Glossary of Helpful Information
The constants, functions, and relationships provided here are accessable from
anywhere in the world.
- Adiabatic Process
- A thermodynamic process during which no heat is allowed to enter or escape.
- Angstrom (Ao)
- This very small unit of length is usually associated with wavelengths, and is equal to
1 x 10-8 cm.
- ASCII Code
- Astronomical Unit (AU)
- A unit of length used in astronomy equal to the mean distance of the earth from the
sun or about 93 million miles (~ 150 million km).
- AU = 1.496 x 108 km
- Atmosphere (atm.) = 1.01325 x 105Pa = (1.01325 x 105 N/m2) =
76 cm Hg
- Atomic mass unit (amu)
- amu = mu = 1.660 538 73 x 10-27 kg
- Avogadro's number
- The number of molecules in a mole or in a mass in grams of substance equal numerically to
its molecular weight, i.e., 6.0235 x 1023 molecules/mole
- Babylonian Numbers
Babylonian Numbers in Cuniform format
- Black body
- If, for all values of wavelength of the incident radiant energy, all of the energy is
absorbed the body is called a black body.
- Boltzmann's constant (k)
- Thermal energy coefficient = 1.380 6503 x 10-23 Joule K-1(SI Units)
- Thermal energy coefficient = 1.380 6503 x 10-16 erg K-1(cgs Units)
- Boyle's Law
- An empirical law, exact only for an ideal gas, which states that the volume of a gas is
inversely proportional to its pressure at constant temperature. PV = constant
- P1V1 = P2V2
- British Thermal Unit (BTU)
- The amount of heat required to raise the temperature of 1 lb. of water through
1oF. Usually the temperature range is from 60o to 61oF.
It is written BTU. 1 BTU = 252 calories = 778.3 ft-lb. = 1,055 joules.
Catenary curve of hanging string or rope
- A catenary curve is traced out by a perfectly flexible rope or chain when suspended
between two points. The equation of a catenary curve is y = a cosh(x/a). The radius of
curvature at any point along the catenary is y2/a.
- Celsius scale
- Also previously known as Centigrade scale. On the Celsius scale, the temperature of
freezing water is defined as 0oC, and the temperature of water boiling under normal
conditions is defined as 100oC. To convert Fahrenheit readings to Celsius use the
following equation: C = (5/9)(F - 32). Temperature Conversions
- Charles' Law
- An empirical law, exact only for an ideal gas, which states that the volume of a gas is
directly proportional to its temperature at constant pressure. P/T = constant
- V1 / T1 = V2 / T2
- Classification of Animals and Plants
- In taxonomy, organisms are classified into categories called taxa (singular, taxon). A
species is given a name consisting of a species name and a genus (plural, genera) name. For
example, the domesticated dog is categorized into the genus Canis and is given the name
Canis familiaris. Closely related animals are grouped in the same genus. Thus, the wolf,
Canis lupis, and the coyote, Canis latrans, share the same genus with the
domesticated dog. Genera that share related features are grouped in a family. Related families,
in turn, are grouped in orders, which are grouped successively in classes, phyla (singular,
phylum) (or divisions for fungi and plants), and finally, kingdoms. A good way to remember the
classification order of taxa is to recall the phrase "Kings Play Chess On Fine Green Sand," in
which each word gives the first letter of each taxon from kingdom to species.
- Coulomb constant
- K = 1/(4p eo) = 8.988 x 109N-m2
- Curie point (magnetic)
- All ferro-magnetic substances (alloys) have a definite temperature of transition at which
the phenomena of ferro-magnetism disappear and the substances becomes merely paramagnetic. This
transition temperature is called the "Curie Point" and is usually lower than the melting point.
Above the Curie temperature, a ferromagnetic solid is paramagnetic.
- Dalton's law of partial pressures
- The pressure exerted by a mixture of gases is equal to the sum of the separate pressures
which each gas would exert if it alone occupied the whole volume. This fact is expressed in the
- PV = V(p1 + p2 + p3, etc.)
- Degrees of Freedom
- The number of variables (temperature, pressure, and composition) which can be changed
independently without changing the phase or phases of the system.
- Diamagnetic Substances
- Diamagnetic substancs are those which tend to move away from a stronger magnetic field
(weakly repelled). The permeability of a diamagnetic substance is less than unity, which tends
to disperse lines of magnetic flux. i.e., bismuth, beryllium, carbon, silicon, sulfur, zinc,
and others are diamagnetic. (See also, paramagnetic and ferromagnetic substances.)
- A change that light undergoes in passing by the edges of opaque bodies, or through narrow
slits, or in being reflected from ruled surfaces and in which the rays appear to be deflected
and to produce patterns of fringes of parallel light and dark or colored bands. Similar
effects can be produced by other waves such as sound waves.
- The transfer of matter within another solid, liquid or gas. The process has to do with
particles of solids, liquids, or gases intermingling as the result of their spontaneous
movement caused by thermal agitation and in the case of dissolved substances movement from
a region of higher concentration to one of lower concentration. Diffusion in solids is
important for doping semiconductors, surface hardening metals, annealing, and envirnmental
embrittlement. Solid state mechanisms include: vacancy diffusion and interstitial diffusion.
- Diffusion, Steady State
- Fick's 1st Law: J = -D(dC/dx), where J is the flux in g/m2sec, D is the diffusion
coefficient in cm/sec, C is the concentration of diffusing species in g/cm3 and x is
the diffusion path length in cm.
- Diffusion, Transient (Non-Steady State)
- Fick's 2nd Law: dC/dt=d(D*dC/dx)/
- Doppler Effect
- Named for Christian J. Doppler (~ 1905). It has to do with the change in frequency with
which waves, such as sound or light, from a given source reach an observer when the source and
the observer are in motion with respect to each other. The frequency increases or decreases
according to the speed at which the distance inversely decreases or increases between the source
and the observer.
- e = 2.71828 18284 59045 23536
- eccentricity (of an ellipse or astronomical orbit)
- Ratio of the distance between the foci to the length of the major axis. It is used to
measure an ellipse's deviation from circularity and is by definition less than one. The
orbital eccentricity of earth is 0.017 (a perfect circle approaches zero).
- Electron charge
- e = -1.602 176 462 x 10-19 Coulomb (SI Units)
- Electron mass
- me = 9.109 381 88 x 10-31 kg
- A term applied to a mixture of two or more substances which has the lowest melting point.
- Tendency to fracture under cyclic stresses.
- Ferromagnectic substances
- Ferromagnetic substances are strongly attracted by magnetic fields. The permeability of
a ferromagnetic substance is much greater than unity (i.e., 5,000), which tends to greatly
concentrate the lines of flux. Cobalt, Iron and Nickel are examples of ferromagnetic metals.
(See also, diamagnetic and paramagnetic substances.)
- Fibonacci Numbers
- An infinite sequence of integers 1,1,2,3,5,8,13,21,34,... of which the first term is 1 and
each succeeding term is the sum of the two immediately preceding terms. This series was
discovered by the medieval Italian mathematician, Leonardo ("Fibonacci") da Pisa about 1250.
It commonly is found in naturally occurring spiral-shaped patterns of flowers and sea shells.
- The daisy has a double spiraling pattern of florets in it's head. There are 21 spirals in a
clockwise direction and 34 counterclockwise. The daisy's spiral ratio of 21:34 corresponds
to two adjacent Fibonacci numbers, as do the pine cone's 5:8 and the pineapple's 8:13 -- and
the same is true of many other plants with a spiral leaf-growth pattern.
- Fibonacci numbers, besides bearing a curious relationship to botany, also appear to exert
a strange influence on art and architecture. The ratio between any two adjacent Fibonacci
numbers after 3 is 1:1.618. This is the so-called Golden Ratio, or Golden Section, which has
intrigued experts for centuries because of its connection with esthetics. The ratio occurs in
pentagons, circles and decagons -- but is most notable in the Golden
Rectangle, a figure whose two sides bear the magic relationship to each other.
- Rules for generating Fibonacci Numbers: F0 = 0, F1 = 1, Fn + 2 = F
n + 1 + Fn, n >= 0
- Fraunhofer Lines
- The dark absorption lines in the solar spectrum.
- Gas constant
- R = 8.31 J/mole K = 1.99 cal/mole K
- Gibbs energy (G)
- An important function in chemical thermodynamics, defined by G = H - TS, where H is the
enthalpy, S is entropy, and T the thermodynamic temperature, or referred to simply as "free
- Gibbs phase rule
- The statement that at equilibrium, F = C - P + 2, where F = Degrees of Freedom, C = the
number of components, and P = the number of phases.
- Golden Rectangle
- The Golden Rectangle is said to be one of the most visually satisfying of all geometric
forms; for years experts have been finding examples in everything from the edifices of ancient
Greece to art master pieces.
- The dimensions of the sides of a Golden Rectangle are based on the ratio of two adjacent
Fibonacci numbers -- 1:1.618. This is sometimes called the Golden Ratio,
or Golden Section.
Golden Rectangle Construction
- The geometric construction of a Golden Rectangle begins with a square (in green blue),
which is then divided in two equal parts by the dotted line EF. Point F now serves as the
center whose radius is the diagonal FC. An arc of the circle is drawn (CG) and the base
line AD is extended to intersect it. This becomes the base of the rectangle. The new side
HG is now drawn at right angle to the new base, with the line BH brought out to meet it.
The resultant Golden Rectangle has one unusal property: if the original square is taken away,
what remains will still be a Golden Rectangle CDGH. Once again, the ratio of the different
sides of the Golden Rectangle is always, 1 to 1.618. The Golden Rectangle was used in the
Parthenon design as seen in the following figures.
- Graham's law
- The relative ratios of diffusion of gases under the same conditions are inversely
proportional to the square roots of the densities of those gases.
- Gram mole, gram formula weight, gram equivalent
- A mass in grams numerically equal to the molecular weight, formula weight, or chemical
equivalent, respectively. Gram mole = gram molecular weight or gram molecular.
- Gravitational constant: G = 6.670 x 10-11 N-m3/kg2
- Acceleration due to gravity at sea level, lat. 45o: g = 9.806 m/s2
- Greek alphabet
- A; a; alpha (a)
- B; b; beta (b)
- G; g; gamma (g)
- D; d; delta (d)
- E; e; epsilon (e)
- Z; z; zeta (z)
- H; h; eta (h)
- Q; q; theta (q)
- I; i; iota (i)
- K; k; kappa (k)
- L; l; lambda (l)
- M; m; mu (m)
- N; n; nu (n)
- X; x; xi (x)
- O; o; omicron (o)
- P; p; pi (p)
- R; r; rho (r)
- S; s; sigma (s)
- T; t; tau (t)
- U; u; upsilon (u)
- F; f; phi (f)
- C; c; chi (c)
- Y; y; psi (y)
- W; w; omega (w)
- Hall effect
- When a steady current is flowing in a steady magnetic field, electromotive forces are
developed which are at right angles both to the magnetic force and to the current and are
proportional to the product of the intensity of the current, the magnetic force and the sine
of the angle between the directions of these quantities.
- Hardness Conversion Chart
- Helmholz energy (A)
- A thermodynamic function defined as, A = E - TS, where E is the internal energy, S the
entropy, and T the thermodynamic temperature.
- Hyperbolic functions
- sinh x = (ex - e-x)/2
- cosh x = (ex + e-x)/2
- tanh x = sinh x / cosh x
- ctnh x = 1/tanh x
- sech x = 1/cosh x
- csch x = 1/sinh x
- cosh2x - sinh2x = 1
- Index of refraction
- For any substance, this is the ratio of the velocity of light in a vacuum to its velocity
in the substance. It is also the ratio of the sine of the angle of incidence to the sine of the
angle of refraction. In general, the index of refraction for any substance varies with the
wavelength of the refracted light.
- Isothermal Process
- A thermodynamic process in which the temperature is maintained constant.
- Joule is a unit of energy or work. Joule = newton-meter = watt-second = 107 ergs.
- Kepler's Laws
- 1. The orbits of the planets are ellipses with the sun at one focus.
- 2. An imaginery line from a planet to the sun sweeps out equal areas in equal time intervals
whether the planet is close to or far from the sun.
- 3. The ratio of the average radius of a planet's orbit about the sun, r, cubed and the
planet's period, T, (the time for it to travel around the sun once) squared, is a constant for
all planets. This law can be expressed as, r3/T2 = k. Therefore, the ratio of the squares of the periods of revolution of two planets is the
same as the ratio of the cubes of their average distances from the sun, as T12/
T22 = r13/ r23.
- A unit of load equalling 1000 pounds, or 453.59 kilograms.
- kips per square inch = 1000 psi = 6.894 MPa. It is a common English unit of pressure.
- Leaf Identification Forms
- The speed of light in a vacuum (c) = 2.997 925 0 x 108 m s-1(SI Units)
- The speed of light in a vacuum (c) = 2.997 925 0 x 1010 cm s-1(cgs Units)
- Line, Straight
- The straight line equation at data point (x, y) is: y = mx + b
- (where, m = slope, b = intercept)
- Logarithm conversion
- ln x = 2.3026 log x
- log x = 0.4343 ln x
- Mechanical/Heat equivalence
- Mechanical equivalent of heat = 4.185 J/cal
- megapascal = 1,000,000 pascals = 145.03 psi. It is a common metric unit of pressure.
- Unit of conductance; reciprocal of ohm
- An old hardness scale used mainly for testing the hardness of minerals. It has a
range of 10:
- 1. Talc (softest)
- 2. Gypsum
- 3. Calcite
- 4. Fluorite
- 5. Apatite
- 6. Orthoclase
- 7. Quartz
- 8. Topaz
- 9. Corundum
- 10. Diamond (hardest)
- You can remember these ten by using the following odd sentence as a memory device: "The
Girls Can Flirt And Other Queer Things Can Do." Some other common references: fingernail ~ 2.5,
penny ~ 3, window glass or a knife blade ~ 5.5, steel file ~ 6.5
- Molal solution
- Contains one mole per 1000 grams of solvent.
- Molar solution
- Contains one mole or gram molecular weight of the solute in one liter of solution.
- A mass numerically equal to the molecular weight.
- Momentum (p): p = mv
- Moore's Law
- In 1965, Intel's Gordon Moore created a "law" that became shorthand for the rapid growth of
technology. He predicted that the number of transistors on a chip would grow exponentially
- Assemblages of tens to hundreds of atoms or molecules in a space with a diameter of less
than 50 nanometers (a nanometer is about the size of two large atoms or four small ones).
- Newton's Law of Cooling
- The rate of cooling of a body under given conditions is proportional to the temperature
difference between the body and and its surroundings.
- Newton's Laws of Motion
- 1. Inertia (Unless acted upon by an outside force, an object at rest will remain at rest
and an object in motion will remain in motion at the same speed and in the same direction.)
- 2. F = ma (When an outside force acts on an object, the object will accelerate, and the
rate of acceleration will be proportional to the force and inversely proportional to the
- 3. Force = -Force (For every action force there is a reaction force equal in magnitude and
opposite in direction.)
- Occam's Razor
- When choosing between two competing theories to describe a phenomenon, medieval English
scholastic philosopher William Occam (ca. 1337)said, the simplest explanation is the best.
Sure, maybe dachshunds exist on Earth not because of selective breeding but because aliens
brought them here, but why make more assumptions than necessary? (a.k.a. William of Ockham)
- Ohm's Law:
- Current flowing in a conductor varies diectly with the potential
difference (voltage) and inversely with the resistance. (I = V/R) First attributed to Georg
Simon Ohm (1863)
- Paramagnetic Substances
- Paramagnetic substances tend to move into a stronger magnetic field (weakly attracked).
The permeability of a paramagnetic substance is greater than unity, which tends to concentrate
the lines of flux. Aluminum, Chromium, Manganese, Molybdenum, Sodium are some examples of
paramagnetic metals. (See also, diamagnetic and ferromagnetic substances.)
- Pareto Chart
- Histogram chart useful for categorizing a sample or population and identifying the 20%
of the categories that are causing 80% of the problems or activity.
- pc = 3.0856 x 1013 km = 3.2615 LY = 2.06265 x 105 AU
- Peltier Effect
- In 1834, the French physicist, Jean C. Peltier (1785-1845), observed that heat energy was
absorbed at one junction and liberated at the other when a electrical current passed around a
circuit of two dissimilar metal conductors in series. This is basis of the operation of
non-mechanical refrigeration modules. (See also the complementary Seebeck effect.)
- Periodic table
- An arrangement of chemical elements based on the periodic law.
- Permeability of free space
- mo = 4p x 10-7
- Permittivity of free space
- eo = 8.85 x 10-12 C2
/N m2 (farad meter)
- pH and Acid/Base Concentration
- pH = - log10[H+]; molar concentration
- 1 2
3 4 5
8 9 10 11
12 13 14
- Strong Acid
Weak Acid Neutral Weak
Base Strong Base
- Bases turn red-litmus >> blue
turn blue-litmus >> red
- Acid salt: NH4Cl (results from weak base + strong acid)
- Basic salt: NaCN (results from strong base + weak acid)
- Neutral salt: NaCl (results from strong base + strong acid)
- Amphoteric: Capable of reacting chemically either as an acid or as a base.
- p = 3.14159 26535 89793 23846
- Pilot's Phonetic Alphabet
- A ~ Alpha
- B ~ Bravo
- C ~ Charlie
- D ~ Delta
- E ~ Echo
- F ~ Foxtrot
- G ~ Golf
- H ~ Hotel
- I ~ India
- J ~ Juliet
- K ~ Kilo
- L ~ Lima
- M ~ Mike
- N ~ November
- O ~ Oscar
- P ~ Papa
- Q ~ Quebec
- R ~ Romeo
- S ~ Sierra
- T ~ Tango
- U ~ Uniform
- V ~ Victor
- W ~ Whiskey
- X ~ X-ray
- Y ~ Yankee
- Z ~ Zulu
- Planck's constant (h)
- h = 6.626 196 x 10-34 joule sec (SI Units) = 4.136 x 10-15 eV sec
- h = 6.626 196 x 10-27 erg sec (cgs Units)
- 1 atm = 760 mm Hg = 14.70 lb/in = 101,325 Pa = 1.01325 bar
- Prime Numbers
- Prime numbers are numbers which cannot be evenly divided except by themselves or by 1.
They are useful
- in number theory. The following is a list of 168 prime numbers that can be found between 1
- 2 3 5 7
11 13 17 19 23 29
31 37 41 43 47
53 59 61 67 71
- 73 79 83 89 97 101
103 107 109 113 127 131 137 139
149 151 157 163 167 173
- 179 181 191 193 197 199 211 223
227 229 233 239 241 251 257 263 269
271 277 281
- 283 293 307 311 313 317 331 337
347 349 353 359 367 373 379 383 389
397 401 409
- 419 421 431 433 439 443 449 457
461 463 467 479 487 491 499 503 509
521 523 541
- 547 557 563 569 571 577 587 593
599 601 607 613 617 619 631 641 643
647 653 659
- 661 673 677 683 691 701 709 719
727 733 739 743 751 757 761 769 773
787 797 809
- 811 821 823 827 829 839 853 857
859 863 877 881 883 887 907 911 919
929 937 941
- 947 953 967 971 977 983 991 997
- Proton mass
- mp = 1836me = 1.672 621 58 x 10-27 kg
- Quadratic equations
- Any of several elementary particles that are postulated to come in pairs (as in the up and
down varieties)of similar mass with one member having a charge of + 2/3 and the other a charge
of - 1/3 and are held to make up hadrons. In about 1964, the term quark was coined by Murray
- 1 radian = 57.29577 95131 degrees
- Rydberg constant
- RINFINITY = 10 973 731.568 549 m-1
- Seebeck Effect
- The effect by which an electromotive force (voltage) is developed in a closed circuit
consisting of conductors of dissimilar metals in series whose junction points are maintained
at different temperatures. Such a device is known as a thermocouple, and the cold junction is
usually maintained at 0oC. Iron-constantan, chromel-alumel, and platinum-rhodium
are typical metal pairings for thermocouples. The effect was discovered in 1822 by Thomas
Johann Seebeck (1770-1831). (See also the complementary Peltier effect.)
- Snell's Law
- The relation between the angle of incidence i and the angle of reflection r of a light beam
which passes from a medium of refractive index no to a medium of index ni :
sin i / sin r = ni / no
- Solar constant
- Solar constant (radiation from sun at earth's mean distance) = 1.35 kw/m2
- Speed of sound in air at STP = 331 m/s
- Specific Heat
- q = m c(T2 - T1)
- where, q is the heat absorbed by the material object , m is the mass of the object,
(T2 - T1) is the change in temperature, and c is the specific heat of the
- Surface Area of sphere = 4pR2 = 12.5663R2
- Surface Area of sphere = pD2
- Volume of sphere = (4/3)pR3 = 4.1888R3
- Volume of sphere = (1/6)pD3
- Standard Deviations
- 1s = 68.268% of area under normal curve
- 2s = 95.45% of area under normal curve
- 3s = 99.73% of area under normal curve
- Stefan's Law of Radiation
- The rate at which energy is radiated from a hot body is proportional to the fourth power
of the body's absolute temperature.
- Temperature Conversions
- First Law of Thermodynamics: The total increase in the thermal energy of a system is the
sum of the work done on it and the heat added to it.
- Second Law of Thermodynamics: Heat flows from an area of high temperature to an
area of low temperature: natural processes go in the direction that increases the
total entropy of the universe. Where entropy is the disorder in a system.
- Trigonometry Functions
- tan x = opposite/adjacent = 1/cot x
- cot x = adjacent/opposite = 1/tan x
- sin x = opposite/hypotenuse = 1/csc x
- cos x = adjacent/hypotenuse = 1/sec x
- sec x = hypotenuse/adjacent = 1/cos x
- csc x = hypotenuse/opposite = 1/sin x
- Law of Cosines (any triangle): c2 = a2 + b2 - 2ab cos C.
- Law of Sines (any triangle): a/sin A = b/sin B = c/sin C.
- sin2A + cos2A = 1
- tan2A + 1 = sec2A
- 1 + cot2A = csc2A
- sin(A ± B) = sin A cos B ± cos A sin B
- cos(A +/- B) = cos A cos B -/+ sin A sin B
- 2sin A cos B = sin(A + B) + sin(A - B)
- 2sin A sin B = cos(A - B) - cos(A + B)
- 2cos A cos B = cos(A + B) + cos(A - B)
- sin2A = 2sin A cos A
- cos2A = cos2A - sin2A
- sin x = (1/2i)(eix - e-ix), i = +(-1)1/2,
- cos x = (1/2)(eix + e-ix)
- eix = cos x + i sin x
- Ultimate strength
- The maximum stress (tensile, compression, or shear) a material can sustain without
fracture; determined by dividing maximum load by the original cross-sectional area of the
specimen. Also known as nominal strength or maximum strength.
- Volume per gram mole of ideal gas at STP = 22.4 liters
- Heat of fusion of ice = 79.7 cal/g = 3.34 x 105 J/kg
- Heat of vaporization of water at STP = 539.6 cal/g = 2.26 x 106 J/kg
- l = 1/frequency(Hz)
- Widmanstätten structure
- The structure is characterized by a geometrical pattern resembling a basketweave.
It was first observed in meteorites, but is readily produced in many alloys, such as
titanium, by appropriate heat treatment. The pattern results from the formation of a new
phase along certain crystallographic planes of the parent solid solution. The orientation
of the lattice in the new phase is related crystallographically to the orientation of the
lattice in the parent phase.
Iron Meteorite with Widmanstätten Pattern
- Year, Sidereal
- The time in which the earth completes one revolution in its orbit around the sun measured
with respect to the fixed stars: 365 days, 6 hours, 9 minutes, and 9.5 seconds of mean time.
- Year, Tropical
- Period of revolution of the earth about the sun with respect to the vernal equinox:
365.24 days = 3.1556925 x 107 secs
- Yield strength
- The stress at which a material exhibits a specified deviation from proportionality of
stress and strain. An offset of 0.2% is most commonly used when testing metals.
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