A hospital in a developing country is considering replacing their separate heating and power systems with a combined heat and power system (CHP). (a) In the existing set-up, 1 MW of electricity is supplied by a coal-fired plant that runs on the Rankine cycle. The coal-fired plant has a thermal efficiency of 36%. What is the rate of coal consumption, assuming bituminous coal with HV = 32,500 kJ/kg? (b) In the existing set-up, a furnace that burns diesel fuel is used to generate heat at a rate of 240 kW for use in the heating the hospital and for sterilization of medical equipment. What is the efficiency of the boiler if diesel is consumed by the boiler at a rate of 27 kg/hour? (HV diesel = 42,934 kJ/kg) (c) What is the total rate of energy consumed by the existing setup? (d) What is the total thermal efficiency of the existing (Rankine + boiler) setup, where both the useful power and heat are considered and their respective energy carriers? (e) The proposed CHP replacement plant is projected to achieve an efficiency of 75% and will be powered by natural gas. Assuming the same amount of electricity and heat is to