Energy, heat and temperature Olivia Jensen – 13/10/11... for 666 Module 2

Since the work of Lord Kelvin (William Thompson), we have recognized that the Earth's interior is hot and cooling. Wildly assuming a starting temperature, he calculated that the Earth would have to have been leaking heat at its present and greater past rate for at least 100 million years.

Global distribution of heat flow Rate: 44.2 TW

A chondritic Earth should contain enough U, Th and K to account for much of the heat flow from the surface. Fe32.0 % O29.7 Si16.1 Mg15.4 Ca, Al, Na 3.5 K160 ppm ( K) Th0.055 U0.015 McDonough, %

Bulk Earth Silicate Earth (70.6%) McDonough, 2003 ? ?

Another estimate of concentrations of radiogenic isotopes: heat production in the mantle Note much higher concentrations than McDonough's models

Temperature and pressure within Earth Mao and Hemley, 2007

Adiabatic compression Consider a cube of mantle material under pressure

Mantle temperature?

The 660km spinel-perovskite transition The negative Clapyron slope shows an endothermic effect as the mantle rises through the 660km transition. The absorbed heat contributes a slight cooling and relative density increase that retards convection. The effect reverses for a descending lithospheric plate or slab. adiabat

D'' – postperovskite transition?  Recently, it has been determined that the perovskite mineral phase of [Mg, Fe]SiO 3 compresses into a denser postperovskite phase (same stoichiometry?) at about 120GPa pressure and 2500K temperature.  This condition is interpreted to be the cause of the seismic, velocity-slowing anomaly of the D'' layer.  This is not entirely out-of-line with our adiabatic temperature estimate; we don't have tight measures of thermal expansivity, α p, and heat capacity, C p, throughout the mantle. The missing ingredient: Kie Hirose

Heat conduction through D''  The D'' layer is between 100 and 200 km thick.  It's area is about ¼ that of the Earth's surface area.  The heat flow from the core into the mantle is variously estimated* to be ~9 TW. The heat flux, then, is about 40 mW m -2.  If the thermal conductivity is similar to that of the lithosphere, ~4 W m -2 K -1, the temperature gradient through the D'' layer takes us to a temperature of K. *See Don Anderson: Energetics of the Earth

Temperature and pressure within Earth Mao and Hemley, 2007

Seismotectonics estimated that earthquakes release (use) about 5 x J per year. The theoretical limit of the annual energy available from the convective heat engine is about 5.4 x J per year. The work “done” by earthquakes accounts for only about 0.1% of the annual energy available to the convection engine. What else?...possibly feeding biology to build and drive geology. Moving masses laterally across the geoid requires no work apart from the resistance or friction of the motions. On long time scales, we believe that the topography of the Earth is approximately stable: uplift and erosion are in balance. The energy required to uplift the topography must somehow be provided by the convection engine. Kanimori (1977)

Seismotectonics The heat engine that is expressed in mantle convection works on the body and surface of the Earth. It is not an especially thermodynamically “efficient”: its theoretically limiting efficiency is determined by the temperature differences at the bottom and top of the circulating mantle. We might expect, then, that the convection engine could accomplish “work” at the rate of about 17TW. This is a tremendous power to move and uplift continents, spread ocean basins, lift mountain-building magmas above the surface and fracture surface rocks in earthquakes.