Earth’s Radius

One of the estimates for the age of the Earth given by Lord Kelvin in the 1860s assumed that Earth was initially molten at a constant tem- perature Tm and that it subsequently cooled by con- duction with a constant surface temperature T0. The age of the Earth could then be determined from the present surface thermal gradient (dT/dy)0. Re- produce Kelvin’s result assuming Tm − T0 = 1700 K, c=1 kJ kg−1 K−1, L =400 kJ kg−1, κ =1 mm2 s−1, and (dT/dy)0 = 25 K km−1 . In addition, determine the thickness of the solidified lithosphere. Note: Since the solidified layer is thin compared with the Earth’s radius, the curvature of the surface may be neglected.