2. Steam power plant

1. (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?

2. (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?

3. (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?

4. (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?

5. (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?

6. (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?

7. (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?

8. (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 2b).

9. (i) The convective heat transfer coefficients in the furnace and inside the tubes containing the water can be assumed to be 500W/m2K. Ignore the conduction through the tubes and ignoring radia- tion, assuming that the mean temperature of the gases in the furnace is 800oC while the average temperature of the water/steam in the tubes is around 400oC, determine the surface area needed to effect the heat transfer. If the tubes have a diameter of 2 cm, what is the minimum length of tubing required?

10. (j) Keeping the same convective heat transfer coefficients and ignoring radiation again, determine the temperature of the wall of the tube. Note that since we are ignoring conduction through the tube wall, the inner and outer walls of the tube are at the same temperature.

11. (k) Write the equations for Problem 2i that accounts for the radiation between the furnace and the outer wall of the tube, assuming emissivity of 0.9. Note that this time, you can’t easily solve. You have to do trial and error type solutions. Try to find a solution starting from the value that you obtain from Problem 2j.

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(l) Steam exits the turbine in the power plant and enters the condenser at a pressure of 0.5 bar (this is below atmospheric) and at temperature of 81oC. This is the boiling point of water at this pressure. The steam condenses and the condensate water maintains the temperature of 81oC. Determine the amount of heat released by 1 kg of steam. If cooling water enters the condenser at 20oC and leaves the condenser at 50oC, determine the minimum amount of cooling water required. You need your values from Problem 2b

13. (m) Assuming a convective heat transfer of 400W/m2K on both the inside and outside of the condenser tubes, and assume an average outside temperature of 81oC and the average temperature of the water inside of the tube is 35oC, determine the minimum length of tubing of 1cm diameter needed. Neglect effects of conduction through the tube wall.

14. (n) The cooling water is drawn from a river on whose banks the power plant is located. The flow rate of the river is 100,000 cu.ft/s and has a water temperature of 20oC. If the cooling water after the condenser at 50oC is returned to the river(called once through cooling), determine the temperature increase in the water after the cooling water mixes with the rest of the water in the river. Discharging cooling water directly to a water body is a common source of thermal pollution. Read up on this online.

15. (o) If 30% of the electricity generated is consumed by the residential sector (i.e. homes) while the remainder is consumed by industry and commercial enterprises, determine the number of house- holds that the power plant can support if an average American household consumes 10,840 kWh of electricity per year. What sort of county or city would this power plant be able to supply electricity with?

16. (p) The burning of coal from the Central Appalachia region produces about 205 pounds of carbon dioxide for every million BTUs of energy burned by coal. Determine the amount of carbon dioxide in metric tons that is generated by this power plant. Another significant pollutant that can be released by burning coal is sulfur dioxide. If 1 kg of sulfur converts to 2 kg of sulfur dioxide and the coal contains 0.8% sulfur by weight, determine the amount of sulfur dioxide in metric tons that is released from this power plant.