A very large mass M of hot porous rock equal to 10¹² kg is to be utilized to generate electricity by injecting water and using the resulting hot steam to drive a turbine. As a result of heat extraction, the temperature of the rock drops according to Q̇ = −MC_P dT /dt, where C_P is the specific heat of the rock which is assumed to be independent of temperature. If the plant produces 1.36 × 10⁹ kW hr of energy per year, and only 25 percent of the heat extracted from the rock can be converted to work, how long will it take for the temperature of the rock to drop from 600^◦C to 110°C? Assume that for the rock C_P = 1 J/(g K).