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Homework Help: Deriving Peng-Robinson Entropy Departure Function

  1. Apr 22, 2013 #1
    EDIT: Nevermind. I figured it out. The two expressions are, in fact, equal.

    An excerpt from a book at this link, http://webpages.sdsmt.edu/~ddixon/Departure_Fxns.pdf, states that the entropy departure function for any equation of state is equal to the following (Eqn. 4.4-28):


    And that the specific entropy departure function for the Peng-Robinson EOS is (Eqn. 4.4-30):


    The Peng-Robinson EOS is:





    κ is a constant that depends on the acentricity of the specific chemical species.

    The other parameters A,B, and Z used in the above equations are:




    My problem is that I can't figure out how to derive the Peng-Robinson entropy departure function from the integral definition I gave above. When I evaluate [itex](\frac{∂P}{∂T})_{v}[/itex], I get:


    And when I evaluate the integral using this equation, I get:


    After simplifying, I get:


    I've been able to find that [itex]Rln[\frac{Z(v-b)}{v}]=Rln(Z-B)[/itex], thus, the equation becomes:


    But I can't show whether this is the same as the equation given in the link (the second equation I gave in this post). And if it's not, where did I go wrong in the derivation?


    EDIT: Nevermind. I figured it out. The two expressions are, in fact, equal.
    Last edited: Apr 22, 2013
  2. jcsd
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