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# virial equation of states z 1 bt vm ct vm2

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Unformatted text preview: P + C’(T) P2 + D’(T) P3 + .... (VIRIAL EQUATION OF STATES) Z = 1 + B(T) / Vm + C(T) / Vm2 + D(T) / Vm3 + ....(VIRIAL EQUATION OF STATES) Mathematical Definition of Critical Point = Inflection Point in P vs. V (or Vm) diagram (first and second derivatives of P vs. V (or Vm) are equal to 0 at the critical point) Mathematical Definition of Boyle’s Temperature: B(Tb) = B’(Tb) = 0 # ∂U & CV = % ( \$ ∂T 'V 1 # ∂V & α= % ( V \$ ∂T ' P € # ∂H & CP = % ( \$ ∂T ' P −1 # ∂V & κT = % ( V \$ ∂P 'T If F is a state function of two variables X and Y, then: ⎛ྎ ∂F ⎞ྏ ⎛ྎ ∂F ⎞ྏ dF = ⎜ྎ ⎟ྏ dX + ⎜ྎ ⎟ྏ dY ⎝ྎ ∂X ⎠ྏ Y ⎝ྎ ∂Y ⎠ྏ X # ∂ # ∂F & & # ∂ # ∂ F & & F(x, y) is a state function ⇔ dF is an exact differential ⇔ % % ( ( = % % ( ( \$ ∂x \$ ∂y ' x ' y \$ ∂y \$ ∂ x ' y ' x # ∂x & # ∂y & # ∂z & # ∂x & 1 For any set of three variables: % ( % ( % ( = −1 % ( =# & ∂y \$ ∂y ' z \$ ∂z ' x...
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## This note was uploaded on 01/26/2014 for the course CHEM 3615 taught by Professor Aresker during the Spring '07 term at Virginia Tech.

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