Final answer:
The unit cost of the electricity produced by the turbine is approximately $0.0706 per kWh, calculated using the annual work output, the exergy cost of the steam input, the operational costs, and the exergetic efficiency of the turbine.
Step-by-step explanation:
To calculate the unit cost of the power developed by the turbine, we need to use the cost balance in rate form, which relates the cost of inputs to the cost of outputs for a system at steady state. The turbine produces 18 x 107 kW annually operating 8000 hours a year. With an annual operating cost of $5 x 105 and the steam valued at $0.02 per kWh of exergy, we can determine the unit cost of electricity.
First, we calculate the total annual work output: 18 x 107 kW * 8000 h = 1.44 x 1011 kWh. The steam's specific flow exergy is 1500 kJ/kg, and we need to convert this to kWh: (1500 kJ/kg) / (3600 kJ/kWh) = 0.4167 kWh/kg. The mass flow rate is given as 2420 kg/min, which we convert to an hourly rate: 2420 kg/min * 60 min/h = 145,200 kg/h.
Then we calculate the exergy flow rate: 0.4167 kWh/kg * 145,200 kg/h = 60,469.2 kWh/h. Given 8000 operating hours, the annual exergy input is 60,469.2 kWh/h * 8000 h = 4.837 x 108 kWh. The exergetic efficiency is 85%, so the exergy used for work is 0.85 * 4.837 x 108 kWh = 4.111 x 108 kWh.
Now we can calculate the costs. The annual exergy cost: (4.837 x 108 kWh) * ($0.02/kWh) = $9.674 x 106. Adding the operating cost, we have a total annual cost of $9.674 x 106 + $5 x 105 = $1.0174 x 107. Dividing by the total annual work output gives the unit cost of electricity: ($1.0174 x 107) / (1.44 x 1011 kWh) = $0.0706/kWh.