However, since the models used for interpolation usually cover only a restricted range of densities 1, the models obtained by interpolating between them still cover only a restricted range of densities and are therefore not truly global. It was often obtained by interpolating between different EOS models 2, 3, 4, 5, 6, 7. A global equation of state (EOS) model is needed to describe these large-range behaviors of matter. In these processes, matter may experience large ranges of densities, with correspondingly large ranges of behaviors exhibited 1. Various extreme dynamic processes such as explosive and impact loading of materials, shock wave propagation, and planetary or stellar interior evolution have attracted increasing attention. 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. The global model is shown to work well in extreme applied sciences. 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. Verifications for 4He 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. 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. The proposed global model is thermodynamically consistent and continuous.
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. 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. Recently, an ideal dense matter EOS model for the high-density limit symmetric to the ideal gas model has been developed. The ideal gas equation of state (EOS) model is a well-known low-density limiting model.
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