Basic Information
Appendix A
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
Radius of the moon = 1,738 km
Radius of the earth at equator = 6,400 km
Radius of the sun = 700,000 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:
Example: 2x102 +10-1-0.3x101=(2x100)+(1x0.1)-(0.3x10)=200+.01-3=197.1
Multiplication: 10a.10b=10a+b
Example: 102.103=105 ; (2x10-3).(4x102) = 8x 10-3+2 = 8x10-1 = 0.8
Division: 10a/10b=10a-b
495
Example: 102/103 = 102-3 = 10-1 ; (2x10-2)/(10-3) = 2x10-2+3 = 2x101 = 20
Power: (10a)b=10a.b
Example: (102)3=102.3 =106 ; (2x102)-1.5 = 2x 10-2x1.5 = 2x10-3 = 0.002
Power
Value
Name
10-12
0.000000000001
Trillionth
10-9
0.000000001
Billionth
10-6
0.000001
Millionth
10-3
0.001
100
1
103
1,000
106
1,000,000
Million
9
10
1,000,000,000
Billion
12
10
1,000,000,000,000
Trillion
Thousands
One
Thousand
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)
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
Example: log (1.5) = log (3/2) = log 3 - log 2 =0.477 - .0301 = 0.176
Power: log (a)b = b. log(a)
Example: log (100.3) = 0.3 log (10)=0.3x1 = 0.3 ; log (5-2) = -2 log (5) = -1.398
N
0
1
2
3
4
5
6
7
8
9
10
496
log10 N
-0
0.301
0.477
0.602
0.699
0.778
0.845
0.903
0.954
1.000
ln N
-0
0.693
1.099
1.386
1.609
1.792
1.946
2.079
2.197
2.303
ex
1.000
2.718
7.389
20.086
54.598
148.41
403.43
1096.6
2981.0
8103.1
22026
e-x
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
Appendix B
Unit Conversion
Metric Units and Abbreviation
Quantity
Unit
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
Symbol
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 = 3.15x107 s
Length
1 micron = 1 mm = 10-6 m
1 kilometer (km) = 1,000 m = 0.62 mi = 3,281 ft
1 mile (mi) = 1.609 km = 1,609 m = 1,760 yd = 5,280 ft
1 meter (m) = 1,000 m = 6.214x10-4 mile
1 foot (ft) = 12 in = 0.305 m
1 light year = 9.46x1015 m
1 astronomical unit (AU) (average distance between earth
and sun) = 1.49x1011 m
Speed (Velocity)
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 =
2.59x106 m2
1 square meter (m2) =10.76 ft2
Volume
1 cubic meter (m3) = 1,000 L = 264 U.S. gallon = 35.3 ft3 = 6.29
bbl
1 barrel (bbl) = 42 US gallon = 0.159 m3 = 159.1 L
1 bushel = 8 gallon = 35.24 L
497
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 = 2,205 lbs
1 short ton = 2,000 lb = 907 kg Pressure
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 Calorie (food calorie) = 1 kcal = 4.184 kJ = 3.968 Btu
1 therm = 105 Btu = 1.055x105 kJ
1 kiloton of TNT = 4.2x1012 J
Power
1 watt (W) = 1 J/s
1 kilowatt (kW) = 1.34 hp = 0.239 kcal/s = 0.948 Btu/s
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
498
Into
Multiply By
Btu
joule
1,055
Btu
kilowatt-hour
2.93x10-4
Btu
calorie
242
Btu/hour
watt
0.293
Btu/hour
horsepower
3.93x10-4
calorie
Btu
3.968x10-3
cubic meter
cubic foot
35.31
cubic meter
gallon (US)
264.2
cubic meter
liter
1,000
day
second
86,400
foot
meter
0.3048
foot/second
meter/second
0.3048
foot/second
mile/hour
0.68
gallon
cubic foot
0.1337
gallon
liter
3.785
gallon (Imperial)
gallon (US)
1.200
gallon (US)
gallon (Imperial)
0.833
horsepower
kilowatt
0.746
hour
day
4.167x10-2
To Convert
Into
Multiply By
hour
second
3,600
joule
Btu
9.48x10-4
kilogram
gram
1,000
kilogram
pound
2.205
kilometer
meter
1,000
kilometer
mile
0.6214
kilometer/hour
mile/hour
0.6214
kilowatt
horsepower
1.341
kilowatt-hour
Btu
3,413
kilowatt-hour
joule
3.6x106
liter
cubic centimeter
1,000
liter
cubic foot
0.0353
liter
cubic meter
0.001
liter
gallon (US)
0.264
meter
foot
3.28
meter
yard
1.094
meter/second
kilometer/hour
3.6
meter/second
mile/hour
2.237
mile
foot
5,280
mile (nautical)
mile
1.15
mile/hour
foot/second
1.467
mile/hour
kilometer/hour
1.609
minute
second
60
pound
kilogram
0.453
quad
Btu
1015
square foot
square meter
0.093
square meter
square foot
10.76
square kilometer
acre
247
square kilometer
square mile
0.386
ton (metric)
kilogram
1,000
ton (short)
pound
2,000
watt
Btu/hour
3.413
watt
horsepower
1.341x10-3
watt
kilowatt
0.001
yard
meter
0.9144
499
Density
Water
1 g/cm3 = 1 kg/L= 1,000 kg/m3 = 62.4 lb/ft3
Natural gas 0.72 kg/m3
Crude oil
0.86 kg/L= 136 kg/bbl = 7.16 lb/gallon
Fuel Equivalents
1 quad = 170 million barrels of crude 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
10
15
20
25
30
35
40
45
50
55
60
Miles/L
2.64
3.96
5.28
6.60
7.92
9.25
10.57
11.89
13.21
14.53
15.85
Km/L
L/100 km
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
Heat Contents of Various Fuels
Fuel
Crude oil
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%)
Heat Content*
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
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
500
Exponential Expiration Time
Appendix C
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:
..ERT
(C.1)
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
LN 4
R
R
2
(C.2)
where 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:
1
4
° .T DT . R 4
E Ÿ 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.
%%4 R LNR1 . (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.
501
Solution: Substituting into Equations C-1 through C-3, we
will have:
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:
502
r (% per
year)
EET (years)
1
58.3
2
47.4
3
40.5
4
35.7
5
32.0
6
29.1
7
26.8
8
24.9
9
23.3
10
21.9
Abbreviations and Acronyms
Acronyms
AQMD
DNA
DOD
DOE
DOT
EPA
FERC
GAO
IAEA
IMF
INPO
NASA
NATO
NIST
NRC
OPEC
UN
USSR
WANO
WHO
WTO
Appendix D
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
Abbreviations
ABM
AQI
BACT
BEV
BMI
BMR
Btu
BWR
CAA
CAD
CAFÉ CAFTA
CAM
CFC
CHP
CNG
COLA
COP
CPI
CWA
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
503
DNA
DU
EER
FFV
GDP
GNP
HCFC
HTGR
HWR
ICE
IOU
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
SOS
START
TFTR
TNT
ULEV
USCS
VOC
ZEV
504
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
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