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1. Steam power plant (a) The boiler of a power plant operates at a maximum temperature...

1. Steam power plant
(a) The boiler of a power plant operates at a maximum temperature of 750oC. The condenser of the
power plant draws in cooling water at 20oC. What is the theoretical maximum efficiency of the plant?
(b) Now suppose that a real power plant is built to have an efficiency that is 80% of the theoretical efficiency. The power plant needs to generate 1GW (giga-watt) of power. How much energy (per second) needs to be supplied by the boiler? How much energy needs to be removed by the cooling water?
(c) If the boiler burns coal that comes from Central Appalachia that has a heating value of 12500 BTU/lbm, how much coal (in kg) is needed for one day?
(d) Coal enters the power plant by a coal train that is composed for coal cars that can each hold 120 tons of coal. How many cars are needed for the power plant in a day? If one train can haul 100 coal cars, how many trains will need to ply to this power plant in a week?
(e) The density of coal from Central Appalachia is around 55 lb/ft3. Determine how much volume of coal would be needed to run the plant for a week? Coal mining is done by mountain top removal. There are plenty of videos and websites talking about this process. Think through what this means for a mountain? i.e. how much of a mountain is removed? How much material that is not useful coal (such as rock, dirt etc.) would have to be removed?
(f) The current cost of coal from Central Appalachia is around $53.00 per short ton where 1 short ton = 907 kg. How much does the power plant spend in coal per month?
(g) The cost of electricity from coal is about $50/MWh where MWh stands for megawatt-hour. Use the definition of kilowatt-hour. What fraction of the cost the cost of electricity is the fuel cost?
(h) The boiler operates at a pressure of 60 bar (i.e. 60 atm) and has a maximum temperature of 750oC. Water enters the boiler at 80oC. (Use steam tables or use online calculators). Determine the amount of heat required for producing 1 kg of steam. How much water would be needed per second? (Use the answer from Problem 1b).

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