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Archived Entropy of Mixing Calculation

  1. Oct 29, 2013 #1
    I think I actually have solved it. I was right with the PV=nkT, I believe I previously messed up with the algebra.

    1. The problem statement, all variables and given/known data

    Using the same meathod as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, A and B, whose relative proportion is arbitrary. Let N be the total number of molecules and let x be the fraction of these that are species B. You should find that

    ΔS=-Nk[xlnx+(1-x)ln(1-x)]

    Check that this expression reduces to the one given in the text when x= 1/2.

    2. Relevant equations
    That S=Nk[ln(V(a/3n)^(3/2))+3/2] where a is just a whole bunch of stuff that I believe is irrelevant to the problem.

    PV=nkT might be useful

    also the fact that ln(x/y)=ln(x)-ln(y)

    3. The attempt at a solution

    I know that the change of entropy will just be S_final-S_original but I do not know what really changes between the final and the original situations. Do I have to use the Ideal Gas law find out how big the volume would be?
     
    Last edited: Oct 30, 2013
  2. jcsd
  3. Aug 7, 2016 #2

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    This is a constant single pressure process; the original statement is about as obfuscated as is possible. "n" volumes of pure gases are mixed by volume fraction.
     
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