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The behavior of thermal parameters pressure (P) and thermoelastic parameters i.e. Isothermal bulk modulus (K_T), its pressure derivative (K'T) and Thermal expansivity (α) has been analyzed for Na-majorite and knorringite-majorite systems at different compressions down to a maximum value of 0.3 for temperature ranges from 300 K to 1500 K. The pressure dependent compressibility of these garnets have been studied. The comprehensive study of thermodynamic and thermoelastic behavior at different isotherms and isobars respectively has been achieved by employing both Vinet equation of state and Anderson-Isaak equation. The study of thermal expansivity (α) using Anderson-Isaak and Stacy-Davis approach shows a similar trend of MgO system. Based on the validation of Kumar's approach, the lattice parameter of garnet system is computed using Kumar and modified Kumar's approach at high temperature and is found to be very less deviated from the value of lattice parameter at room temperature.

The thermodynamic parameters of MgSiO3-MgO system have been calculated by employing the modified Shanker equation of state (EOS) named “Higher Order Shanker (HOS) EOS ”. The modification is based on the inclusion of higher order terms in Shanker EOS. The Higher Order Shanker (HOS) EOS has been assessed for consistency with Stacey criteria for the variation of the pressure dependence of isothermal bulk modulus. The comparative analysis of the thermodynamic properties obtained from Higher Order Shanker (HOS) EOS with existing classical EOS such as the Birch-Murnagham, the Shanker, the Vinet, the Stacey, and electronic contribution analysis demonstrate that the proposed Higher Order Shanker (HOS) EOS is reliable EOS for computing thermodynamic properties of similar systems at higher pressures. Expressions for the bulk modulus and its pressure derivatives have been derived and reduced to the limit of infinite pressure. The expression thus obtained are useful for further analysis of higher derivatives thermoelastic properties.