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.
Highlights
In a series of works, some simple linear regularities were derived from experimental data in dense liquids.1–3 According to a linear isotherm regularity equation of state (EOS) by Parsafar and Mason,1 (Z − 1)V2 is linear in V−2 for 13 fluids, where ZPV RT is the compressibility factor,V is the molar volume, P is the pressure, R is the gas constant, andT is the temperature
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 − 1)V2 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 with pressure
By substituting Eqs. (6) and (7) into the linear isotherm regularity EOS of Eq (5), we can calculate the approximated values of the compressibility factor Z′ as a function of pressure, and so the calculated pressure range of the linear regularity along each isotherm in this work is determined by the absolute value of the relative error between Z′ and Z by Eq (1), which is smaller than 1%
Summary
In a series of works, some simple linear regularities were derived from experimental data in dense liquids. According to a linear isotherm regularity EOS by Parsafar and Mason, (Z − 1)V2 is linear in V−2 for 13 fluids, where Z. The reason for the crucial importance of the V term in some solids is suggested to be related to the contributions from the repulsive and attractive forces among molecules Based on these linear regularities, several new equation of states have been developed which could predict PVT data with high accuracy. Many thermodynamic quantities of solid sodium can be calculated by using the derived analytical expression of the reliable EOS along the isotherms, such as isobaric thermal expansion coefficient, adiabatic bulk modulus, and isochoric heat capacity, except the isobaric heat capacity, heat capacity ratio, and Grüneisen parameter. Our purpose here is to find new regularities from predicted properties by the modified form of Holzapfel EOS, such as isobaric thermal expansion coefficient, adiabatic bulk modulus, isochoric heat capacity, isobaric heat capacity, heat capacity ratio, and Grüneisen parameter. We find new linear isotherm regularities from the available thermodynamic data, and several other regularities are reported
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