[Thermo] Derivation of compressibility factor vs reduced pressure

  1. 1. The problem statement, all variables and given/known data
    derivation of compressibility factor vs. reduced pressure
    I am supposed to derive the graph by solving equations

    2. Relevant equations
    Van der Waals equation of state
    compressibility factor, Z = (Pv)/(RT)
    reduced pressure = P/critical pressure
    Z = f(Tr, Pr)

    3. The attempt at a solution
    I sat for 12 hours attempting to find a solution but just spent time trying to understand what I was doing instead.
    Is there a way to get the graph mathematically without using any values for critical pressure or temperature?

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

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Compressibility charts are derived from experimental data from 10 gases such as propane, Nitrogen, Carbon Dioxide etc. Select a gas you have properties for such as propane. Tc propane is 370 K. Pc propane is 42.7 bar. Assume a constant temperature of let's say 555 K to generate the Tr=1.5 line. Vary pressure from 42.7 to 300 bars (Pr 1 to 6). Use propane tables to find v (specific volume) solve for Z. Plot Tr(Z,Pr)
  4. After solving the Van der Waals equation for the compressibility factor and
    deriving the critical temperature, pressure, and volume

    knowing that a horizontal inflection point occurs on the isotherm at critical point

    am I supposed to solve PV3-(Pb+RT)V2+aV-ab=0
    for the cubic root?
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