can be given a geometrical interpretation in y-space, first proposed by Willard Gibbs, and which has proved of extreme value in the development of the statistical theory of matter. This involves the concept of the ensemble. This is a collection of an indefinitely large number Γ of identical virtually independent copies of the original system.

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

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