Lecture20Ch161April13

Rn n i j u ri 1 n rj u ri 2i j n rj now

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Unformatted text preview: i ( 1 N rj = u ri 2i j N ) ( rj ) Now the configurational part of CPF can be presented as: u ri rj i< j Z N = dr1dr2 ....drN e ( ) Now we consider first a low density, I.e. (almost) ideal system where we expect ri rj intermolecular collisions to be rare. The interaction potential vanishes when Unfortunately the exponentials in the expression of the partition function do not vanish when interparticle distance grows (rather they tend to 1). Therefore we can define Mayer functions: fij ri And get for the CPF: ( rj = e ) u ri ( rj ) 1 N N N Z N (V,T ) = d r 3N j<m (1 + f ) = jm d r 1+ 3N j<m f jm + j<m r<s f jm frs + ..... Interacting Particles (Cont) The above expression fo CPF appears like an expansion in number (and instances) of interacting particlesMayer functions have a simple graphical interpretation of two intercating particles, so that first term corresponds to instances when only two particles in the whole vessel interact (though such particles could be any) and the next term corresponds to two pairs of particles interacting simultaneously etc etc. It is relatively easy to evaluate tw...
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This note was uploaded on 05/04/2010 for the course CHEM 161 taught by Professor Shaklovich during the Spring '10 term at Harvard.

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