Tallarida, R.J. “Section XII – Mathematics, Symbols, and Physical Constants”
The Electrical Engineering Handbook
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
The mathematical equation used to generate this three-dimensional figure is worth a
thousand words. It represents a single-solitron surface for the sine-Gordon equation w
uv
=
sin w. Among the areas in which the sine-Gordon equation arises is that of wave propagation
on nonlinear transmission lines and in semi-conductors. The equation is famous because
it is known to have a nonlinear superposition principle obtainable by means of a B?cklund
Transformation. The sine-Gordon equation is an example of an evolution equation which
has an infinite sequence of non-trivial conservation laws so important in the fields of
engineering and physics. For further information on the B?cklund Transformation see B?ck-
lund Transformations and their Application, Rogers and Shadwick, Academic Press, 1982.
This three-dimensional projection was generated using the MAPLE? software package.
MAPLE? is one of three important mathematical computer packages that offer a variety
of analytical and numerical software for use by scientists, engineers, and mathematicians.
This figure was developed by W.K. Schief and C. Rogers and the Center for Dynamical
Systems and Nonlinear Studies at Georgia Institute of Technology and the University of
New South Wales in Sydney, Australia. (Figure courtesy of Schief and Rogers.)
? 2000 by CRC Press LLC
XII
Mathematics, Symbols,
and Physical Constants
Greek Alphabet
International System of Units (SI)
Definitions of SI Base Units?Names and Symbols for the SI Base Units?SI Derived Units
with Special Names and Symbols?Units in Use Together with the SI
Conversion Constants and Multipliers
Recommended Decimal Multiples and Submultiples?Conversion Factors—Metric to English?
Conversion Factors—English to Metric?Conversion Factors—General?Temperature Factors?
Conversion of Temperatures
Physical Constants
General? p Constants?Constants Involving e?Numerical Constants
Symbols and Terminology for Physical and Chemical Quantities
Classical Mechanics?Electricity and Magnetism?Electromagnetic Radiation?Solid State
Credits
Ronald J. Tallarida
Temple University
HE GREAT ACHIEVEMENTS in engineering deeply affect the lives of all of us and also serve to remind
us of the importance of mathematics. Interest in mathematics has grown steadily with these engineering
achievements and with concomitant advances in pure physical science. Whereas scholars in nonscien-
tific fields, and even in such fields as botany, medicine, geology, etc., can communicate most of the problems
and results in nonmathematical language, this is virtually impossible in present-day engineering and physics.
Yet it is interesting to note that until the beginning of the twentieth century engineers regarded calculus as
something of a mystery. Modern students of engineering now study calculus, as well as differential equations,
complex variables, vector analysis, orthogonal functions, and a variety of other topics in applied analysis. The
study of systems has ushered in matrix algebra and, indeed, most engineering students now take linear algebra
as a core topic early in their mathematical education.
This section contains concise summaries of relevant topics in applied engineering mathematics and certain
key formulas, that is, those formulas that are most often needed in the formulation and solution of engineering
problems. Whereas even inexpensive electronic calculators contain tabular material (e.g., tables of trigonometric
and logarithmic functions) that used to be needed in this kind of handbook, most calculators do not give
symbolic results. Hence, we have included formulas along with brief summaries that guide their use. In many
cases we have added numerical examples, as in the discussions of matrices, their inverses, and their use in the
solutions of linear systems. A table of derivatives is included, as well as key applications of the derivative in the
solution of problems in maxima and minima, related rates, analysis of curvature, and finding approximate
T
? 2000 by CRC Press LLC
roots by numerical methods. A list of infinite series, along with the interval of convergence of each, is also
included.
Of the two branches of calculus, integral calculus is richer in its applications, as well as in its theoretical
content. Though the theory is not emphasized here, important applications such as finding areas, lengths,
volumes, centroids, and the work done by a nonconstant force are included. Both cylindrical and spherical
polar coordinates are discussed, and a table of integrals is included. Vector analysis is summarized in a separate
section and includes a summary of the algebraic formulas involving dot and cross multiplication, frequently
needed in the study of fields, as well as the important theorems of Stokes and Gauss. The part on special
functions includes the gamma function, hyperbolic functions, Fourier series, orthogonal functions, and both
Laplace and z-transforms. The Laplace transform provides a basis for the solution of differential equations and
is fundamental to all concepts and definitions underlying analytical tools for describing feedback control
systems. The z-transform, not discussed in most applied mathematics books, is most useful in the analysis of
discrete signals as, for example, when a computer receives data sampled at some prespecified time interval. The
Bessel functions, also called cylindrical functions, arise in many physical applications, such as the heat transfer
in a “long” cylinder, whereas the other orthogonal functions discussed—Legendre, Hermite, and Laguerre
polynomials—are needed in quantum mechanics and many other subjects (e.g., solid-state electronics) that
use concepts of modern physics.
The world of mathematics, even applied mathematics, is vast. Even the best mathematicians cannot keep up
with more than a small piece of this world. The topics included in this section, however, have withstood the
test of time and, thus, are truly core for the modern engineer.
This section also incorporates tables of physical constants and symbols widely used by engineers. While not
exhaustive, the constants, conversion factors, and symbols provided will enable the reader to accommodate a
majority of the needs that arise in design, test, and manufacturing functions.
? 2000 by CRC Press LLC
Mathematics,
Symbols, and
Physical Constants
Greek Alphabet
International System of Units (SI)
The International System of units (SI) was adopted by the 11th General Conference on Weights and Measures
(CGPM) in 1960. It is a coherent system of units built form seven SI base units, one for each of the seven
dimensionally independent base quantities: they are the meter, kilogram, second, ampere, kelvin, mole, and
candela, for the dimensions length, mass, time, electric current, thermodynamic temperature, amount of
substance, and luminous intensity, respectively. The definitions of the SI base units are given below. The SI
derived units are expressed as products of powers of the base units, analogous to the corresponding relations
between physical quantities but with numerical factors equal to unity.
In the International System there is only one SI unit for each physical quantity. This is either the appropriate
SI base unit itself or the appropriate SI derived unit. However, any of the approved decimal prefixes, called SI
prefixes, may be used to construct decimal multiples or submultiples of SI units.
It is recommended that only SI units be used in science and technology (with SI prefixes where appropriate).
Where there are special reasons for making an exception to this rule, it is recommended always to define the
units used in terms of SI units. This section is based on information supplied by IUPAC.
Definitions of SI Base Units
Meter—The meter is the length of path traveled by light in vacuum during a time interval of 1/299 792 458
of a second (17th CGPM, 1983).
Kilogram—The kilogram is the unit of mass; it is equal to the mass of the international prototype of the
kilogram (3rd CGPM, 1901).
Second—The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition
between the two hyperfine levels of the ground state of the cesium-133 atom (13th CGPM, 1967).
Ampere—The ampere is that constant current which, if maintained in two straight parallel conductors of
infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between
these conductors a force equal to 2 ′ 10
–7
newton per meter of length (9th CGPM, 1948).
Greek Greek English Greek Greek English
letter name equivalent letter name equivalent
Aa Alpha a Nn Nu n
Bb Beta b Xx Xi x
Gg Gamma g Oo Omicron ?o
Dd Delta d Pp Pi p
Ee Epsilon ?e Rr Rho r
Zz Zeta z Ss Sigma s
Hh Eta e
–
Tt Tau t
QqJTheta th Uu Upsilon u
Ii Iota i FfjPhi ph
Kk Kappa k Cc Chi ch
Ll Lambda l Yy Psi ps
Mm Mu m Ww Omega o
–
? 2000 by CRC Press LLC
Kelvin—The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic
temperature of the triple point of water (13th CGPM, 1967).
Mole—The mole is the amount of substance of a system which contains as many elementary entities as there
are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified
and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles (14th
CGPM, 1971).
Examples of the use of the mole:
1 mol of H
2
contains about 6.022 ′ 10
23
H
2
molecules, or 12.044 ′ 10
23
H atoms
1 mol of HgCl has a mass of 236.04 g
1 mol of Hg
2
Cl
2
has a mass of 472.08 g
1 mol of Hg
2
2+
has a mass of 401.18 g and a charge of 192.97 kC
1 mol of Fe
0.91
S has a mass of 82.88 g
1 mol of e
–
has a mass of 548.60 mg and a charge of –96.49 kC
1 mol of photons whose frequency is 10
14
Hz has energy of about 39.90 kJ
Candela—The candela is the luminous intensity, in a given direction, of a source that emits monochromatic
radiation of frequency 540 ′ 10
12
hertz and that has a radiant intensity in that direction of (1/683) watt per
steradian (16th CGPM, 1979).
Names and Symbols for the SI Base Units
SI Derived Units with Special Names and Symbols
Physical quantity Name of SI unit Symbol for SI unit
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
Name of Symbol for Expression in
terms of SI base unitsPhysical quantity SI unit SI unit
frequency
1
hertz Hz s
–1
force newton N m kg s
–2
pressure, stress pascal Pa N m
–2
=m
–1
kg s
–2
energy, work, heat joule J N m = m
2
kg s
–2
power, radiant flux watt W J s
–1
= m
2
kg s
–3
electric charge coulomb C A s
electric potential, volt V J C
–1
= m
2
kg s
–3
A
–1
electromotive force
electric resistance ohm W V A
–1
= m
2
kg s
–3
A
–2
electric conductance siemens S W
–1
= m
–2
kg
–1
s
3
A
2
electric capacitance farad F C V
–1
= m
–2
kg
–1
s
4
A
2
magnetic flux density tesla T V s m
–2
= kg s
–2
A
–1
magnetic flux weber Wb V s = m
2
kg s
–2
A
–1
inductance henry H V A
–1
s= m
2
kg s
–2
A
–2
Celsius temperature
2
degree Celsius °CK
luminous flux lumen lm cd sr
illuminance lux lx cd sr m
–2
activity (radioactive) becquerel Bq s
–1
absorbed dose (of radiation) gray Gy J kg
–1
= m
2
s
–2
dose equivalent sievert Sv J kg
–1
= m
2
s
–2
(dose equivalent index)
? 2000 by CRC Press LLC
Units in Use Together with the SI
These units are not part of the SI, but it is recognized that they will continue to be used in appropriate contexts.
SI prefixes may be attached to some of these units, such as milliliter, ml; millibar, mbar; megaelectronvolt, MeV;
kilotonne, ktonne.
Conversion Constants and Multipliers
Recommended Decimal Multiples and Submultiples
plane angle radian rad 1 = m m
–1
solid angle steradian sr 1 = m
2
m
–2
1
For radial (circular) frequency and for angular velocity the unit rad s
–1
, or simply s
–1
, should
be used, and this may not be simplified to Hz. The unit Hz should be used only for frequency
in the sense of cycles per second.
2
The Celsius temperature q is defined by the equation:
q/°C = T/K – 273.15
The SI unit of Celsius temperature interval is the degree Celsius, °C, which is equal to the
kelvin, K. °C should be treated as a single symbol, with no space between the ° sign and the
letter C. (The symbol °K, and the symbol °, should no longer be used.)
Physical Symbol
Value in SI unitsquantity Name of unit for unit
time minute min 60 s
time hour h 3600 s
time day d 86 400 s
plane angle degree ° (p/180) rad
plane angle minute ￠ (p/10 800) rad
plane angle second 2 (p/648 000) rad
length ?ngstrom
1
?10
–10
m
area barn b 10
–28
m
2
volume litre l, L dm
3
= 10
–3
m
3
mass tonne t Mg = 10
3
kg
pressure bar
1
bar 10
5
Pa = 10
5
N m
–2
energy electronvolt
2
eV (= e ′ V) ?1.60218 ′ 10
–19
J
mass unified atomic
mass unit
2,3
u (=m
a
(
12
C)/12) ?1.66054 ′ 10
–27
kg
1
The ?ngstrom and the bar are approved by CIPM for “temporary use with
SI units,” until CIPM makes a further recommendation. However, they should
not be introduced where they are not used at present.
2
The values of these units in terms of the corresponding SI units are not
exact, since they depend on the values of the physical constants e (for the
electronvolt) and N
a
(for the unified atomic mass unit), which are determined
by experiment.
3
The unified atomic mass unit is also sometimes called the dalton, with
symbol Da, although the name and symbol have not been approved by CGPM.
Multiples and Multiples and
submultiples Prefixes Symbols submultiples Prefixes Symbols
10
18
exa E 10
–1
deci d
10
15
peta P 10
–2
centi c
10
12
tera T 10
–3
milli m
10
9
giga G 10
–6
micro m (Greek mu)
Name of Symbol for Expression in
terms of SI base unitsPhysical quantity SI unit SI unit
? 2000 by CRC Press LLC
Conversion Factors—Metric to English
Conversion Factors—English to Metric*
Conversion Factors—General*
10
6
mega M 10
–9
nano n
10
3
kilo k 10
–12
pico p
10
2
hecto h 10
–15
femto f
10 deca da 10
–18
atto a
To obtain Multiply By
Inches Centimeters 0.3937007874
Feet Meters 3.280839895
Yards Meters 1.093613298
Miles Kilometers 0.6213711922
Ounces Grams 3.527396195 ′ 10
–2
Pounds Kilogram 2.204622622
Gallons (U.S. Liquid) Liters 0.2641720524
Fluid ounces Milliliters (cc) 3.381402270 ′ 10
–2
Square inches Square centimeters 0.155003100
Square feet Square meters 10.76391042
Square yards Square meters 1.195990046
Cubic inches Milliliters (cc) 6.102374409 ′ 10
–2
Cubic feet Cubic meters 35.31466672
Cubic yards Cubic meters 1.307950619
To obtain Multiply By
Microns Mils 25.4
Centimeters Inches 2.54
Meters Feet 0.3048
Meters Yards 0.9144
Kilometers Miles 1.609344
Grams Ounces 28.34952313
Kilograms Pounds 0.45359237
Liters Gallons (U.S. Liquid) 3.785411784
Millimeters (cc) Fluid ounces 29.57352956
Square centimeters Square inches 6.4516
Square meters Square feet 0.09290304
Square meters Square yards 0.83612736
Milliliters (cc) Cubic inches 16.387064
Cubic meters Cubic feet 2.831684659 ′ 10
–2
Cubic meters Cubic yards 0.764554858
To obtain Multiply By
Atmospheres Feet of water @ 4°C 2.950 ′ 10
–2
Atmospheres Inches of mercury @ 0°C 3.342 ′ 10
–2
Atmospheres Pounds per square inch 6.804 ′ 10
–2
BTU Foot-pounds 1.285 ′ 10
–3
BTU Joules 9.480 ′ 10
–4
Cubic feet Cords 128
Degree (angle) Radians 57.2958
Ergs Foot-pounds 1.356 ′ 10
7
Multiples and Multiples and
submultiples Prefixes Symbols submultiples Prefixes Symbols
*Boldface numbers are exact; others are given to ten significant figures where so indicated by the multiplier factor.
? 2000 by CRC Press LLC
Temperature Factors
°F = 9/5 (°C) + 32
Fahrenheit temperature = 1.8 (temperature in kelvins) – 459.67
°C = 5/9 [(°F) – 32)]
Celsius temperature = temperature in kelvins – 273.15
Fahrenheit temperature = 1.8 (Celsius temperature) + 32
Conversion of Temperatures
Physical Constants
General
Equatorial radius of the earth = 6378.388 km = 3963.34 miles (statute).
Polar radius of the earth, 6356.912 km = 3949.99 miles (statute).
1 degree of latitude at 40° = 69 miles.
1 international nautical mile = 1.15078 miles (statute) = 1852 m = 6076.115 ft.
Mean density of the earth = 5.522 g/cm
3
= 344.7 lb/ft
3
Constant of gravitation (6.673 ± 0.003) ′ 10
–8
cm
3
gm
–1
s
–2
.
Feet Miles 5280
Feet of water @ 4°C Atmospheres 33.90
Foot-pounds Horsepower-hours 1.98 ′ 10
6
Foot-pounds Kilowatt-hours 2.655 ′ 10
6
Foot-pounds per min Horsepower 3.3 ′ 10
4
Horsepower Foot-pounds per sec 1.818 ′ 10
–3
Inches of mercury @ 0°C Pounds per square inch 2.036
Joules BTU 1054.8
Joules Foot-pounds 1.35582
Kilowatts BTU per min 1.758 ′ 10
–2
Kilowatts Foot-pounds per min 2.26 ′ 10
–5
Kilowatts Horsepower 0.745712
Knots Miles per hour 0.86897624
Miles Feet 1.894 ′ 10
–4
Nautical miles Miles 0.86897624
Radians Degrees 1.745 ′ 10
–2
Square feet Acres 43560
Watts BTU per min 17.5796
From To
°Celsius °Fahrenheit t
F
= (t
C
′ 1.8) + 32
Kelvin T
K
= t
C
+ 273.15
°Rankine T
R
= (t
C
+ 273.15) ′ 18
°Fahrenheit °Celsius t
C
=
Kelvin T
k
= + 273.15
°Rankine T
R
= t
F
+ 459.67
Kelvin °Celsius t
C
= T
K
– 273.15
°Rankine T
R
= T
K
′ 1.8
°Rankine Kelvin T
K
=
°Farenheit t
F
= T
R
– 459.67
To obtain Multiply By
t
F
32–
1.8
----------------
t
F
32–
1.8
----------------
T
R
1.8
-------
? 2000 by CRC Press LLC
Acceleration due to gravity at sea level, latitude 45° = 980.6194 cm/s
2
= 32.1726 ft/s
2
.
Length of seconds pendulum at sea level, latitude 45° = 99.3575 cm = 39.1171 in.
1 knot (international) = 101.269 ft/min = 1.6878 ft/s = 1.1508 miles (statute)/h.
1 micron = 10
–4
cm.
1 ?ngstrom = 10
–8
cm.
Mass of hydrogen atom = (1.67339 ± 0.0031) ′ 10
–24
g.
Density of mercury at 0°C = 13.5955 g/ml.
Density of water at 3.98°C = 1.000000 g/ml.
Density, maximum, of water, at 3.98°C = 0.999973 g/cm
3
.
Density of dry air at 0°C, 760 mm = 1.2929 g/l.
Velocity of sound in dry air at 0°C = 331.36 m/s – 1087.1 ft/s.
Velocity of light in vacuum = (2.997925 ± 0.000002) ′ 10
10
cm/s.
Heat of fusion of water 0°C = 79.71 cal/g.
Heat of vaporization of water 100°C = 539.55 cal/g.
Electrochemical equivalent of silver 0.001118 g/s international amp.
Absolute wavelength of red cadmium light in air at 15°C, 760 mm pressure = 6438.4696 ?.
Wavelength of orange-red line of krypton 86 = 6057.802 ?.
p Constants
p = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37511
1/p = 0.31830 98861 83790 67153 77675 26745 02872 40689 19291 48091
p
2
= 9.8690 44010 89358 61883 44909 99876 15113 53136 99407 24079
log
e
p = 1.14472 98858 49400 17414 34273 51353 05871 16472 94812 91531
log
10
p = 0.49714 98726 94133 85435 12682 88290 89887 36516 78324 38044
log
10
u2p = 0.39908 99341 79057 52478 25035 91507 69595 02099 34102 92128
Constants Involving e
e = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69996
1/e = 0.36787 94411 71442 32159 55237 70161 46086 74458 11131 03177
e
2
= 7.38905 60989 30650 22723 04274 60575 00781 31803 15570 55185
M = log
10
e = 0.43429 44819 03251 82765 11289 18916 60508 22943 97005 80367
1/M·=log
e
10 = 2.30258 50929 94045 68401 79914 54684 36420 67011 01488 62877
log
10
M = 9.63778 43113 00536 78912 29674 98645 –10
Numerical Constants
u2 = 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37695
3u2 = 1.25992 10498 94873 16476 72106 07278 22835 05702 51464 70151
log
e
2 = 0.69314 71805 59945 30941 72321 21458 17656 80755 00134 36026
log
10
2 = 0.30102 99956 63981 19521 37388 94724 49302 67881 89881 46211
u3 = 1.73205 08075 68877 29352 74463 41505 87236 69428 05253 81039
3
u3 = 1.44224 95703 07408 38232 16383 10780 10958 83918 69253 49935
log
e
3 = 1.09861 22886 68109 69139 52452 36922 52570 46474 90557 82275
log
10
3 = 0.47712 12547 19662 43729 50279 03255 11530 92001 28864 19070
Symbols and Terminology for Physical and Chemical Quantities
Name Symbol Definition SI unit
Classical Mechanics
mass m kg
reduced mass mm = m
1
m
2
/(m
1
+ m
2
)kg
density, mass density rr = M/V kg m
–3
relative density dd = r/r
q
l
surface density r
A
, r
S
r
A
= m/A kg m
–2
? 2000 by CRC Press LLC
Symbols and Terminology for Physical and Chemical Quantities (continued)
Name Symbol Definition SI unit
Classical Mechanics (continued)
momentum pp = mv kg m s
–1
angular momentum, action L l = r ￥ p J s
moment of inertia I, JI = Sm
i
r
i
2
kg m
2
force FF = dp/dt = ma N
torque, moment of a force T, (M) T = r ′ F N m
energy E J
potential energy E
p
, V, F E
p
= –òF · ds J
kinetic energy E
k
, T, Ke
k
= (1/2)mv
2
J
work W, w w = òF · ds J
Hamilton function HH(q, p)J
= T(q, p) + V(q)
Lagrange function LL(q,
·
q
T(q,
·
q) – V(q)
pressure p, P p = F/A Pa, N m
–2
surface tension g, sg = dW/dA N m
–1
, J m
–2
weight G, (W, P) G = mg N
gravitational constant GF= Gm
1
m
2
/r
2
N m
2
kg
–2
normal stress ss = F/A Pa
shear stress tt = F/A Pa
linear strain, e, e e = Dl/l l
relative elongation
modulus of elasticity, EE = s/e Pa
Young’s modulus
shear strain gg = Dx/d l
shear modulus G G = t/g Pa
volume strain, bulk strain qq = DV/V
0
l
bulk modulus, KK = –V
0
(dp/dV)Pa
compression modulus h, mt
x,z
= h(dv
x
/dz) Pa s
viscosity, dynamic viscosity
fluidity ff = 1/h m kg
–1
s
kinematic viscosity nn = h/r m
2
s
–1
friction coefficient m, ( f ) F
frict
= mF
norm
l
power PP = dW/dt W
sound energy flux P, P
a
P = dE/dt W
acoustic factors
reflection factor rr = P
t
/P
0
l
acoustic absorption factor a
a
, (a) a
a
= 1 – r l
transmission factor tt = P
tr
/P
0
l
dissipation factor dd = a
a
– t l
Electricity and Magnetism
quantity of electricity,
electric charge
Q C
charge density rr = Q/V C m
–3
surface charge density ss = Q/A C m
–2
electric potential V, f V = dW/dQ V, J C
–1
electric potential difference U, DV, Df U = V
2
– V
1
V
electromotive force EE = ò(F/Q) · ds V
electric field strength = F/Q = –grad V V m
–1
electric flux YY = òD · dA C
electric displacement DD = eE C m
–2
capacitance CC = Q/U F, C V
–1
permittivity e D = eE F m
–1
permittivity of vacuum e
0
e
0
= m
0
–1
c
0
–2
F m
–1
relative permittivity e
r
e
r
= e/e
0
l
dielectric polarization PP = D – e
0
E C m
–2
? 2000 by CRC Press LLC
Symbols and Terminology for Physical and Chemical Quantities (continued)
Name Symbol Definition SI unit
Electricity and Magnetism (continued)
(dipole moment per volume)
electric susceptibility c
e
c
e
= e
r
– 1 l
electric dipole moment p, m p = Qr C m
electric current II = dQ/dt A
electric current density j, J I = òj · dA A m
–2
magnetic flux density, magnetic
induction
BF = Qv ′ B T
magnetic flux FF = òB · dA Wb
magnetic field strength HB = mH A M
–1
permeability m B = mH N A
–2
, H m
–1
permeability of vacuum m
0
H m
–1
relative permeability m
r
m
r
= m/m
0
l
magnetization (magnetic dipole
moment per volume)
MM = B/m
0
– H A m
–1
magnetic susceptibility c, k, (c
m
) c = m
r
– 1 l
molar magnetic susceptibility c
m
c
m
= V
m
c m
3
mol
–1
magnetic dipole moment m, m E
p
= –m · B A m
2
, J T
–1
electrical resistance R R = U/I W
conductance GG = 1/R S
loss angle dd = (p/2) + f
I
– f
U
1, rad
reactance XX = (U/I)sin dW
impedance (complex impedance) ZZ = R + iX W
admittance (complex admittance) YY = 1/Z S
susceptance B Y = G + iB S
resistivity rr = E/j W m
conductivity k, g, sk = 1/r S m
–1
self-inductance LE = –L(dI/dt)H
mutual inductance M, L
12
E
1
= L
12
(Di
2
/dt
magnetic vector potential AB = ? ′ A Wb m
–1
Poynting vector SS = E ′ H W m
–2
Electromagnetic Radiation
wavelength l m
speed of light
in vacuum
in a medium
c
0
cc = c
0
/n
m s
–1
wavenumber in vacuum n
~
n
~
=n/c
0
= 1/nl m
–1
wavenumber (in a medium) ss = 1/l m
–1
frequency nn = c/l Hz
circular frequency, pulsatance ww = 2pn s
–1
, rad s
–1
refractive index nn = c
0
/c l
Planck constant h J s
Planck constant/2p \\ = h/2p J s
radiant energy Q, W J
radiant energy density r, w r = Q/V J m
–3
spectral radiant energy density
in terms of frequency r
n
, w
n
r
n
= dr /dn J m
–3
Hz
–1
in terms of wavenumber r
n
–
, w n
– r
n
– = dr/dn
–
J m
–2
in terms of wavelength r
l
, w
l
r
l
= dr /dl J m
–4
Einstein transition probabilities
spontaneous emission A
nm
dN
n
/dt = –A
nm
N
n
s
–1
stimulated emission B
nm
dn
n
/dt = –r
n
–
(n
–
nm
) ′ B
nm
N
n
s kg
–1
radiant power,
radiant energy per time
F, P F = dQ/dt W
radiant intensity II = dF/dW W sr
–1
radiant exitance (emitted radiant flux) MM = dF/dA
source
W m
–2
? 2000 by CRC Press LLC
Symbols and Terminology for Physical and Chemical Quantities (continued)
Name Symbol Definition SI unit
Electromagnetic Radiation (continued)
irradiance (radiant flux received) E, (I) E = dF/dA W m
–2
emittance ee = M/M
bb
l
Stefan-Boltzmann constant s M
bb
= sT
4
W m
–2
K
–4
first radiation constant c
1
c
1
= 2phc
0
2
W m
2
second radiation constant c
2
c
2
= hc
0
/k K m
transmittance, transmission factor t, T t = F
tr
/F
0
l
absorptance, absorption factor aa = f
abs
/f
0
l
reflectance, reflection factor rr = f
refl
/F
0
l
(decadic) absorbance AA = lg(1 – a
i
)l
napierian absorbance BB = ln(1 – a
i
absorption coefficient
(linear) decadic a, K a = A/l m
–1
(linear) napierian aa = B/l m
–1
molar (decadic) ee = a/c = A/cl m
2
mol
–1
molar napierian kk = a/c = B/cl m
2
mol
–1
absorption index = a/4pn
–
l
complex refractive index ?n ?n = n + ik l
molar refraction R, R
m
R = V
m
m
3
mol
–1
angle of optical rotation a l, rad
Solid State
lattice vector R, R
0
m
fundamental translation vectors for the
crystal lattice
a
1
; a
2
; a
3
,
a; b; c
R = n
1
a
1
+ n
2
a
2
+ n
3
a
3
m
(circular) reciprocal lattice vector GG · R = 2pm m
–1
(circular) fundamental translation
vectors for the reciprocal lattice
b
1
; b
2
; b
3
,
a*; b*; c*
a
i
· b
k
= 2pd
ik
m
–1
lattice plane spacing d m
Bragg angle q nl = 2d sin q l, rad
order of reflection n l
order parameters
short range s l
long range s 1
Burgers vector b m
particle position vector r, R
j
m
equilibrium position vector of an ion R
o
m
displacement vector of an ion uu = R – R
0
m
Debye-Waller factor B, D l
Debye circular wavenumber q
D
m
–1
Debye circular frequency w
D
s
–1
Grüneisen parameter g, Gg = aV/kC
V
l
Madelung constant a, M
a N
A
z
+
z
–
e
2
E
coul
= ————
4pe
0
R
0
l
density of states N
E
N
E
= dN(E)/dE J
–1
m
–3
(spectral) density of vibrational modes N
w
, gN
w
= dN(w)/dw s m
–3
resistivity tensor r
ik
E = r · j W m
conductivity tensor s
ik
s = r
–1
S m
–1
thermal conductivity tensor l
ik
J
q
= –l · grad T W m
–1
K
–1
residual resistivity r
R
W m
relaxation time tt = l/v
F
s
Lorenz coefficient LL = l/sT V
2
K
–2
Hall coefficient A
H
, R
H
E = r · j + R
H
(B ′ j)m
3
C
–1
thermoelectric force E V
Peltier coefficient P V
Thomson coefficient m, (t )V K
–1
n
2
1–()
n
2
2+()
-------------------
? 2000 by CRC Press LLC
Credits
Material in Section XII was reprinted from the following sources:
D. R. Lide, Ed., CRC Handbook of Chemistry and Physics, 76th ed., Boca Raton, Fla.: CRC Press, 1992:
International System of Units (SI), conversion constants and multipliers (conversion of temperatures), symbols
and terminology for physical and chemical quantities, fundamental physical constants, classification of elec-
tromagnetic radiation.
D. Zwillinger, Ed., CRC Standard Mathematical Tables and Formulae, 30th ed., Boca Raton, Fla.: CRC Press,
1996: Greek alphabet, conversion constants and multipliers (recommended decimal multiples and submultiples,
metric to English, English to metric, general, temperature factors), physical constants, series expansion.
Symbols and Terminology for Physical and Chemical Quantities (continued)
Name Symbol Definition SI unit
Solid State (continued)
work function FF = E
￥
– E
F
J
number density, number concentration n, (p)m
–3
gap energy E
g
J
donor ionization energy E
d
J
acceptor ionization energy E
a
J
Fermi energy E
F
, e
F
J
circular wave vector,
propagation vector
k, q k = 2p/l m
–1
Bloch function u
k
(r) y(r) = u
k
(r) exp(ik · r)m
–3/2
charge density of electrons rr(r) = –ey*(r)y
·
( r)C m
–3
effective mass m*kg
mobility mm = n
drift
/E m
2
V
–1
s
–1
mobility ratio bb = m
n
/m
p
l
diffusion coefficient D dN/dt = –DA(dn/dx)m
2
s
–1
diffusion length LL = m
characteristic (Weiss) temperature f, f
W
K
Curie temperature T
C
K
Néel temperature T
N
K
Dt
? 2000 by CRC Press LLC
