A New Non-Extensive Equation of State for the Fluid Phases of Argon, Including the Metastable States, from the Melting Line to 2300 K and 50 GPa

A new equation of state for argon was developed with the view of extending the range of validity of the equation of state previously proposed by Tegeler et al. and obtaining a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase, metastable, and saturation states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However, in this work, the fundamental equation for Helmholtz free energy was derived from the measured quantities <i>C_V</i>(<i>ρ</i>, <i>T</i>) and <i>P</i>(<i>ρ</i>, <i>T</i>). The empirical description of the isochoric heat capacity <i>C_V</i>(<i>ρ</i>, <i>T</i>) was based on an original empirical description explicitly containing the metastable states. The thermodynamic properties (internal energy, entropy, and free energy) were then obtained by combining the integration of <i>C_V</i>(<i>ρ</i>, <i>T</i>). The arbitrary functions introduced by the integration process were deduced from a comparison between calculated and experimental pressure <i>P</i>(<i>ρ</i>, <i>T</i>) data. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 GPa. It also predicts the existence of a maximum of the isochoric heat capacity <i>C_V</i> along isochors, as experimentally observed in several other fluids. For many applications, an approximate form of the equation of state for the liquid phase may be sufficient. A Tait–Tammann equation is therefore proposed between the triple-point temperature and 148 K.