a) A cube of "hot rock" of side "h" has its top surface at a depth "d" below the Earth's surface. The rock has a density "p" and specific heat capacity "c". The material above the cube has thermal conductivity "k". If the rock is treated as an isothermal mass at temperature T above the Earth's surface with no internal heat source, show that the time constant for cooling is given by: phed k b) Calculate t for a cubic mass of granite (of side 10 km, density 2.7 x 10** kg/m", specific heat capacity 0.82 x 103 J kg"K"), positioned 10 km below ground under layer material of thermal conductivity 0.40 Jmlski c) Compare the natural conductive loss of heat from the granite with commercial extraction at 100 MW from the whole source