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Unformatted text preview: o first terms in this expansion:
ZN = V N + N (N 2 1) VN
2 ( dr1dr2 f ( r1 r2 ) + . ) Now we can select new variable for the integral above: r = r1 r2 and get: N(N 1) N 1 N V drf ( r ) = V N 1 N B2 2 V 1 1 where B2 = drf ( r ) = dr 1 e u(r ) 2 2 ZN = V N + ( ) ( ) Is called second virial coefficient. Now we get for pressure: ln Z N N 2 p = = + 2 B2 (T ) = + B2 (T ) V V V kT 2 i.e. we got first term of virial expansion of pressure in terms of density Virial Expansion: general approach Unfortunately we cannot continue this expression as the number of terms and their complexity and diversity blows up quickly. A systematic approach - cluster expansion - was proposed by Mayer. It is based (as we saw earlier) on the idea to switch...
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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