The entropy based contribution to bulk modulus: A thermodynamic analysis

It is suggested that bulk modulus at any finite temperature can be split into two fundamental contributions, viz., the one arising from internal energy or enthalpy effects and the rest from the effect of entropy. A rigorous thermodynamic analysis of the latter quantity, namely the entropy-based contribution to bulk modulus is presented in this study. In particular, it is shown that this contribution governs the intrinsic or pure thermal sensitivity of bulk modulus and can be negative, positive or even zero depending upon the relative magnitudes of the pressure derivative of bulk modulus and the isothermal Anderson–Grüneisen parameter. It is also identified that this entropy-based contribution is related to the thermal pressure, and hence is expected to play a significant role in deciding the overall temperature sensitivity of bulk modulus at high temperature. A few simple approximations are suggested for estimating this quantity in terms of readily available thermal property data. In addition, an illustrative calculation is presented for MgO.