• 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_rr, and
    reduced temperature T_rr.

   – The Z values are tabulated (graphed) as a function of P_rr, T_rr, thus Z
    depends on P, T.

  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.