22 - Thermodynamics of convection

Summary

Preamble

We have a good measure of the rate of heat loss from the solid Earth to the atmosphere and oceans, 44.2 × 10¹² W (Pollack et al. 1993). Although the final stage is observed as conduction through the crust and hydrothermal circulation of sea water through young ocean floor, most of the heat comes from the deep interior. Thermal diffusion in a body the size of the Earth is too slow to have cooled the lower mantle noticeably in its lifetime. The deep heat is transported upwards by hot material, driven by the buoyancy of its thermal dilation relative to the cooler material that sinks to replace it. The global scale motion is evident at the surface as tectonic activity, including continental drift and earthquakes, with volcanism as a side effect. Chapter 13 considers the stresses involved in this process and relates them to the mechanical energy derived from convection. The calculation of the energy is presented in this chapter. It is an application of classical thermodynamics.

The mechanical power of convection is the product of heat transport and a thermodynamic efficiency that we can calculate in two ways. First, we recognize that the mantle is a heat engine in the classical thermodynamic sense and that we can apply the Carnot theorem to derive the mechanical power of convection without an explicit consideration of the forces involved.