Expanded Formulation of Thermodynamic Scaling in the Critical Region

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Chemistry

Background:

• Understanding critical phenomena is crucial for physical systems.
• Existing models often assume symmetry, which may not hold universally.
• Deviations from symmetry can significantly impact observable properties.

Purpose of the Study:

• To develop a scaled expression for free-energy to describe thermodynamic properties in the critical region.
• To predict and analyze nonsymmetric coexistence curves.
• To explain deviations from established laws, such as the law of rectilinear diameter, in fluids.

Main Methods:

• Utilizing a scaled expression for free-energy, F(ρ, T).
• Analyzing the implications of nonsymmetric coexistence curves.
• Deriving expressions for average density and specific heat discontinuities.

Main Results:

• A general prediction of nonsymmetric coexistence curves, with symmetric cases as a special instance.
• An expression for average fluid density below the critical point that is nonlinear with temperature.
• Identification of asymmetry contributions to specific heat discontinuity along the critical isochore.

Conclusions:

• The scaled free-energy approach provides a comprehensive description of critical phenomena.
• Nonsymmetric coexistence curves are a general feature, impacting fluid properties.
• The model reconciles classical equations of state with observed deviations.