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Unformatted text preview: N Which looks like an exponential... from definition of the GCPF we can see that pressure can be presented as expansion in z: ( ) Z =1 b = ( 2!V ) ( Z Z ) b = ( 3!V ) ( Z 3Z Z
b1 = 1!V
2 1 1 1 2 2 1 1 3 3 2 j =1 bj z j 1 + 2Z13 ) But wait - we wanted expansion in density, not chemical potential! Now comes an old trick - consider Expansion for N and derive z from it in a consistent manner: Virial Expansion: A General Consideration
In other words: N = V V ln
V ,T = z V ln z =
V ,T z kT p z V ,T =
j =1 jb j z j Now we seek expansion of z in powers of density: z = a1 + a2 2 + a3 3 + ..... Now we insert this expansion into the expression for density in powers of z above and make sure that Powers on the l.h.s and r.h.s match. That gives: a1 = 1 a2 = a3 = 2b2
2 3b3 + 8b2 Virial Expansion: A General Consideration
We get aft...
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- Spring '10