A global equation-of-state model from mathematical interpolation between low- and high-density limits

• Published in: Scientific reports Vol. 12; no. 1; p. 12533
• Main Authors: Xue, Ti-Wei, Guo, Zeng-Yuan
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group 22.07.2022; Nature Publishing Group UK; Nature Portfolio
• Subjects: Behavior; Entropy; Mathematical models; Radiation
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-022-16016-6

Abstract The ideal gas equation of state (EOS) model is a well-known low-density limiting model. Recently, an ideal dense matter EOS model for the high-density limit symmetric to the ideal gas model has been developed. Here, by mathematically interpolating between the ideal gas and ideal dense matter limiting models, we establish a global model containing two EOS in the form of P-V-T and P-S-T for arbitrary ranges of densities. Different from empirical or semi-empirical EOS, the coefficients in the global EOS have a clear physical meaning and can be determined from a priori knowledge. The proposed global model is thermodynamically consistent and continuous. It reduces to the ideal gas model when approaching the low-density limit and to the ideal dense matter model when approaching the high-density limit. Verifications for 4 He show that the global model reproduces the large-range behavior of matter well, along with providing important insight into the nature of the large-range behavior. Compared to the third-order virial EOS and the Benedict–Webb–Rubin EOS, the global P-V-T EOS has higher descriptive accuracy with fewer coefficients over a wide range of data for N 2 . The global model is shown to work well in extreme applied sciences. It predicts a linear, inverse relationship between entropy and volume when the temperature-to-pressure ratio is constant, which can explain the entropy-production behavior in shock-Hugoniots.