You are designing a Rankine heat engine which must produce 10,000 kJ/min of NET shaft work. The heat source is at T = 200°C and the low-temperature reservoir at T= 25°C. The turbine efficiency is 75%, and there are no restrictions on the temperature, pressure, or quality of the water leaving the turbine. Your job is to design the most cost-effective Rankine engine possible. The boiler can be designed to operate at T = 190°C, T = 185°C, or T = 180°C, and the condenser can be designed to operate at T = 35°C or T = 40°C. Costs of these heat exchangers can be determined from the formulas in the table on the right. Notice that the cost of the heat exchanger goes up as the heat duty goes up, and goes down as the ΔT between the heat reservoir and the fluid increases.

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Operating Temp (°C) Formula 180 C = 10000+ 0 185 C = 12000+ 1.50 190 C = 15000+ 20 35 C = 10000+ 1.50 40 C=7000+ O In all formulas, C represents the cost in dollars and Q represents the absolute value of the heat transferred in that exchanger in kJ/min. Exchanger Boiler Boiler Boiler Condenser Condenser The cost of the heat added to the boiler is $15/GJ. The heat removed in the condenser has neither cost nor value. Assume that the heat engine will be oper- ating 24 hours per day, 350 days per year. A. For each of the six possible Rankine cycles, de- termine QQ, the cost of the two heat exchang- ers, and the yearly cost of the heat. B. Recommend which variation of the Rankine heat engine should be used if it's expected to be in service for 5 years.