[Thermo] Derivation of compressibility factor vs reduced pressure

by -Nita
Tags: compressibility, derivation, factor, pressure, reduced, thermo
 P: 2 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
 P: 366 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)
 P: 2 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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