Universal Equation of States are Derived from the Isothermal Relationships of Elastic Solids

Universal P-V-T equations of states are derived from the original isothermal expressions of Birch-Murnaghan and the Vinet EoSs by using absolute reference frame and incorporating the temperature dependence of the parameters. The equations are tested against the experiments of perovskite [MgSiO3] and periclase [MgO]. The determined parameters of the EoSs are valid throughout the entire pressure and temperature ranges, which cover 0-142 GPa and 293-3000 K and 0-109 GPa and 293-2199 K for periclase and perovskite respectively. The root-mean-square (RMS) misfits of the universal Birch-Murnaghan EoS are 0.73 and 0.33 GPa and the misfit of the Vinet EoS are 0.74 and 0.32 GPa for perovskite and periclase respectively.