b. The HECO cost of electricity is about 27 cents per kwh. At that rate, what are your electricity costs for the year to run these devices?

Transcription

1 OCN 120 Spring 2011 Name: Problem Set #2, Power and energy calculations Due Thursday, Feb a. Using Table 14.2, attached, calculate your annual energy consumption in Kilowatt hours (kwh) due to your personal use of computers, stereo/radio, TV, and DVD/video players. b. The HECO cost of electricity is about 27 cents per kwh. At that rate, what are your electricity costs for the year to run these devices? c. Using Table 3.3, attached, how much oil would need to be burned to supply the electricity for these devices? 2. The average human diet has an energy content of about 2000 kcal. Using the energy and power definitions in Table 3.1, attached, show through a series of unit conversions that this 2000 kcal/day is about equivalent to 100 watts. 3. Power output of engines is often rated in terms of horsepower (hp). You can also calculate power output if you know the gas mileage and the speed. Your friend s car engine is rated at 250 hp. It gets 20 miles per gallon when driving 60 miles per hour. a. Convert the nominal engine power output of 250 hp to watts. b. Calculate the actual power output from the above data. Start by calculating the gasoline consumption rate (gal/hr) and, using Table 3.3 s energy equivalent for gasoline, convert the result to a power in watts. c. Compare the two calculations and comment on why they don t agree. 4. The US imports about 12 million barrels of oil each day. a. Using Tables 3.1 and 3.3, convert this quantity to an equivalent power, measured in watts. b. If we wanted to replace all that imported oil with wind power, how many 5 MW wind turbines would we have to build?

2 2gg CHAPTER i4 E n e r g ys: o m e B a s i c s

3 3.3 Quonrifying Energy Energy unils loule (J) Joule equivolent* tj kilowatt-hour (krx/h) t,,^ grg"*un-y.ut,british : ).6 MJ 3.15PJ calorie(cal) 4.184J thermalunit (Btu) 1, o 5J4. 5l loc. iof, very roughly.r..,i.,.. quad (Q) 1.054EJ exajoule.., ,. e. r g1 0-7 I. electron volt (ey) I /. X 1 n JT Energy gained by an electron dropping through an electrjc potential differenceof 1 volt; usedin atomic and nuclear phvsics J Energyunit in the Englishsysrem,equalto cheenergyinvolvedin applying a force of I pound over a disranceof I foor. 4r.9 GJ Energycontentof i metric tonne (1,000 kg, roughly 1 English ton) ofoil. li:: foor-potrnd tr tonne oil equivalenr(toe) barrel ofoil equivalent (boe) G J Power unils watt (rv) horsepower(hp) Btu per hour (Brulh, or Btuh) Bnergycontentof<lne42.gallonbaneloftlil,,. Wotf equlvolenf Descripllon,1W Equivalent to I JA. 746W Unit derivedoriginally lrom powersupplieclby horses;now usedprimarily to describeenginesan.l morors W.Usedprim"rily in rh9unite.l States,usually to describeheating an<l.ooling,yst"-s. +SeeTable 3.2 for Sl prefixes. used in the Unired Statesto describethe capacityof heating and air conditioning systems is the Btu per hour (Btu/h, but often wrirren, misleadingly, as simply Btuh). As Table 3.1 shows,1 Btu/h is just under one-third of a watt. My housel-rold furnaceis rated at 112,000Bru/h; Example3.1 showsthar this number is consistentwitl-rits fuel consumption rate of about 1 gallon of oil per hour. The British thermal unir is at the basis of a unit widely used in describingenergyconsumptionof enrire counrries,namely rhe quad (Q).One quad is 1 quadriilionbtu, or 1011Bru. The United Statesrateof energy consumptionin the early twenry-firsr cenrury,for example,is just about 100 Q per year, a figure that accountsfor approximateiyone-fourth of humankinds total yearly energy consumption.

4 54 Chopter 3 ENERGy: A Closer Look l/lulfiplier ?4.,: I l0- r8 10- r5... t0.t2:,,.li 10-e l0olr 1) l0e IOL2 l0lt l0r8 102 r lo24 Preflx :., j :YOCto zepro..:r: u *, femto.,, t, : _, plco, nano rmlcro l milli.,, kilo rnega Siga tera Pera exa Symbol I a f n,l+ m k M G P E Z Y routinely throughout this book, and you can find them here and inside the front cover. Note that the symbols for SI prefixes that multiply by less than 1 are in rowercase, while those that multiply by more than 1 (except for the kilo) are capitalized,. Back to Table 3.1, which arso lists several units for power. A-ong those in common use is horsepower (hp), a holdover from the day when horses suppliedluch of the energy coming from beyond our own bodies. one horsepower is 746 w, or about three_ quarters ofa kilowatt. So a 400-hp car engine can, in principle, supply energy at the rare of about 300 k\7 (most of the time the actual rate may be much less, and very little of that energy ends up propelling the car; more on this in Chapter 5). Fuels-those substances that store potential energy in ihe configurations of mole_ cules or atomic nuclei-are characterized by their energy conrent, expressed as energy

5 aa//r- 3,3 A*ff rz*&/ o{ #^-lt Typlcol energy conlent (vorles wlth fuel source) 9l units Olher unlls 43MJtkE ab t wr,rgaton 138 kbtuigallon glatural gas 30 k$fhl100 cubic feet 1,000 Btu/cubic foot Hydrogen gas (H2) burned to produce H2O \+zu1rug 320 Btu/cubic foot Hydrogen, deuterium-deurerium nuclear fusion Pure deuterium :, f i,, Norrnalwater )30TJtkg 12GJtks 13 MlU7h/gallon, 350 gallons gasoline equivalent per gallon water contained in a given mass or volume. Table 3.3 lists the energy conrents of some common fuels Some of these quantities find their way into alternative units for energy and for energy-consumption rate, as in the tonne oil equivalent and barrel of oil equivalent listed in Table 3.1. Related power units of millions of barrels of oil equivalent per day often describe the production of fossil fuels, and narional energy-consumprion rares are sometimes given in millions of barrels of oil equivalent per year. Anorher handy figure to use in considering fossil fuel energy is to approximate rhe energy conrent ofa gallon ofpeffoleum product--oil, kerosene, gasoline-as being about 40 k$7h (the exact amounr varies with the fuel, and the amount ofuseful energy obtained depends on the efficiency of the energy-conversion process; more on this in the next chapter). Finally, Table 3.3 hints at the huge quantitative difference between chemical and nuclear fuels; just compare the energy per kilogram of petroleum with that of uranium! Youll find Tables 3.1 through 3.3 sufficiently useful that theyre printed inside the front cover for easy reference, along with other useful energy-related information.