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Equation of state for non-ideal gases

  • The P-V-T relationship for real gas needs modification of ideal gas laws.
     1) Compressibility factor
       The compressibility factor Z is a correction term to the ideal gas laws.
     PV=ZRT, z : compressibility factor
  - Z can be estimated using the concept of “corresponding states”.
    It states that gases behave similarly with respect to non-ideality;
    that is, they have the same Z value when they are in corresponding
    states relative to their respective critical pressure and critical

   - Thus, Z can be determined by knowing reduced pressure P\(r\), and
    reduced temperature T\(r\).

   - The Z values are tabulated (graphed) as a function of P\(r\), T\(r\), thus Z
    depends on P, T.

                \(Pr=\frac{P}{Pc}, Tr=\frac{T}{Tc}\)

     where P, and T are the actual pressure and temperature and Pc
     and Tc are the critical values.

 2) Van der Waals (vdw) equation of state
From ideal gas law, corrections in
① Volume
    Real gas has finite volume (ideal gas = volume-less)
    → subtract the gas volume from the total volume.

② Another consideration
    Particles are interacting each other. This correction should be     considered in the pressure term.

              \((P\)+\(\frac {a}{V^2})\)   \((V\)−\(b)\)=\(RT\) \(per\) \(mole\)

     Interaction correction     Volume correction

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This article is from the free online course:

Thermodynamics in Energy Engineering

Hanyang University