Question

12. Consider a proposal to extract heat directly from the Earth's core by drilling a cylindrical shaft of radius 1 m and depth 100 km through the earth's mantle and filling it with copper Estimate the power output assuming the temperature difference is 1,000 °C and the thermal conductivity is 3.5 x 102 W/m °c

Answer 1

When copper is filled into the cylindrical shaft, due to temperature difference thermal conduction takes places. Given temperature difference angle t = 1000 degree c Length of copper rod = 100 km = 10^5 m coefficient of thermal conductivity (k) = 3.5 times 10^2 Area of cross - section (A) = pi r^2 = 22/7 times 1^2 = 3.14 m^2 The rate at which heat conduction takes place from hot - inner end of copper rod is, dQ/dt = kA (angle t)/l = 3.5 times 10^2 times 3.14 times 10^3/100 times 10^3 = 10.99 TildeEqual 11 W Therefore dQ/dt = 11 Js^-1