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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.
- Spring '10