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Derivation of Residual Thermal Properties from Cubic Equations of State when the Discriminant of Quadratic Term Changes Sign with Temperature

  • CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY
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Abstract

A cubic equation of state (EOS) always contains a quadratic term, or a quadratic term and a cubic term, where the quadratic term may contain temperature dependent parameters(s). Therefore, the discriminant (Δ) of quadratic term may change sign in the variation of temperature. If so, the functional forms of the residual thermal properties (such as residual internal energy, enthalpy, entropy, isochoric and isobaric heat capacity) derived from the EOS will change accordingly. When Δ = 0, the quadratic term degenerates into a perfect square of volume, which can be used to derive fugacity coefficient, residual Gibbs and Helmholtz free energy, but cannot give correct residual thermal properties. To solve this problem, non-degenerate transformation of quadratic fraction must be used. When Δ < 0, the residual thermal properties are derived by the method of undetermined coefficients or integration by parts. For the sake of generality, the general form of cubic equations of state is used to derive residual thermal properties according to the sign of Δ. The derivation starts from residual internal energy and fugacity coefficient, and then extends to other residual properties. These results and approaches can be used in the efforts to improve the accuracy of the cubic EOS, or to extend cubic EOS to the supercritical region that is very far from the critical points of pure fluids.

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ACKNOWLEDGMENTS

This work was supported by the Natural Science Foundation of Hebei Province (grant no. D2018403089) and the Key Project of Scientific and Technologic Research of Hebei Provincial Universities (grant no. ZD2018026).

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Authors and Affiliations

  1. Hebei Key Laboratory of Strategic Critical Mineral Resources, Hebei GEO University, 050031, Shijiazhuang, China

    J. W. Hu

  2. Hebei Technology Innovation Center for Intelligent Development and Control of Underground Built Environment, 050031, Shijiazhuang, China

    J. W. Hu

  3. College of Earth Sciences, Hebei GEO University, 050031, Shijiazhuang, China

    J. W. Hu

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Hu, J.W. Derivation of Residual Thermal Properties from Cubic Equations of State when the Discriminant of Quadratic Term Changes Sign with Temperature. Russ. J. Phys. Chem. 97, 2395–2404 (2023). https://doi.org/10.1134/S0036024423110122

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