The Entropy of van der Waals Fluid

Thermodynamic state functions are fundamental quantities in many fields. In this work, the van der Waals (vdW) equation of state and calculation formulas of state functions are derived with statistical thermodynamic method in three-dimensional (3D) and two-dimensional (2D) spaces. The heat capacity at constant volume (C_V,m ) or area (C_A,m ) is exactly the same as that of ideal gas, but the heat capacity at constant pressure (C_p,m ) and other state functions are different from those of ideal gas. The vdW equation of state is a cubic equation, which leads to the fact that the entropy and free energy changes of vdW fluid can be expressed as explicit expressions of volume rather than pressure. Therefore, the adsorbate entropy at constant area can still be theoretically proven to have a linear relationship with the gas-phase entropy at constant volume. However, the linear correlation between it and gas-phase entropy at constant pressure is no longer strictly true in theory. In addition, since the vdW equation of state is applicable to both gas and liquid, the linear correlation between adsorbate entropy and liquid-phase entropy can also be found. At last, the reference state for real gas or fluid at a constant molar volume is suggested.