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Pennsylvania State University *

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101H

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Mechanical Engineering

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Apr 3, 2024

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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*
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