A very large mass M of porous hot rock is to be utilized to generate electricity by injecting water and utilizing the resulting hot steam to drive a turbine. As a result of heat extraction, the temperature of the rock drops, according to dQh = – MCdTh, where C is the specific heat of the rock, assumed to be temperature independent. If the plant operates at the Carnot limit, calculate the total amount W of electrical energy extractable from the rock, if the temperature of the rock was initially Th = Tf. Assume that the lower reservoir temperature Tl stays constant.
At the end of the calculation, give a numerical value, in kWh, for M = 1214 kg (about 30 km3),
C = 1 Jg-1 K-1, Tj = 600 C. Tf = 110 C, Tl = 20C,
Watch the units and explain all steps! For comparison: The total electricity produced in the world in 1976 was between 1 and 2 times 1014 kWh.