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Equation of state for non-ideal gases

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
    temperature.

   – 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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Thermodynamics in Energy Engineering

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