A stable continental province has radiogenic heat production decaying exponentially…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth

Problem

A stable continental province has radiogenic heat production decaying exponentially with depth,

A_{\rm rad}(z) = A_0 e^{-z/h_r}

, with

A_0 = 2.0\,\mathrm{\mu W\,m^{-3}}

and e-folding depth

h_r = 8\,\mathrm{km}

. Its reduced heat flow (the flux entering the base of the radiogenic layer) is

q_r = 32\,\mathrm{mW\,m^{-2}}

, the thermal conductivity is uniform at

k = 2.5\,\mathrm{W\,m^{-1}\,K^{-1}}

, and the surface temperature is

T_0 = 5\,{}^{\circ}\mathrm{C}

. The Moho is at

40\,\mathrm{km}

depth. Assume steady, purely conductive, one-dimensional heat flow. ((a)) Find the surface heat flow

q_0

. ((b)) Find the temperature at the Moho.

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