Reexamining the Equation of State: A Crucial Advancement in Practical Thermodynamics
DOI:
https://doi.org/10.5281/zenodo.16156810Keywords:
Equation of State, SAFT Equation of State, Xue-Guo Equation of State, Gibbs FunctionAbstract
Thermodynamics has been wrestling with finding a single equation that ties together pressure, volume, and temperature for ages. The usual suspects, such as the ideal gas law and the van der Waals equation, often struggle when conditions become extremely extreme. However, Xue and Guo arrived in 2025 with a different approach. They developed a macroscopic model, based entirely on the laws of thermodynamics, without needing to delve into molecular details. What's neat is how their approach links up what gases do when they're sparse with how dense matter acts when crammed together, all thanks to a smooth, continuous mathematical expression that needs no extra tweaking. We are diving into that equation. We'll examine the theory behind it, its performance, and the extent to which it can be applied. It turns out that the model aligns well with real-world data for a wide range of gases, solids, and liquids. It’s simple, accurate, fast to compute, and holds solemn promise in engineering, maybe even planetary science, education, and, definitely, more complex systems down the road.
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Rapp-Kindner, I., Ősz, K. & Lente, G. (2025). The ideal gas law: derivations and intellectual background. ChemTexts, 11, 1. https://doi.org/10.1007/s40828-024-00198-9.
Garrett, S.L. (2020). Ideal gas laws. In: Understanding Acoustics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-44787-8_7.
Bruylants, G. (2015). Van der Waals forces. In: Gargaud, M., et al. Encyclopedia of Astrobiology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44185-5_1647.
Dogra, L.H., Martirosyan, G., & Hilker, T.A. et al. (2023). Universal equation of state for wave turbulence in a quantum gas. Nature, 620, 521–524. https://doi.org/10.1038/s41586-023-06240-z.
W.G. Chapman, K.E. Gubbins, G. Jackson, & M. Radosz. (1989). SAFT: Equation-of-state solution model for associating fluids. Fluid Phase Equilibria, 52, 31-38. https://doi.org/10.1016/0378-3812(89)80308-5.
Srivastava, A.P., & Pandey, B.K. (2025). A constructive approach to formulating pressure-dependent binding energy using the equation of state. Ionics. https://doi.org/10.1007/s11581-025-06183-7.
Xue, TW., & Guo, ZY. (2022). A global equation-of-state model from mathematical interpolation between low- and high-density limits. Sci Rep, 12, 12533. https://doi.org/10.1038/s41598- 022-16016-6.
Abhay P. Srivastava, Brijesh K. Pandey, & Abhishek K. Gupta. (2024). Explore the fascinating realm of comparing metal melting curves by applying the equation of state and Lindemann's law. Computational Condensed Matter, 40, e00952. https://doi.org/10.1016/j.cocom.2024.e00952.
Alexander Laugier, & József Garai. (2007). Derivation of the ideal gas law. J. Chem. Educ., 84(11), 1832. https://doi.org/10.1021/ed084p1832.
Abhay P. Srivastava, Brijesh K. Pandey, & Abhishek Kumar Gupta. (2025). Calculation of the melting curve of metals using equations of state and Lindemann's law. Computational Condensed Matter, 42, e00986. https://doi.org/10.1016/j.cocom.2024.e00986.
Takabe, H. (2024). Physical of warm dense matters. In: The Physics of Laser Plasmas and Applications, 2. Springer Series in Plasma Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-45473-8_9.
Kumar, A., Das, H.C., & Biswal, S.K. et al. (2020). Warm dense matter and cooling of supernovae remnants. Eur. Phys. J., C, 80, 775. https://doi.org/10.1140/epjc/s10052-020-8353-4.
Shivam Srivastava, Prachi Singh, Anjani K. Pandey, & Chandra K. Dixit. (2024). Unified EOS incorporating the finite strain theory for explaining thermo elastic properties of high temperature superconductors, nanomaterials and bulk metallic glasses. Solid State Communications, 377, 115387. https://doi.org/10.1016/j.ssc.2023.115387.
V. Lipovac, O. Duran, E. Keilegavlen, F.A. Radu, & I. Berre. (2024). Unified flash calculations with isenthalpic and isochoric constraints. Fluid Phase Equilibria, 578, 113991. https://doi.org/10.1016/j.fluid.2023.113991.
Huebner, W.F., & Barfield, W.D. (2014). Equation of State (EOS). In: Opacity. Astrophysics and Space Science Library, 402. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8797-5_4.
Romain Privat, & Jean-Noël Jaubert. (2023). The state of the art of cubic equations of state with temperature-dependent binary interaction coefficients: From correlation to prediction. Fluid Phase Equilibria, 567, 113697. https://doi.org/10.1016/j.fluid.2022.113697.
Yang, X., Frotscher, O. & Richter, M. (2025). Symbolic-regression aided development of a new cubic equation of state for improved liquid phase density calculation at pressures up to 100 MPa. Int J Thermophys, 46, 29. https://doi.org/10.1007/s10765-024-03490-5.
Hertanto Adidharma, & Maciej Radosz. (1999). A study of square-well statistical associating fluid theory approximations. Fluid Phase Equilibria, 161(1), 1-20. https://doi.org/10.1016/S0378-3812(99)00167-3.
Gil-Villegas, A., Galindo, A., & Jackson, G. (2001). A statistical associating fluid theory for electrolyte solutions (SAFT-VRE). Molecular Physics, 99(6), 531–546. https://doi.org/10.1080/00268970010018666.
Chaparro, G., & Müller, E.A. (2024). Development of a Helmholtz free energy equation of state for fluid and solid phases via artificial neural networks. Commun Phys, 7, 406. https://doi.org/10.1038/s42005-024-01892-3.
Akasaka, R., & Lemmon, E.W. (2024). A helmholtz energy equation of state for calculations of thermodynamic properties of trans-1, 2-difluoroethene [R-1132(E)]. Int J Thermophys, 45, 174. https://doi.org/10.1007/s10765-024-03447-8.
Seo, H.M., & Park, B.H. (2025). Application of EOS based on machine learning method on CFD study of rapid hydrogen refueling process. Korean J. Chem. Eng., 42, 1637–1653. https://doi.org/10.1007/s11814-025-00460-x.
Fangxuan Chen, Sheng Luo, Shihao Wang, & Hadi Nasrabadi. (2022). A generalized machine learning-assisted phase-equilibrium calculation model for shale reservoirs. Fluid Phase Equilibria, 558, 113423. https://doi.org/10.1016/j.fluid.2022.113423.
Srivastava, A. P., Pandey, B. K., & Upadhyay, M. (2024). Anticipating pressure changes in halides under compression. East European Journal of Physics, (3), 333-339. https://doi.org/10.26565/2312-4334-2024-3-37.
J Shanker, S.S Kushwah, & M.P Sharma. (1999). On the universality of phenomenological isothermal equations of state for solids. Physica B: Condensed Matter, 271(1–4), 158-164. https://doi.org/10.1016/S0921-4526(99)00240-9.
P. Tripathi, G. Misra, & S.C. Goyal. (2006). Equation of state for group IV–IV semiconductors. Solid State Communications, 139(3), 132-137. https://doi.org/10.1016/j.ssc.2006.03.038.
Srivastava, A.P., Pandey, B.K., & Gupta, A.K. et al. (2024). A new approach to evaluate pressure of solids at high compression. Natl. Acad. Sci. Lett., 47, 713–718. https://doi.org/10.1007/s40009-024-01409-0.
Priyanka Singh, B.K. Pandey, Saurav Mishra, & Abhay Prakash Srivastava. (2023). Formulation for the prediction of melting temperature of metallic solids using suitable equation of states. Computational Condensed Matter, 35(e00807), 2352-2143. https://doi.org/10.1016/j.cocom.2023.e00807.
Raduta, A.R., Nacu, F. & Oertel, M. (2021). Equations of state for hot neutron stars. Eur. Phys. J. A, 57, 329. https://doi.org/10.1140/epja/s10050-021-00628-z.
Berkowicz, S., Andronis, I., & Girelli, A. et al. (2024). Supercritical density fluctuations and structural heterogeneity in supercooled water-glycerol microdroplets. Nat Commun, 15, 10610. https://doi.org/10.1038/s41467-024-54890-y.
Srivastava, A.P., Pandey, B.K., & Gupta, A.K. et al. (2024). Theoretical prediction of thermoelastic properties of bismuth ferrite by a new approach. J Math Chem, 62, 2253–2264. https://doi.org/10.1007/s10910-024-01647-z.
Kat, C. J., & Els, P. S. (2012). Validation metric based on relative error. Mathematical and Computer Modelling of Dynamical Systems, 18(5), 487–520. https://doi.org/10.1080/13873954.2012.663392.
Ross, S.R.PJ., Arnoldi, JF., & Loreau, M. et al. (2021). Universal scaling of robustness of ecosystem services to species loss. Nat Commun, 12, 5167. https://doi.org/10.1038/s41467-021-25507-5.
Edelman, A., & Fradet, A. (1988). Application of equation-of-state theories to some polymeric liquids. Polymer Bulletin, 19, 555–560. https://doi.org/10.1007/BF00283101.
Torben Smith Sørensen, & Vicente Compañ. (1997). On the Gibbs-Duhem equation for thermodynamic systems of mixed Euler order with special reference to gravitational and nonelectroneutral systems. Electrochimica Acta, 42(4), 639-649. https://doi.org/10.1016/S0013-4686(96)00209-5.
P. Colonna, N.R. Nannan, A. Guardone, & T.P. van der Stelt. (2009). On the computation of the fundamental derivative of gas dynamics using equations of state. Fluid Phase Equilibria, 286(1), 43-54. https://doi.org/10.1016/j.fluid.2009.07.021.
Ball, J.M. (1976). Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal., 63, 337–403. https://doi.org/10.1007/BF00279992.
van Nieuwenburg, E., Liu, YH. & Huber, S. (2017). Learning phase transitions by confusion. Nature Phys, 13, 435–439. https://doi.org/10.1038/nphys4037.
Sana Dridi, Mounir Ben Amar, Manef Abderraba, & Jean-Philippe Passarello. (2022). Development of a fully analytical equation of state using ab initio interaction potentials. Application to pure simple fluids: Noble gases Ne, Ar, Kr, and Xe. Fluid Phase Equilibria, 562, 113563. https://doi.org/10.1016/j.fluid.2022.113563.
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Copyright (c) 2025 Abhay P Srivastava, Brijesh K Pandey
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