On the thermal gradient in the Earth's deep interior

Abstract

Temperature variations in large portions of the mantle are mainly controlled by the reversible and irreversible transformation of mechanical energy related to pressure and viscous forces into internal energy along with diffusion of heat and chemical reactions. The simplest approach to determine the temperature gradient is to assume that the dynamic process involved is adiabatic and reversible, which means that entropy remains constant in the system. However, heat conduction and viscous dissipation during dynamic processes effectively create entropy. The adiabatic and non-adiabatic temperature variation under the influence of a constant or varying gravitational field are discussed in this study from the perspective of the Joule-Thomson (JT) throttling system in relation to the transport equation for change of entropy. The JT model describes a dynamic irreversible process in which entropy in the system increases but enthalpy remains constant (at least in an equipotential gravitational field). A comparison is made between the thermal gradient from the JT model and the thermal gradient from two models, a mantle convection and a plume geodynamic model, coupled with thermodynamics including a complete description of the entropy variation. The results show that the difference is relatively small and suggests that thermal structure of the asthenospheric mantle can be well approximated by an isenthalpic model when the formulation includes the effect of the gravitational field. For non-dynamic or parameterized mantle dynamic studies, the JT formulation provides a better description of the thermal gradient than the classic isentropic formulation.