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Unformatted text preview: PHYS 333 Winter 2009 Assignment 7 Due: 5:00 pm Friday March 20 1. The Helmholtz function The Helmholtz function is defined as F = U- TS Starting from this definition, prove the following identities F T V,N =- S (1) F V T,N =- P (2) F N T,V = (3) T 2 ( F/T ) T V,N =- U (4) F = N- PV (5) Explicitly verify these identities for the Ideal Gas, for which PV = Nk B T U = 3 2 Nk B T S = Nk B [ln A ( V/N ) T 3 / 2 + (5 / 2)] =- k B T ln A ( V/N ) T 3 / 2 and for the VdW gas, for which ( P + a ? N 2 V 2 )( V- b ? N ) = Nk B T U = C V T- a ? N 2 V + U S = C V ln T/T + Nk B ln[( V- b ? N ) /N ] + S =- k B T ln[( V- b ? N ) /N ]- ( C V /N ) T ln T/T + k B Tb ? N/ ( V- b ? N )- 2 a ? N/V + [ C V + Nk B- S ] T/N + U /N The parameters C V , U and S are not constants: they are proportional to N . However, the parameters A , a ? , b ? and T are all constants. In order to show N explicitly, I have defined the parameters in the VdW equation to be a ?...
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This note was uploaded on 04/11/2010 for the course PHYS 333 taught by Professor Harris during the Winter '09 term at McGill.
- Winter '09