Basic Information Fundamental Constants Avogadro’s number = 6.023x1023 Charge of the electron = 1.60x10-19 C Density of air = 1.03 kg/m3 Density of water = 1000 kg/m3 = 1 g/cm3 = 62.4 lb/ft3 Heat capacity of water = 4.18 kJ/kg.K = 1 g-cal/g.°C = 1 Btu/lb.°F = 1.163 kWh/kg.K Mass of an electron = 9.1x10-31 kg Mass of a neutron = 1.675x10-27 kg Mass of a proton = 1.672x10-27 kg Mass of the moon = 7.4x1022 kg Mass of the earth = 6x1024 kg Mass of the sun = 2x1030 kg Size of hydrogen atom (Bohr radius) = 5.29x10-11 m Radius of the moon = 1,738 km Radius of the earth (at equator) = 6,400 km Radius of the sun = 700,000 km Average distance between the earth and the sun = 1.495x108 km Average distance between the earth and the moon = 3.84x105 km Solar constant = 1,340 W/m2 Speed of light (in vacuum) = 3.00 x 108 m/s Speed of sound in air (at STP) = 331 m/s One light year = 9.46x1012 km Stephan-Boltzmann’s constant = 5.67 x 10-8 W/m2.K4 Acceleration of gravity on earth’s Surface = g = 9.81 m/s2 Gravitational constant = G = 6.67×10-11 m3/kg-s2 = 6.67×10-11 N-m2/kg2 Useful Arithmetic Skills Powers of Ten Addition and Subtraction: Multiplication: 10a.10b=10a+b Appendix A Example: 2x102 +10-1-0.3x101=(2x100)+(1x0.1)-(0.3x10)=200+.01-3=197.1 Example: 102.103=105 ; (2x10-3).(4x102) = 8x 10-3+2 = 8x10-1 = 0.8 Division: 10a/10b=10a-b Power: (10a)b=10a.b Example: 102/103 = 102-3 = 10-1 ; (2x10-2)/(10-3) = 2x10-2+3 = 2x101 = 20 Example: (102)3=102.3 =106 ; (2x102)-1.5 = 2x 10-2x1.5 = 2x10-3 = 0.002 Power Value Name 10 -12 -9 -6 0.000000000001 0.000000001 0.000001 0.001 1 1,000 1,000,000 1,000,000,000 1,000,000,000,000 Trillionth Billionth Millionth Thousands One Thousand Million Billion Trillion 10 10 10-3 100 10 10 3 6 109 1012 Logarithms Definition: N = ax ; x = logaN for a = e = 2.71828; N = ex ; x = ln N (natural logarithm) for a = 10 ; N = 10x ; x = log10 N = log N (logarithm base 10) Base other than 10: logba = log a/log b Example: log3 5 + log 5/log 3 = 0.699 / 0.477 = 1.465 Addition and Subtraction: Example: log (3) + log (2) = 0.477 + 0.301 = 0.778 Multiplication: log (a.b) = log a + log b Example: log 6 = log (3x2) = log 3 + log 2 = 0.477 + 0.301 = 0.778 Division: log (a/b) = log a - log b Power: log (a)b = b. log(a) Example: log (1.5) = log (3/2) = log 3 - log 2 =0.477 - .0301 = 0.176 Example: log (100.3) = 0.3 log (10)=0.3x1 = 0.3 ; log (5-2) = -2 log (5) = -1.398 N log10 N ln N ex e-x 0 1 2 3 4 5 6 7 8 9 10 -0 0.301 0.477 0.602 0.699 0.778 0.845 0.903 0.954 1.000 -0 0.693 1.099 1.386 1.609 1.792 1.946 2.079 2.197 2.303 1.000 2.718 7.389 20.086 54.598 148.41 403.43 1096.6 2981.0 8103.1 22026 1.000 0.368 0.135 0.050 0.018 6.74x10-3 2.48x10-3 9.12x10-4 3.35x10-4 1.23x10-4 4.54x10-5 474 Appendices Unit Conversion Metric Units and Abbreviation Quantity Unit Symbol Appendix B Time Length Speed Volume Mass Weight (Force) Torque Energy Power Specific power Power density second meter meter/s cubic meter kilogram newton newton-meter joule watt watt per kilogram watt per cu. meter s m m/s m3 kg N = kg.m/s2 N.m = J J W = J/s W/kg W/m3 Conversion Tables Time 1 year = 365.25 d = 8,766 h = 3.16x107 s Length 1 micron =1 mm = 10-6 m 1 nanometer = 1 nm = 10-9 m 1 meter (m) = 1.094 yd = 3.281ft 1 kilometer (km) = 1,000 m = 0.62 mi = 3,281 ft 1 foot (ft) = 12 in = 0.305 m 1 mile (mi) = 1.609 km = 1,609 m = 1,760 yd = 5,280 ft 1 light year = 9.46x1015 m 1 astronomical unit (AU) (average distance between earth and sun) = 1.49x1011 m Speed (Velocity) 1 m/s = 3.28 ft/s = 3.6 km/hr = 2.24 mph 1 km/h = 0.62 mph = 0.278 m/s 1 mph = 1.609 km/h = 1.467 ft/s Area 1 square mile (mi2) = 2.59 km2 = 640 acre = 2.79x107 ft2 1 square meter (m2) = 10.76 ft2 1 hectacre = 2.47 acre Volume 1 gallon (U.S.) = 3.785 L I gallon (Imperial) = 1.2 gallon (U.S.) 1 cubic meter (m3) = 1,000 L = 264 U.S. gallons = 35.3 ft3 = 6.29 bbl 1 barrel (bbl) = 42 US gallons = 0.159 m3 = 159.1 L Mass 1 kilogram (kg) = 1,000 g = 2.21 lb = 10-3 ton (metric) 1 pound (lb) = 0.453 kg = 4.536x10-4 ton (metric) 1 ton (metric) = 1,000 kg = 2,240 lbs 1 short ton = 2,000 lb = 907 kg Density 475 Pressure 1 g/cm3 = 1 kg/L = 1,000 kg/m3 = 62.4 lb/ft3 = 8.35 lb/gallon 1 pound/gallon U.S.) = 0.12 kg/L 1 pascal (Pa) = 1 N/m2 1 atmosphere (atm) = 101 kPa = 760 mm Hg = 14.7 lb/in2 Energy 1 quad = 1015 Btu = 1.055 EJ 1 Megajoule (MJ) = 106 J = 0.278 kWh = 948 Btu 1 Btu = 1,055 J =2.93x10-4 kWh = 0.252 kcal 1 kWh = 3.6x106 J = 3412 Btu 1 Calorie (food calorie) = 1 kcal = 4.184 kJ = 3.968 Btu 1 therm = 105 Btu = 1.055x105 kJ 1 ton of TNT = 4.184x109 J = 106 food Calorie 1 electron-volt (eV) = 1.602x10-19 J Power 1 watt (W) = 1 J/s 1 kilowatt (kW) = 1.34 hp = 0.239 kcal/s = 0.948 Btu/s 1 TW = 30 quads/yr 1 horsepower (hp) = 0.746 kW = 0.178 kcal/s = 0.707 Btu/s 1 ton refrigeration = 12,000 Btu/hr = 3.517 kW To Convert Into Multiply By Btu Btu Btu Btu/hour Btu/hour calorie cubic meter cubic meter cubic meter day electron-volt foot foot foot/second foot/second gallon (U.S.) gallon (U.S.) horsepower hour joule joule kilogram kilometer kilometer 476 joule kilowatt-hour calorie watt horsepower Btu cubic foot gallon (U.S.) liter second joule inch meter meter/second mile/hour cubic foot liter kilowatt second electron-volt Btu pound meter mile 1,055 2.93x10-4 242 0.293 3.93x10-4 3.968x10-3 35.31 264.2 1,000 86,400 1.6x10-19 12 0.3048 0.3048 0.68 0.1337 3.785 0.746 3,600 6.24x1018 9.48x10-4 2.205 1,000 0.6214 Appendices To Convert Into Multiply By kilometer/hour kilometer/hour kilometer/hour kilopascal kilowatt kilowatt-hour kilowatt-hour knot knot knots liter liter liter liter meter meter meter/second meter/second metric ton mile mile (nautical) mile/hour mile/hour minute pound quad square foot square meter square kilometer square kilometer ton (metric) ton (short) watt watt yard meters/second mile/hour knots inch of water (4o ) horsepower Btu joule nautical mile/hr kilometers/hour miles/hour cubic centimeter cubic foot cubic meter gallon (US) foot yard kilometer/hour mile/hour kilogram foot mile foot/second kilometer/hour second kilogram Btu square meter square foot acre square mile kilogram pound Btu/hour horsepower meter 0.278 0.6214 0.54 4.015 1.341 3,413 3.6x106 1.000 1.852 1.151 1,000 0.0353 0.001 0.264 3.28 1.094 3.6 2.237 1,000 5,280 1.15 1.467 1.609 60 0.453 1015 0.093 10.76 247 0.386 1,000 2,000 3.413 1.341x10-3 0.9144 477 Density of Air @ STP Water @ 4oC Natural gas Crude oil 1.2 kg/m3 = 1 kg/L = 1,000 kg/m3 = 62.4 lb/ft3 0.72 kg/m3 = 44.9 lb/ft3 0.86 kg/L = 136 kg/bbl = 7.16 lb/gallon Fuel Equivalents 1 quad = 170 million barrels of crude oil = 0.273 cubic kilometer of oil = 40 million tons of coal = 28 billion m3 natural gas 1 bbl of oil = 6.1 giga joule = 5.8 million Btu = 0.2 tons of coal = 164 cubic meters of natural gas 1 kg of U-235 fuel (3.5%) = 100 tons of coal = 2.6x1012 J Fuel Efficiency Conversions MPG Miles/L Km/L L/100 km 10 15 20 25 30 35 40 45 50 55 60 2.64 3.96 5.28 6.60 7.92 9.25 10.57 11.89 13.21 14.53 15.85 4.25 6.38 8.50 10.63 12.75 14.88 17.00 19.13 21.25 23.38 25.51 23.52 15.68 11.76 9.41 7.84 6.72 5.88 5.23 4.70 4.28 3.92 Energy Contents of Various Fuels Fuel Crude oil (kerosene) Gasoline Diesel Ethanol Biodiesel Hydrogen @ 35MPa Standard coal Bituminous Lignite Natural gas @ STP CNG @ 20 MPa LPG @ 1.5 MPa Methanol Uranium (fissioned) Uranium(0.5%) 38.5 32.2 35.6 21.2 33.0 2.7 30.0 20-30 10-19 37.0 9.3 23.0 16.7 80 400 Energy Density* MJ/L “ “ “ “ “ MJ/kg “ “ MJ/m3 MJ/L “ “ GJ/g GJ/kg 6 115 128 76 121 9.9 12.9 8.6-12.9 4.3-8.2 84 33 84 53 34 172 MBtu/bbl kBtu/gal “ “ “ “ kBtu/lb “ “ kBtu/gal “ “ “ GBtu/lb MBtu/lb *Lower Heating Value (Net) except for hydrogen which is for HHV 478 Appendices Exponential Expiration Time One of the pressing questions of our time is that for how long our nonrenewable resources last. When a quantity such as the rate of consumption of a resource is growing at a fixed percentage rate, r, after time t we have: N = N0 ert (C.1) Appendix C Where; N0 is the initial rate of consumption per year (t = 0), N is the rate of consumption per year at a later time, and r is the annual growth rate The consumption rate will grow to twice the initial value (N/N0 = 2) after time T2 = ln 2 0. 693 70 = ≅ r r R (C.2) W here R is the percentage growth per year (R = 100.r) The cumulative consumption of the resource between the present time t = 0 and time t = T in the future is: Q= T 0 N(t). dt = N0 r T (e − 1) r (C.3) We can rearrange this equation to give the exponential expiration time, i.e. time it takes for the resource to be depleted. EET = (1 /r ) ln(rQ / N0 + 1) (C.4) In this equation, Q represents the ultimate size of the resource (given in barrels of oil, tons of coal, etc.), N0 is the consumption rate (given in barrels of oil per year, tons of coal per day, etc.) at time t = 0. Example C-1: The US energy consumption increased from 76.8 quads in 1984 to 100.4 quads in 2004 (See Table 1-3). Assuming that the consumption followed an exponential growth pattern, find a. The annual growth rate, b. The doubling-time, c. Total US energy consumption during this period. Solution: Substituting into Equations C-1 through C-3, we will have: 479 a. 100.4 = 76.8 e 20r; or r = 1/20 ln (100.4/76.8) = 0.013 (1.3% per year) b. T2 = 70/1.3 = 52.2 years c. Q = 76.8/0.013 (e0.013x20-1) = 1,754 quads Example C-2: The total world petroleum endowment (that already produced and that will remain to be exploited) is estimated at 3,563 billion barrels (See Table 7-3). The same data indicates the cumulative production of 708 billion barrels and proven (remaining) reserves of 2,855 billion barrels. Assuming that the oil consumption was at 98.9 million barrels a day in 2000, calculate the remaining life expectancy (exponential expiration time) of the world’s petroleum reserves. Solution: Substituting for the total size of remaining reserves (Q = 2,855 bbo), the annual consumption rate of N0 = 98.9x106x365 = 36.1x109 barrels/year (36.1 bbo/year) at the turn of the century, the exponential expiration time is calculated for different rate of consumption growth as: r (% per year) 1 2 3 4 5 6 7 8 9 10 EET (years) 58.3 47.4 40.5 35.7 32.0 29.1 26.8 24.9 23.3 21.9 480 Appendices Abbreviations and Acronyms Acronyms AQMD DNA DOD DOE DOT EPA FERC GAO Air Quality Management District Defense Nuclear Agency Department of Defense Department of Energy Department of Transportation Environmental Protection Agency Federal Energy Regulatory Commission Government Accountability Office (Formerly General Accounting Office) International Atomic Energy Commission International Monetary Fund Institute of Nuclear Power Operation National Aeronautics and Space Administration North Atlantic Treaty Organization National Institute of Standards and Technology Nuclear Regulatory Commission Organization of Petroleum Exporting Countries United Nations Union of Soviet Socialist Republics World Association of Nuclear Operators World Health Organization World Trade Organization Anti Ballistic Missile Air Quality Index Best Available Control Technology Battery-operated Electric Vehicle Body Mass Index Basal Metabolic Rate British Thermal Unit Boiling Water Reactor Clean Air Act Computer Aided Design Corporate Average Fuel Economy Central American Free Trade Agreement Computer Aided Manufacturing Chlorofluorocarbon Combined Heat and Power Compressed Natural Gas Cost of Living Adjustment Coefficient of Performance Consumer Price Index Clean Water Act Appendix D IAEA IMF INPO NASA NATO NIST NRC OPEC UN USSR WANO WHO WTO Abbreviations ABM AQI BACT BEV BMI BMR Btu BWR CAA CAD CAFÉ CAFTA CAM CFC CHP CNG COLA COP CPI CWA 481 DNA DU EER FFV GDP GNP HCFC HTGR HWR ICE IOU IPCC IPP ISO ITER JET LDC LEV LMFBR LNG LWR MHD MRI MTBE NAAQS NAFTA NMD NNW NPV OEM OTEC PNGV PSC PWR PX QF RAD RNA SALT SDI SI SOC START TFTR TNT ULEV USCS VOC ZEV 482 Deoxyribo Nucleic Acid Depleted Uranium Energy Efficiency Ratio Flexible Fuel Vehicle Gross Domestic Products Gross National Products Hydrochlorofluorocarbon High Temperature Gas-Cooled Reactors Heavy Water Reactor Internal Combustion Engine Investor Owned Utility Intergovernmental Panel on Climate Change Independent Power Producers Independent System Operators International Thermonuclear Experimental Reactor Joint European Torus Load Demand Curve Low Emission Vehicle Liquid Metal Fast Breeder Reactor Liquefied Natural Gas Light Water Reactor Magneto Hydro Dynamics Magnetic Resonance Imaging Methyl Tertiary Butyl Ether National Ambient Air Quality Standards North Atlantic Free Trade Agreement. National Missile Defense System Net National Welfare Net Present Value Original Equipment Manufacturer Ocean Thermal Energy Conversion Partnership for New Generation of Vehicles Polar Stratospheric Cloud Pressurized Water Reactor California Power Exchange Corporation Qualifying Facility Radiation Adsorbed Dose Ribonucleic Acid Strategic Arms Limitation Treaty Strategic Defense Initiative International System (of units) State of Charge STrategic Arms Reduction Treaty Tokomak Fusion Test Reactor Trinitrotoluene Ultra Low Emission Vehicle United States Customary System Volatile Organic Compounds Zero Emission Vehicle