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What is initial slopes of the plot Z versus P ?

  1. Jun 2, 2017 #1
    1. The problem statement, all variables and given/known data
    Use the van der waals constant for ##H_2## and ##O_2## to calculate the initial slopes of the plots of compressibility factor Z versus P.

    2. Relevant equations


    3. The attempt at a solution

    Using virial expansion for van der waal gas in terms of ##P##

    I get ##Z = 1 + \dfrac{1}{RT}\left(b - \dfrac{a}{RT} \right)P + \cdots##

    Using first approximation,

    Then ##\dfrac{dZ}{dP} = \dfrac{1}{RT}\left(b - \dfrac{a}{RT} \right)##.

    What is initial slope in this context ? ##T = 0 ## ?
     
  2. jcsd
  3. Jun 2, 2017 #2
    What you calculated is the initial slope.
     
  4. Jun 4, 2017 #3
    But the answer does not involve ##T##.

    For ##O_2## it is ##-4.07 \times 10^{-3} bar^{-1}## and for ##H_2## it is ##-6.92 times 10^{-4} bar^{-1}##.

    Which value of ##T## should I take ?
     
  5. Jun 4, 2017 #4
    I confirm you virial expansion for Z in terms of P and T. Can you please determine the value of T that gives the "book" answers?
     
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