A simple equation of state (EoS) has recently been introduced (J. Phys. Chem. B 2009, 113, 11977-11987) as (Z - 1)v(2) = e + f/rho + g rho(2), where Z equivalent to pv/RT is the compressibility factor, v = 1/rho is molar volume, and e, f, and g are temperature dependent parameters. This EoS has been found to be accurate for all types of nano and bulk solids and bulk fluids, in the entire temperature and pressure ranges for which experimental data are reported, except for the isotherms within 1 <= T-r = T/T-c <= 1.1 for the spherical and near spherical species and for a wider temperature range for the cylindrical molecules. The aim of this work is to investigate the validity of a three-term expression similar to the mentioned EoS for both thermal and internal contributions to the compressibility factor, separately. Such investigation shows that although the total pressure obeys the EoS well, neither its thermal nor its internal contributions follow a similar three-term expression. Therefore, there are some terms in the individual pressure contributions, which cancel each other out in the total pressure, which makes the EoS so simple. However, we have found that there is one extra term in each contribution which does not cancel out in the total pressure, for the isotherms within the critical region. Such a term significantly improves the isotherms near the critical isotherm, compared to the original EoS. The added term to the pressure components also improves both thermal and internal pressures in the entire temperature range. The results of this work show that, although semiempirical EoSs such as van der Wags, Redlich-Kwong and EoS-III are fairly accurate in describing the pressure behavior of fluids, except in the critical region, they may show a remarkable deviation for the thermal and internal pressures. Finally, the obtained expression for the internal compressibility factor along with the EoS is used to derive internal energy, enthalpy, entropy, heat capacity at constant volume, and constant pressure each as a quadric function in density, for each isotherm, out of the critical region.