If we take M = 5.97×1024 kg, the mass of the Earth, and Q = 4.43×1013 W, we find H = 7.42 × 10−12 W kg−1. However, on the basis of geochemical studies, we can argue that the core cannot contain a significant fraction of the heat-producing elements. In this case, the mass in Equation (4–5) should be the mass of the mantle, M = 4.0×1024 kg and H = 11.1×10−12 W kg−1. A further reduction must be made in the value of H appropriate to the mantle because a substantial fraction of the heat lost from the ontinents
Heat Generation by the Decay of Radioactive Elements 245 originates in the highly concentrated radioactive isotopes of the continental crust. Although the mean continental heat flux of 65 mW m−2 is known with some certainty, we are uncertain as to the fraction that can be attributed tothe heat producing elements. Based on estimates of the mean concentrations of these elements in the continental crust, we attribute 37 mW m−2 to the heat-producing elements. The remaining 28 mW m−2 is attributed to basal heating of the continental lithosphere by mantle convection. This heat is then conducted through the mantle portion of the continental lithosphere to the base of the continental crust. Radiogenic heat production in the continental crust corresponds to a total heat flow of 7.4 × 1012 W, or 17% of the total
surface heat flow. Reduction of the mantle heat production by this amount gives H = 9.22 × 10−12 W kg−1.
A further correction to the radiogenic heat production in the mantle must be made because of the secular cooling of the Earth. Only a fraction of the present-day surface heat flow can be attributed to the decay of radioactive isotopes presently in the mantle. Because the radioactive isotopes decay into stable isotopes, heat production due to radioactive decay is decreasing with time. For example, we will show that the heat production 3 billion years ago was about twice as great as it is today. Since less heat is being generated in the Earth through time, less heat is also being convected to the surface. Thus, the vigor of the mantle convection system is decreasing with the age of the Earth. Because the strength of convection is dependent on viscosity and the viscosity of the mantle is a sensitive function of its temperature, a decrease in the heat flux with time leads to a decrease in the mean mantle temperature. This cooling of the Earth in turn contributes to the surface heat flow. We will consider this problem in some detail in Section 7–8 and conclude that about 80% of the present-day surface heat flow can be attributed to the decay of radioactive isotopes presently in the Earth and about 20% comes from the cooling of the Earth. We can thus reduce the present-day mantle heat production accordingly so that our preferred value is H = 7.38 × 10−12 W kg−1.