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Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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Second Law of Thermodynamics

Second Law of Thermodynamics

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Solubility Equilibria: Ionic Product of Water

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The ionic product of water varies with temperature, and its value is 1.0 x 10−14 at standard experimental conditions. Per Le Chatelier's...

Thermodynamic Properties of Ideal Solutions

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For an ideal liquid solution, the standard state of each component is defined as the pure liquid at the temperature and pressure of the solution. Similarly, for solid solutions, the standard state is the pure solid. The chemical potentials of the components in the ideal solution are compared to the chemical potentials of the pure substances in their standard states. These standard states provide a reference point for calculating the thermodynamic properties of ideal solutions.For ideal...

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Anomalous thermodynamic properties of water: What is wrong and/or missing in SAFT equations?

¹Faculty of Science, J. E. Purkinje University, 400 96 Ústí nad Labem, Czech Republic.

The Journal of Chemical Physics

|May 20, 2026

Summary

New theoretical water models accurately predict density and compressibility, unlike existing Statistical Association Fluid Theory (SAFT) equations. These models capture key features but struggle with heat capacity due to missing electrostatic interactions.

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Area of Science:

Physical Chemistry
Thermodynamics
Computational Chemistry

Background:

Statistical Association Fluid Theory (SAFT) equations of state have limitations in accurately predicting water's thermodynamic properties.
Existing SAFT models for water often rely on numerous adjustable parameters and fail to capture essential behaviors across broad conditions.

Purpose of the Study:

To investigate why current SAFT-type equations fail to reproduce water's thermodynamic properties.
To develop and analyze theoretical water models that offer genuine predictions without empirical parameterization.

Main Methods:

Examined two analytically treatable water models: a simple association model and a short-range model derived from TIP4P.
Computed isobaric temperature dependence of density and response functions (isothermal compressibility, isobaric expansivity, heat capacity).
Compared model predictions against experimental data and a leading SAFT equation.

Main Results:

Short-range models successfully reproduced density, isothermal compressibility, critical compressibility factor, and expansivity crossing point.
These models captured features often missing in SAFT-type equations for water.
Failure to reproduce heat capacity was observed, attributed to omitted long-range electrostatic effects.

Conclusions:

Existing SAFT equations for water have shortcomings due to arbitrary reference systems, neglected van der Waals interactions, ambiguous corrections, and parameter estimation strategies.
Theoretical models focusing on essential physics can better predict certain thermodynamic properties than parameterized SAFT approaches.
Accurate prediction of water's heat capacity requires incorporating long-range electrostatic contributions.