Lectures on mineral physics part 1: thermodynamic properties

Abstract

This article explores mineral properties from a thermodynamic perspective, specifically, specific heats, bulk modulus, and Grüneisen parameters. When heat is introduced into a body, it can be stored in the body as internal energy. If the subsequent temperature rise leads to an expansion of volume under pressure, some of this heat can be converted into mechanical energy through work. The combination of these energies is referred to as enthalpy. Specific heat signifies the rate of temperature elevation resulting from heat in a unit amount of material. The isobaric and isochoric specific heats hold relevance in scenarios with or without thermal expansion, respectively, representing enthalpy and internal energy changes. Their relationship is expressed through easily measurable properties. The isobaric specific heat is greater than the isochoric counterpart, with the latter being more fundamental. The article further defines the adiabatic and isothermal bulk moduli, offering a relationship based on easily measurable properties. The ratios between the isobaric and isochoric specific heat and between the adiabatic and isothermal bulk moduli are identical and equal to one plus the product of thermal expansivity, the thermodynamic Grüneisen parameter, and temperature. The isothermal bulk modulus is more fundamental than the adiabatic. The Grüneisen parameter denotes the rate of pressure increase with respect to the increase in internal energy density. The thermodynamic Grüneisen parameter is identical to the Grüneisen parameter. The article provides experimental values of these parameters for various minerals, including forsterite, fayalite, spinel, grossular, pyrope, periclase, corundum, halite, and sylvite. Finally, the adiabatic temperature gradient is deduced and applied to the Earth as the adiabatic geotherm.