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EGEE 101H, Homework #2 –
Unit Conversions and Efficiency February 12, 2013 Due on Tuesday, February 19 by electronic submission to the HW2 drop box, by 11:59 p.m. 1.
Assume that you have graduated from Penn State, found a good job and secured a low-
interest mortgage loan to build your dream house in Pittsburgh. You need a heating system which would provide 125,000,000 Btu of heat per year during the heating season. Below are some options with fuel costs. Which option would you choose, if you want to minimize your energy bill? Calculate the total fuel cost of each option to support your decision. Tabulate your results using the table below. 30 pts
a) burn coal: Heating Value: 25,000,000 Btu/ton, Heating Efficiency: 0.55, Cost: $65 per ton. (125,000,000Btu)* (1Ton/25,000,000Btu)*($65/1Ton)= TC of using coal if 100% efficient $325= TC of using coal if 100% efficient $325*(1/.55)= Actual cost of heating your house with coal $590.91= Actual cost of heating your house with coal b) burn fuel oil Heating value: 140,000 Btu/gallon, Heating Efficiency: 0.65, Cost: $4 per gallon. (125,000,000Btu)*(1Gallon/140,000 Btu)*($4/1 Gallon)= TC of using fuel oil if 100% efficient $3571.43= TC of using fuel oil if 100% efficient $3571.43*(1/.65)= Actual cost of heating your house with fuel oil $5494.51= Actual cost of heating your house with fuel oil c) burn natural gas: Heating Value: 1,000 Btu/cu ft, Heating Efficiency: 0.80, Cost: $2.5/1,000 cu ft. (125,000,000Btu)*(1cu ft/1000Btu)*($2.5/1000cu ft)= TC of using natural gas if 100% efficient $312.5=TC of using natural gas if 100% efficient $312.5*(1/.8)= Actual cost of heating your house with natural gas $390.63= Actual cost of heating your house with natural gas c) Again Burn natural gas at an updated price http://www.eia.gov/dnav/ng/hist/n3010us3m.htm Heating Value: 1,000 Btu/cu ft, Heating Efficiency: 0.80, Cost: $9.97/1,000 cu ft. (125,000,000Btu)*(1cu ft/1000btu)*($9.97/1000cu ft)= TC of using natural gas if 100% efficient TC of using natural gas if 100% efficient =$1246 1246*(1/.8)= Actual cost of heating your house with natural gas $1557.5= Actual cost of heating your house with natural gas
d) use electricity: Conversion Factor: 1 kWh = 3412 Btu, Heating Efficiency: 1.0, Cost: $90/1,000 kWh (125,000,000Btu)*(1kWh/3412)*($90/1000kWh)= AC of heating your house with electricity $3297.19 = Actual Cost of heating your house with electricity System Amount of Fuel Unit Cost Total Cost, $ Coal Stove 9.09 tons $65/ton $590.91 Oil Furnace 1373.63 gallons $4/gallon $5494.51 Gas Furnace 156.252 x1,000 cu ft $2.5 or 9.97 /1,000 cu ft $390.63 or $1557.5 Electric Heat 36.636x1,000 kWh $90/1,000 kWh $3297.19 Note
: Don't forget to include heating efficiencies in your calculations. Remember, when you include efficiency, you will need more heat from the fuels (as input) than the required output (i.e., 125,000,000 Btu). I would choose to heat my house with Natural Gas (if I could get it at 2.5/1,000 cu ft, but not at 9.97/1,000 cu ft) or Coal because it is the least expensive option for my energy needs. 7.5 pts
for each correct answer.
2. What is the heating efficiency of an electric water heater, if you spend 0.11 kilowatt-
hour of electric energy to heat 2 lb. of water from 77 to 212 °F? (Hint: Remember the definition of Btu and 1 kWh = 3412 Btu.) 20 pts
Btu is the amount of energy needed to heat one pound of water by one degree Fahrenheit. (212-77)*2= Total Btu required to heat the water 270= Total Btu required to heat the water .11kWh(3412.14163Btu/1kWh)= total Btus used by the water heater 375.34= total Btus used by the water heater 270/375.34= Heating efficiency .7194= Heating efficiency 3. An inventor claims that he has developed a wonderful new heat engine that operates with a relatively cool flame at 150 °C and discharges waste heat to the environment at 20 °C. His promotional literature advertises that the first law efficiency of his device is 45%. Would you believe him? (Hint: Calculate the maximum efficiency possible for the engine and compare it with the claimed efficiency.) 20 pts *Temperature must be in kelvin*
1-(TC/TH)= Maximum Efficiency of the engine 1-(293.15/423.1500= Maximum Efficiency of the engine .307= Maximum Efficiency of the engine I would not believe him because the maximum efficiency of his machine, based on the specifications he provided, could only be .307, not .45. 4.
West Campus Steam Plant produces steam for heating and cogenerates electricity. The average heating value of the coal used in the plant is 13, 618 Btu/lb and its average sulfur content is 1.28%wt. Natural gas with a heating value of 1,030 Btu/cu ft and negligibly small sulfur content is also burned at the plant. Last year 65,206 tons of coal and 83,669,000 cubic feet of natural gas were burned to produce steam and generate electricity. a) Calculate the amount of SO
2
which were released to the atmosphere last year (1 ton of sulfur in the coal produces 2 tons of sulfur dioxide upon combustion.) 65,206tons *(.0128)= Tons Sulfur burned 834.63= Tons Sulfur burned 834.63*2= Tons Sulfur dioxide released 1669.27= Tons Sulfur dioxide released b) Would this plant be in compliance with the EPA limit if it burned coal only (i.e., maximum allowable emission =1.2 lb SO
2
per million Btu supplied by the coal)? Show your calculations. (Hint: Calculate first how much coal you need to burn to supply one million Btu. ) 1000000Btu*(1lb/13, 618Btu)=Pounds of Coal needed to produce a million BTU 73.43= Pounds of Coal needed to produce a million BTU 73.43*(.0128)=Pounds of Sulfur Burned within the coal .94=Pounds of Sulfur Burned within the coal .94*2= Pounds of SO2 released by burning 1000000 BTU of coal 1.89= Pounds of SO2 released by burning 1000000 BTU of coal No, the plant would not be in compliance with the EPA limit because it would release 1.89 pounds of SO2 per 1000000BTU supplied by coal. c) Calculate the amount of CO
2
(in tons) emitted to the atmosphere only from the coal
burned in the West Campus Steam Plant last year
(Coal contains 85% wt carbon. Assume that
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all the carbon in coal is converted to CO
2
by combustion. One ton of carbon produces 3.67 tons of CO
2
upon combustion. 30 pts
(65,206) *(.85)= Tons of Carbon in the Coal used last year 55425.1= Tons of Carbon in the Coal used last year 55425.1*(3.67)=Tons of CO2 produced by burning the Coal 203410.117= Tons of CO2 produced by burning the Coal
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