2012 Study-Guide-1

V or vm diagram first and second derivatives of p vs

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Unformatted text preview: int = 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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