(a) The observed geothermal output of the Earth is 4.2 1013 W (= 42 TW). Much...

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(a) The observed geothermal output of the Earth is 4.2 1013 W (= 42 TW). Much of this heat escapes at the mid-ocean ridges, but the average continental heat flux is Fe 65 mW/m, as mentioned in class. For normal heat conduction through the Earth's crust, we can write this flux as = dT Fe = -K " dz where K is the crustal material's thermal conductivity and dT/dz is the vertical tem- perature gradient. Assuming an average conductivity for the continental crust of K = 3.0 W/m/K, estimate the average value of dT/dz, in degrees Kelvin per km. (c) At what depth under the continents should the temperature reach the melting point of granite, or 1200 C? This is the approximate thickness of the continental lithosphere, Below this is the aesthenosphere, a layer of partial melting and quasi-fluid behavior where the rigid tectonic surface plates may be thought to 'slide'. (a) The observed geothermal output of the Earth is 4.2 1013 W (= 42 TW). Much of this heat escapes at the mid-ocean ridges, but the average continental heat flux is Fe 65 mW/m, as mentioned in class. For normal heat conduction through the Earth's crust, we can write this flux as = dT Fe = -K " dz where K is the crustal material's thermal conductivity and dT/dz is the vertical tem- perature gradient. Assuming an average conductivity for the continental crust of K = 3.0 W/m/K, estimate the average value of dT/dz, in degrees Kelvin per km. (c) At what depth under the continents should the temperature reach the melting point of granite, or 1200 C? This is the approximate thickness of the continental lithosphere, Below this is the aesthenosphere, a layer of partial melting and quasi-fluid behavior where the rigid tectonic surface plates may be thought to 'slide'.