Linear isotherm regularities of solid sodium under pressure

Abstract

We propose several new regularities in solid sodium from the available experimental data and calculated thermodynamic properties along the isotherms with the equation of state (EOS) of the modified Holzapfel form. Z−1V2 is a linear function in terms of V2 with different intersection points for the isotherms at high temperatures within the considered pressure range, where Z and V are the compressibility factor and molar volume. The calculated isothermal bulk modulus BT and internal pressure Pint of solid sodium vary almost linearly with pressure. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT from the modified Holzapfel EOS are observed to be linear with respect to V−2 with temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity EOS. In addition, analytical expressions of the thermodynamic properties of solid sodium are derived from the linear isothermal regularity EOS, such as internal energy, entropy, enthalpy, free energy, and heat capacity.