Convecting Mantle as a Thermodynamic Engine

Abstract

THE geothermal flux amounts to about 10²⁸ ergs year⁻¹ for the whole Earth and this figure is sufficiently small to act as an important constraint on theories of convection in the mantle. A world-wide system of thermal convection must involve a very efficient conversion of heat to mechanical energy (and back to heat); by imposing a limit to the efficiency we specify a strength which cannot be exceeded in the convecting part of the mantle^1,2. A consideration of earthquake energies is useful in this connexion. The largest shocks release elastic strain energy of about 10²⁵ ergs and the annual release by all earthquakes is about 10²⁶ ergs; that is, 1 per cent of the geothermal flux appears as seismic energy. If earthquakes are merely irregularities in mantle convection the seismic energy cannot be more than a fraction of that released in gradual creep processes and we must contemplate an overall efficiency of order 10 per cent for the conversion of thermal to mechanical energy. The earthquake energies could be overestimates, but a similar figure for efficiency is obtained from a consideration of the strength of the mantle.