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

By G.H. A. Cole

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1) is valid, the general thermodynamic expressions derived from the theory can be rearranged to show explicitly the relation between pairs of particles in the fluid. In this way the fluid spatial features described by the radial distribution function (or its generalisation) can be introduced explicitly into the theoretical formulae. This restricts the validity of the formulae to the description of simple fluids systems, but they are then amenable to evaluation. The problem of determining adequate information about the radial distribution is left for the next chapter, the present chapter being devoted to the deduction of expressions for the fluid thermodynamic functions themselves.

The particle momentum is denoted by p j? with components (pjx, pjy, pjz). In specifying the total system of N particles, j is to range from 1 to N. The total kinetic energy is given by N N J= l 3= 1 (Ό - D Λ Lm and this is not explicitly a function of position or the time. The potential energy, V, is a function of position alone. Two distinct contributions can be recognised : Ψ(τΐ9 r 2 , . . r^) being the potential of interaction between the N particles of the system ; and >K, the potential of interaction between the particles of the system and the containing boundary wall.

Only in this way can the particle pair interactions be accounted for. 31a)) and the other will show explicitly the action of the interparticle force potential. 4. Suppose Q(vN, rN) is some phase function for a system of N interacting particles which does not explicitly involve the time and which always 37 MICROSCOPIC REPRESENTATION remains finite throughout the motion. 29). 4. The left hand side of this expression vanishes because Q is not explicitly a function of time and all phase is to be encompassed in the motion.

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