Thermodynamic Fluid Equations-of-State.

Area of Science:

• Thermodynamics
• Physical Chemistry
• Fluid Mechanics

Background:

• Modern thermodynamic fluid property data banks rely on cubic equations with numerous parameters.
• Existing functional forms for Gibbs density surfaces are inadequate near critical points and in supercritical regions.
• Continuity assumptions for gas and liquid states at the critical point are fundamentally flawed.

Purpose of the Study:

• To identify and characterize a mesophase between gas and liquid states.
• To develop accurate thermodynamic models for fluid properties, especially near critical points.
• To improve the accuracy and reduce the complexity of fluid property data banks.

Main Methods:

• Identification of a mesophase bounded by third-order discontinuities in Gibbs energy derivatives.
• Application of separate, appropriate functional forms for gas and liquid states.
• Utilizing three- or four-term virial expansions to represent deviations from the mesophase.
• Employing physical constants like Boyle temperature (T_B) and critical constants (T_c, p_c).

Main Results:

• A distinct mesophase exists, characterized by linear pressure functions.
• Gas and liquid states exhibit discontinuities, not continuity, at the critical point.
• Virial expansions accurately model gas and liquid behavior on either side of the mesophase.
• The fourth virial term is negligible for simple fluids below the Boyle temperature (T_B).

Conclusions:

• The critical point does not exhibit a singularity, and gas/liquid continuity is absent.
• The proposed mesophase model provides a more accurate representation of fluid behavior.
• This approach simplifies thermodynamic modeling by using fewer parameters and known physical constants.