Lecture20Ch161April13

# Hs and rhs match that gives a1 1 a2 a3 2b2 2 3b3

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Unformatted text preview: er all substitutions: p = kT + B2 (T ) 2 + B3 (T ) 1 3 ...... Z12 B2 (T ) = b2 = 2 B3 (T ) = 4b2 ( 2!V ) ( Z 2b3 = 1 V Z3 3V 2 ( 2 ) 3Z 2 Z1 + 2Z12 ( ) 3( Z 2 Z12 )) 2 This expression looks very different from what we saw before. How comes? Now lest us calculate, e.g. second term above: Z1 = Z2 = Z3 = dr = V 1 U2 e e kT U3 kT drdr2 drdr2 dr 3 U (r12 ) U (r ) kT 1 1 B2 (T ) == Z2 Z12 = 2V 2V ( ) e kT 1 dr1dr2 1 2 e 1 dr Virial Expansion: A general Consideration For third virial coefficient we get after a considerable effort: B3 (T ) = 1 3V f12 f 23 f31dr1dr2 dr3 Using this GCPF formalism Mayer was able to prove the remarkable general theorem: Virial expansion can be expressed in terms of cluster integrals or stars B2 = f12 B3 = f12 f23 +.... f13 Extrapolation to high density: the van der Waals Equation Now we consider the property of the intermolecular potential which consists of weak attr...
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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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