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. $\left(Z-1\right)V^2$ 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 B_T and internal pressure P_int of solid sodium vary almost linearly with pressure. Both the calculated reduced isothermal bulk modulus $B^{*}=\frac{B_{T}V}{RT}$ and the parameter $Z_{int}=\frac{P_{int}V}{RT}$ 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.

中文翻译：

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固体钠在压力下的线性等温规律

我们从可用的实验数据和沿等温线计算的热力学性质，以及修饰的Holzapfel形式的状态方程（EOS），提出了固体钠的几个新规律。 $\left(ž-\mathrm{1个}\right)V^2$是在考虑的压力范围内高温下等温线具有不同交点的V ²的线性函数，其中Z和V是可压缩系数和摩尔体积。固体钠的计算的等温体积模量B _T和内部压力P _int几乎随压力线性变化。两者计算出的降低的等温体积模量${乙}^{*}=\frac{{乙}_{Ť}V}{\mathrm{[R}Ť}$ 和参数 ${ž}_{\mathrm{一世}ñŤ}=\frac{P_{\mathrm{一世}ñŤ}V}{\mathrm{[R}Ť}$观察到，来自改进的Holzapfel EOS的EOS相对于V ^-2在温度T和气体常数R下是线性的，这一点已通过从推导的线性等温规律性EOS得出的解析表达式进行了验证。此外，固体钠的热力学性质的分析表达式是从线性等温规律性EOS得出的，例如内部能量，熵，焓，自由能和热容量。