This page contains a collection of facts and rules, necessary for making ecological estimates and calculations. Print it out for your convenience when studying the topics on this web site.
-- home -- Revised frequently: 20010412,20010830,20020110,20041110,20060901,
Prefixes
| power of ten | 24 | 21 | 18 | 15 | 12 | 9 | 6 | 3 | 2 | 1 |
| prefix | Y | Z | E | P | T | G | M | k | h | da |
| name | yotta | zetta | exa | peta | tera | giga | mega | kilo | hecto | deka |
| power of ten | -24 | -21 | -18 | -15 | -12 | -9 | -6 | -3 | -2 | -1 |
| prefix | y | z | a | f | p | n | µ | m | c | d |
| name | yocto | zepto | atto | femto | pico | nano | micro | milli | centi | deci |
In computing, the K unit is used for 210=1024 instead of 1000. Here are the new conventions:
| power of two | 10 | 20 | 30 | 40 | 50 | 60 |
| approximate
power of ten |
3 | 6 | 9 | 12 | 15 | 18 |
| prefix | Ki | Mi | Gi | Ti | Pi | Ei |
| name | kibi | mebi | gibi | tebi | pebi | exbi |
Basic SI units
| Physical quantity
length mass time temperature electric current luminous intensity amount of substance |
Unit
metre kilogram second Kelvin Ampere candela mole |
Symbol
m kg s ºK A cd mol |
Derived SI units
| Physical quantity
concentration
|
Unit
mole per cubic metre
|
Named after
-
|
Symbol
mol /m3
|
Definition
-
|
Russ Rowlett of the University
of Carolina has a very extensive web site about this.
The International Bureau of Standards
in Paris also has an extensive web site. Bureau International des Poids
et Mesure.
A very precise unit
converter converts one unit into another.
Note! On the Seafriends web site, the powers of ten are often
written as 1E6 rather than 10^6 or 106.
15000 = 15E3 = 1.5E4
Units are spelled the English way: metres rather than meters. Formulas
are spelled out like e = m x c x c, rather
than e=mc2.
In scientific literature it is conventional to spell m/s as
m
s-1 , but this is not followed in this
web site.
1 billion (American) = 1,000,000,000 = 1 thousand millions = 1E9
1 trillion (American) = 1 million millions = 1E12
1 quadrillion (American) = 1 thousand millions = 1E15
1 billion (European) = 1 million millions = 1E12
1 trillion (European) = 1 million million millions = 1E18
1 order of magnitude = 10 x
to decimate originally means, to take 10% (= x 0.9), but is often used
as meaning to leave 10% (= x 0.1).
Magic numbers and ratios
One (1): One is perhaps the most beautiful number of all; the
number of symmetry. Figures drawn with an aspect ratio of one, are all
perfectly symmetric: the circle, square, polygons, stars and so on. It
is the only number for which n / 1 = 1 / n and n = n0
= n1 = nn = nm.
Square root of two: The international paper size A0, A1, A2,
A3, A4, A5, ... series was designed such that an A0 sized sheet cut in
half, would produce two A1 sheets of equal size and equal ratio between
height and width (=aspect). There is only one mathematical number that
has this property: the square root of 2. SQR(2) = 1.4142.
In this series of paper sizes, the height/width ratio is SQR(2). When cut
in half, becomes SQR(2) / 2 = SQR(2) / (SQR(2) * SQR (2)) = 1 / SQR(2).
Thus the ratio remains identical, although the cut sheets need to be turned
ninety degrees.
This is the only number/ratio which inverses when divided by two:
1 / n = n / 2 thus n x n = 2 or n = SQR( 2 )
Golden section: the division of a number so that the whole is
to the greater part as that part is to the smaller part. It is also called
the divine proportion, first defined by Euclid, and is used by architects
in designing buildings (first used for the Parthenon). 1.61803 to
1 or 1 to 0.61803. A rectangle with these proportions is called
a golden rectangle and is thought to be more pleasing to the eye. It is
calculated by solving the equation 1 / n = n + 1 or
n2 + n - 1 = 0
The golden section can directly be calculated as: (1 + SQR(5)) / 2
(see mathematics refresher below)
Graphically it is drawn as follows: First draw a square ABCD. Then,
find the midpoint M of side AB. Next, use a compass to extend AB to a point
E so that ME = MC. Rectangle AEFD is a golden rectangle. To divide
AB according to the golden section, use a compass to find a point G on
AE so that EF = EG.
Two (2): The lowest number that makes counting and arithmetic possible. The only number for which n x n = n + n = nn . It is the number that stands for duplication, replication and redundancy. A rectangle with aspect of two, becomes a smaller rectangle with the same ratio when folded or halved twice.
Natural number or natural logarithm: e = 2.71828
.
e is calculated by the series : e = 1 + 1/1 + 1/2 + 1/(2x3)
+ 1/(2x3x4) + .... + 1/(2x3x4x..n) ... to infinity.
The natural logarithm is an important number for mathematics, especially
when relating to physical quantities. Many formulas have been derived with
it.
e is also related to the most compact notation for information.
Where we use the digital (0-9) number system and computers the binary (0-1)
number system, the value system based on e expresses information in the
most compact way, although it is continuous and not discrete (consisting
of steps). Throughout the universe, e is an important quantity.
Pi: the ratio of circumference to the diameter of a circle 3.14159...
The number obtained by dividing 22 by 7 22/7=3.1428571.. is almost the
same, but slightly larger. Pi can be calculated exactly as follows:
pi / 2 = 2/1 x 2/3 x 4/3 x 4/5 x 6/5 x 6/7 x ..... x (n+1)/n x n/(n+1)
. (John Wallis series), or by a shorter series, which converges more slowly:
pi / 4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 .... (Leibniz series (1673),
also discovered by James Gregory (1671))
Aspect ratios of various images:
1.3333 or 4/3 the television frame, Super-8 film and 16mm film
formats. Thought to be the ideal proportion matching our eyesight. Modern
digital widescreen format is 4x4/3x3= 16/9.
1.5 or 3/2 the 35mm format for both movies (across) and still
pictures (along, 36/24 mm). Other film formats: 6/4 cm, 9/6 cm,
? Cinemascope
Perfect numbers
A number is called perfect, if the sum of its factors adds up to the
number itself, like: 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14. There are
only four such perfect numbers: 6; 28; 496; 8128. (Nichomachus Gerasa,
100 AD). The 6th and 7th are: 8,859,869,056 and 137,438,691,328
(Pietro Cataldi, 1603) What is the fifth perfect number?
Angles
A circle is 360 degrees = 2 x pi radians
One degree = 60 minutes = 60 arcminutes
One minute = 1 arcminute = 60 secondes = 60 arcseconds
1 minute over a meridian = 1 nautical mile = 1.852 km
Density
Density or specific weight is a ratio between weight and volume. Traditionally
gram / cubic centimetre = kg / litre
or ton/m3. Multiply by 27.7 to get lb/in3, and by 1.33 to get ton/yd3.
The density of clean water is defined as 1.000. A rock with density
2.80 weighs 2800 kg / cubic metre = 2.8 t / m3
Density of air at the surface is 0.00013
Densest substance on Earth is iridium 22.5, followed by osmium 22.4,
platinum 21.4, rhenium 21.0, neptunium 20.4, plutonium 19.8, gold 19.3,
tungsten 19.3, uranium 18.9, ... mercury 13.53, ... lead 11.4, ... iron
7.86, ....
Averages
The arithmetic average of a, b, c = (a + b + c ) / 3
The geometric average of a,b,c = (a x b x c ) / 3
An arithmetic series is: a + (a+d) + (a+2d) + (a+3d) + ....
A geometric series is: a + (a x r) + (a x r x r) + ...
An exponential series is: ex = 1 + x + ( x2 )
/ ( 1 x 2 ) + ( x3 )/ (1 x 2 x 3 ) + ... ( xn ) /
n!
A logarithmic series is: ln(1+x) = x - (x2) / 2 + (x3)
/ 4 - (x4) / 4 + ...
| Beer's Law and Lambert's Law
When a quantity changes continually with a fixed rate of change, it follows either exponential growth or logarithmic decay, depending on whether the factor is larger or smaller than one. Example: 1,2,4,8,16,32,64,128,256,... is exponential growth with a fixed factor of 2. Example: 256,128,64,32,16,... is logarithmic decay with a fixed factor of 0.5. Examples from the natural world are: absorption of light/sound by a medium, radio active decay. The difference between Beer and Lambert is that the first was concerned with the density of the medium, whereas the second was concerned with the distance travelled through the medium. Both concerns are captured in the same formula: Id = I0 x e x x d or ln( Id / I0 ) = x x dFor the 1,2,4,8 series above, x can be calculated from the rate of change = 2: 2 = 1 x e x x 1 or x = ln(2) = 0.693. Likewise, x = -0.693 for the 256,128,64,.. series. |
Bel and decibel
Originally used for measuring sound amplitudes, the bel and decibel
are also used for measuring amplification and abatement. The Bel unit is
named after the inventor of the telephone, Alexander Graham Bell (1847-1922).
One Bell louder means ten times louder, measured by amplitude.
1 bel = 1 B = log ( I / I0 ) = 10 decibels ; where
I
= current intensity and I0 is previous intensity, or a sound level
of 2E-10 bar.
1 decibel = 1 dB = 10 x log( I / I0 )
The range of human hearing extends from 0 - 120 dB, at which level sound
becomes painful, while also causing permanent deafness. The critical level
for the start of ear damage is 85 dB. Conversation: 30-60 dB; jet plane
160 dB; Noise from trucks can exceed 80 dB measured at the roadside.
People begin to complain when sound levels in their neighbourhood reach
35-40 dB.
Mathematical series
This section contains the various mathematical series important to
nature.
Fibonacci: Leonardo Fibonacci (1175-1250), was an Italian mathematician
who helped introduce the Hindu-Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7,
8, 9) into western Europe, particularly the zero. He is also known
as the originator of a special series of numbers, now called the Fibonacci
sequence or the Fibonacci numbers.
1, (1+1=2), (1+2=3), (2+3=5), (3+5=8), (5+8=13), .....
Natural logarithm, e: e = 1 + 1/1 + 1/(1x2) + 1/(2x3x4) + 1/(2x3x4x5) + ....
Organisms; weight m in kg.
Basal Metabolic Rate of an organism, related to weight: P = 73.3 x
m ^ 0.75 (kcal/day), where m= kg.
Mammal brain weight, excluding apes & humans = 0.01 x m ^ 0.70
(kg)
Ape brain weight = (0.03-0.04) x m ^ 0.66 (kg)
Life span (not humans nor birds) = 11.8 x m ^ 0.20 (years)
Life span for birds = 28.3 x m ^ 0.19 (years)
Humans; weight m in kg.
Heart weight = 0.005.8 * m ^ 0.98 (kg)
Lung weight = 0.0113 x m ^ 0.98 (kg) about twice the weigh of
the heart.
Brain weight = 0.085 x m ^ 0.66 (kg)
Tidal volume = 7.69 x m ^ 1.04 (ml)
Vital capacity = 56.7 x m ^ 1.03 (ml)
Blood volume = 65.6 x m ^ 1.02 (ml)
Muscle mass = 0.40 x m ^ 1.00 (kg)
Skeletal mass = 0.0608 x m ^ 1.08 (kg)
Heart rate = 241 x m ^ -0.25 (beats/min) Note: heart rate
decreases with weight
Blood circulation time = 17.4 x m ^ 0.25 (seconds)
Respiratory rate = 53.5 x m ^ -0.26 (per min) Respiratory rate
decreases with weight.
Oxygen consumption = 1.94 x m ^ 0.79 (ml/s)
Glucose turnover = 5.59 x m ^ 0.75
Impact damage
Nuclear weapon (power in Mt) area of destruction = 400 x (Mt) ^ 0.67
(km2). (Steel, 1995)
Thus a bomb of 10 Mt TNT destroys 1870 km2, equal
to an asteroid of 25m radius, density 3 and speed 20,000m/s.
Asteroid impact energy for radius r (m), speed v (m/s),
density d = (5.0E-13) x r ^3 x v ^2 x d (Mt
TNT)
Geological time
See Geologic Time Table.
Frequency
1 hertz = 1 Hz = 1/s (per second) = 1 c/s (cycles/second) = 2 x pi
rad/s = 6.28318 rad/s
1 revolution per minute (rpm) = 0.105 rad/s
unit of (radioactive) activity = Becquerel = 1 Bq = 1/s (per second)
1 Curie = 1 Ci = 3.7E10 Bq
degrees Celsius = degrees Kelvin - 273.16 = (5 / 9) x (degrees Fahrenheit
- 32)
degrees Fahrenheit = (9 / 5) x degrees C + 32
0 ºK = -273.15 ºC
Gas constant = 8.317 J/mol/ºK, amount of heat to warm up a gas
Temperature of sun's surface = 6000K of its interior = 15,000,000 K
If the sun was burning coal, it would have burnt up in 1500 years.
Area
1 m2 = 10.76 ft2
= 1.196 yd2
1 km2 = 1000000 m2
= 100 hectares (ha) = 247.1 acres = 0.3861 mi2
1 square nautical mile = 3.4299 km2
1 square mile = 2.59 km2
1 are = 100 m2
1 hectare (ha) = 10,000 m2 = 0.01 km2
1 square inch (in2) = 6.45 cm2
1 square foot (ft2) = 929 cm2 = 0.0929 m2
1 perch = 25.3 m2
1 acre = 0.405 ha = 4050 m2
1 rood (rd) = 0.101 ha
Volume
1 litre (l) = 1000 cm3 = 33.81 fluid
ounces = 1.057 US quarts
1 fluid ounce = 29.57353 ml (USA) = 28.4 ml (Imperial)
1 cu ft = 0.0283 m3; 1 in3 = 16.4 cm3; 1 yd3= 0.765 m3
1 Imperial pint = 0.5682 l
1 Imperial gallon = 1.2009 US gallons = 4.5461 litre
1 US gallon = 0.8327 Imperial gallon = 3.7854 litre
1 m3 = 1000 l = 35.31 ft3
= 264.2 US gallons = 6.290 barrels
1 acre foot = 1230 m3 =43,560 cu ft
1 bushel (US) = 1 bu = 8 (Imperial?) gallon = 35.23907 litre
1 wheat bushel (US) = 60 pound = 27.216 kg. Barley bushel = 48 pound
= 21.772 kg. Oats bu = 32 pound = 14.515 kg
1 rye bu = 56 pound = 25.401 kg.
Volume of one mole of a chemical substance at surface temp & pressure = 22.414 litre/mol = 6.0249E23 molecules
Oil quantities and measurements
1 m3 = 6.29 barrels
(6.7 barrels/tonne for crude oil; 8.5 for motor spirits; avg 7.3)
1 tonne crude oil = 7.3 barrels average = 256 Imp gall = 301 US gall
1 barrel per day = 50 tonnes oil / yr (average)
1 barrel = 34.97 Imperial gallons = 42.00 US gallons = 159.0 l
1 km3 = 1E9 m3 = 0.2399 mi3 = 810600 acre-feet
1 mile-per-gallon US (mpg) = 0.4251 km/l kilometres-per-litre. 50mpg = 21.26 km/l
1 mile-per-gallon IMPERIAL (mpg) = 0.3541 km/l kilometres-per-litre. 50mpg = 17.71 km/l
Sulfur content of gasoline is approximately 350 ppm.Gas quantities and measurements
1 Tcf= 1 Trillion-cubic-foot (USA)= 1E12 cuft = 2.83E10 m3
1 mole of an ideal gas = 22.4136 litre @ 0º C = 24.4651 l @ 25ºC
Geometry
pi = 3.14159
Circumference of a circle = 2 x pi x r, where
pi
= 3.14159 and r = radius
Area of a circle = pi x r x r.
Area of an ellipse with axes a and b = pi x a
x b
Surface area of a sphere = 4 x pi x r x r
Volume of a sphere = 4/3 x pi x r x r x
r
Volume of a cone with height h and base radius r = pi x h
x r x
r / 3
Volume of a pyramid with base area b and height h: = h x b
/ 3
Surface area of a triangle with base b and height h =
b
x h / 2
Area of a regular pentagon with side a, = 1.721 x a x
a.
Hexagon = 2.598 x a x a. Octagon = 4.828 x
a
x a
Area of a trapezium with parallel sides a and b and height
h
= 0.5 x ( a + b ) x h
The distance between two points (x1,y1) and (x2,y2) = SQR( (x2 - x1)2
+ (y2 - y1)2 )
Equation or formula for a parabola: y2 = 4
x a x x, where a = focus
Equation for an ellipse: x2 / a2
+ y2 / b2 = 1
Equation for a hyperbola: x2 / a2-
y2
/ b2 = 1
World dimensions
Radius: equatorial = 6378.163 km. polar = 6356.177 km
Circumference: equatorial = 40074 km. polar = 39942 km
Mean elevation of continents = 800 m (840m). Mean depth of oceans =
3800m (3729m*, 3730m, 3795m). Contains 97% of all water (not ice).
Total surface = 510.1E6 km2. Surface of oceans = 361.3E6 km2
(70.8%)
Mixed surface layer avg depth= 75m. Mixed layer volume=
Surface area of ice-free land = 133E6 km2 Productive land 88E6
km2 = 8.8 Gha.(66%). Sea ice= 33E6km2.
Continents & Islands: 148.8E6 km2. Eurasia= 0.536E14 m2. Africa=
0.298E14 m2. N-America + Central= 0.238E14 m2. S America= 0.179E14 m2.
Antarctica= 0.149E14 m2. Oceania= 0.089E14m2.
Volume of the earth = 1.083E12 km3 *) see formula above.
Average density = 5.518. Internal temperature estimated at 5000ºK
Mass of the earth = 5.976E24 kg. Mass of the oceans = 1.35E21 kg =
1.350E9 km3 *
Mass of ice caps and glaciers = 2.9E19 kg. Mass of lakes and
streams = 1.3E17 kg. Mass of water in atmosphere= 1.3E16 kg.
Mass of the atmosphere = 5.2E18 kg (5.14E18). Mass of N2
in atmosphere 3.95E18 kg.
Mass of all organisms (wet weight) = 5E15 kg= 1.3E15 kg dry weight.
* Turekian, Karl K (1968): Oceans. Prentice-Hall.
Cosmic dimensions
Mean distance to sun = 149.6E6 km = 497 s = 8.28 minutes
Mean distance to moon = 384,000 km = 3.84E8 m = 1.3 light-seconds
Geostationary orbit = 35,900 km from surface = 42,200 km from earth's
centre (?)
Mass of moon = 7.4E22 kg
Mass of Earth = 600E22 kg.
Diameter of the sun = 109 x Earth's =1,380,000 km = 864,000 km
Mass of sun = 330,000 x mass of Earth = 200E26 kg ?
Each second, the sun turns 700 million tonnes of hydrogen into 695
million tons of helium. The difference is radiated out.
The sun rotates around its axis in 27 days.
Sunspot cycles: 11 and 22 years. The more sunspots, the less energy
reaches Earth (0.3% max variation; UV 30%). Year 2002 = year of maximum
sunspots.
In 200 million years, the sun completes an orbit around the centre
of the milky way
The moon does 12 cycles around the Earth in 354 days
Velocity of light in vacuum (Einstein's constant), c = 2.9979E8
m/s (approx 300,000 km/s)
1 light year = 9.454E12 km
Speed, velocity, flow
1 knot = 0.5144 m/s = 1.852 km/hr =1.151 mi/hr
1 mile per hour (mph) = 1.61 km/h = 0.447 m/s
1 cfs (cubic foot per second) = 448.9 gal/min = 8.931E5 m^3/yr = 724.0
acre-ft/yr
Speed of sound in dry air = 331 m/s
Speed of sound in the ocean is between 1450 and 1570 m/s.
Speed of sound increases 1.3 m/s for each 0.1% increase
in salinity and increases also 0.17 m/s for each bar or 10 m depth
Escape velocity from Earth = 11.2 km/s. For orbital velocities see oceans/currents/atmosphere
dynamic viscosity : 1 Poise = 100 cP = 100 m Pa s
kinematic viscosity: 1 Stokes = 100 cSt = 1 cm2 /s = 1E-4
m2 /s
Ocean currents: 1 Sv = 1E6 m3/s
|
[from Karl K Turekian (1968) Oceans. Prentice-Hall] How fast does a small particle sink?
velocity v = [ D x D x ( dp - df
) x g ] / [ 18 x p ] cm/s
See also Heezen& Hollister's diagram of current velocities
for erosion, transportation and sedimentation, oceano/soil51.gif
|
1 bar = 1E5 Pa = 1E5 N/m2 = 10.20 t/m2
= 0.9869 atmosphere = 750 torr
1 atmosphere = 1.013 bar = 14.7 lb/in2
= 76.0 cm of mercury = 1.013E6 dyne/cm/cm = 1013 kPa
1 inch of mercury (inHg) = 33.9 mb = 3.390 Pa
1 torr = 1mm mercury = 1.333 mbar
1 ton/in2 = 15.4 MPa
1 pound/acre = 1.12085 kg/ha
1 pound/in2 (psi) = 1 lbf/in2 = 6895 Pa =6.805E-2 atm = 51.71 mm Hg
= 6.859E-2 bar
1 atomic unit of mass = 1 u = 1.66043E-27 kg
Mass of proton = 1.672614E-27 kg
Mass of neutron = 1.674920E-27 kg
Mass of electron = 9.109558E-31 kg
Standard acceleration of free fall on Earth = 9.80665 m/s/s
Universal gravitational constant G = 6.672E-11 N m2 /kg2
(in calculating the attraction between two masses)
Atmosphere at sea level: mass density = 1.225 kg/m3. Pressure
= 1.01325 bar
Molecules/litre = 2.547E22. Average temperature = 15.0 ºC
Molecular weight of air = 28.96 g/mole. Oxygen = 2 x 16 = 32.
Nitrogen = 2 x 14 = 28.
Centripetal acceleration c = - (m x v x v
) / r , where v = velocity, m = mass and r = radius. (m/s/s)
Gravity attraction of Earth (free fall acceleration) c = ( G
x mE ) / r x r , where G= gravitational constant,
mE= mass of Earth
c= (6.67E-11 x 6E24 ) / r x r = 400E12 / r x r
(attraction of 1 kg by Earth's gravity)
for each orbit, the two above must balance : 400E12
/ (r x r) = v x v / r , thus v = SQR(400E12/ r)
1 litre gasoline = 35.2E6 J = 8413 kcal.
1 kiloton of TNT explosives = 4.2E12 J; 1 ton TNT = 4.2E9J;
1kg TNT = 4.2E6 J (Ehrlich, 1977)
1 tonne of coal = 8000 kWh = 28.8 GJ (Average coal burns at 28.8 MJ/kg)
Combution of dry biomass = 15-30 kJ/g
| A small car example: a small
motor car's engine is about 40 kW energy output = 40 kJ/s = 40 x 1.341
= 53.6 Hp
In one hour (=3600 s), this car can produce 3600 x 40 kJ = 144000 kJ = 144E6 J = 144/4.2E6, equal to 34.2 kg of TNT explosives. An internal combustion motor of this capacity uses about 10 litre fuel per hour (352E6 J), travelling at 120 km/hr (at 32 KW): An internal combustion motor runs at near 30% efficiency, requiring an amount of fuel equal to 3x its energy output. The energy content of gasoline is about 46 MJ/kg or about 37 MJ/litre. The car above would have consumed 144 x 3 MJ = 11.7 litres. |
| Energy statistics relating to
the airplane attack on the World Trade Centre in New York, 11 September
2001:
Towers: 410m tall; total weight 1.25 Mt; Collapse energy = 0.5 x 410 x 1.25E9 x 9.8= 2.5E12 J = 597 t TNT (Sci-Am: 500t ). Fuel: Boeing 767 fuel capaciry 23,980 Gall (USA) = 90,800 litres = 2.7E12 J = 640 t TNT; Together 1280t TNT (Sci-Am: 1170 t) Impact: direct explosion 3000 gall = 180 t TNT; fire afterwards 990 t TNT. Takeoff weight of airplane 412,000 lb = 187 t. Typical cruising speed: 530 mph = 853 km/h = 237 m/s. Kinetic energy of each plane : 0.5 x 187000 x 237 x 237 = 5.2E9 J = 1.24t TNT; Together 2.5 ton TNT (Sci-Am: 2 t). By comparison: Tomahawk cruise missile = 0.5 t TNT; Hiroshima bomb = 20,000 t TNT; a typical tornado = 5,100 t TNT. (Source: Scientific American Nov 2001 p 10) Note that Sci-Am arrives at slightly different values for energy equivalents. |
Solar energy striking top of atmosphere = 1.72E17 W. Solar energy reaching
surface = 8.6E16 W
Solar energy per m2 on outside of atmosphere: average 1.360 kW/m2;
1.406 in June solstice and 1.314 in December solstice.
Evaporation of water = 4.13E15 W. Gross photosynthesis = 2E14
W.
Global gross primary production (V Smil) 1E14 W.
A modern power station = 1 million kW = 1 GW = 1E9 J/s = 1 GJ/s = 1000
MJ/s
This power station consumes 375 tonnes of coal per hour or 3 million
kW. Total generating efficiency is about 30%
Total electricity generating power of the USA = 8.3E11 W = 8.3E5 MW
= 8.3E5 MJ/s. Per year =
United Kingdom consumes an amount of energy equal to 330 million tonnes
of coal/ year = 2.64E12 kWh = 9.5E18 J
Theoretical amount of energy from uranium U-235 burner-type fission
= 79E12 J/kg (2,700,000 x coal), but these reactors run at 1-2% fuel utilisation
(50,000 x coal). A breeder-type of fission can run at 40-70% fuel utilisation
(1,500,000 x coal).
Because Uranium ore contains about 0.2% U3O8 ore, 1 kg of uranium-containing
ore produces as much energy as 100 kg of coal in a standard fission reactor.
Daily intake of a well-nourished Westerner = 3 kWh = 10.8 MJ
Maximum daily output of a manual worker = 0.5 kWh = 1.8 MJ
Work output of a horse in an 8-hour day = 12 kWh = 43.2 MJ
| Energy statistics for 1975
Energy to feed 1 person for 1 day (2400 food calories) Nonfood energy use per person per day, world average Nonfood energy use per person per day, USA average 1 tank of gasoline (15 USgal = 56.8 litre) 1 barrel of oil (42 USgal = 158.9 litre) 1 metric ton of coal (= 1000 kg), average Boeing 707 flight, San Francisco - New York
Total human non-food energy use per day
|
Energy MJ
10 200 1,000 2,000 5,900 29,000 1,400,000
800,000,000,000
|
Energy densities of various fuels and
food
|
Typical energy costs of common materials
(MJ/Kg)
|
1 tonne of coal = 0.585 tonnes of petroleum = 7400 kWh = 708 m3 natural gas = 1430 m3 town gas
1 tonne of petroleum = 1.7 tonne coal = 12500 kWh = 1189 m3 natural gas = 2450 m3 town gas
1 tonne coal = 1.0 t brown coal NZ = 2.0-3.0 t brown coal elsewhere = 2.0 t peat = 0.77 t crude oil = 0.66 t petroleum products = 750 t natural gas = 8000 kWh (United Nations statistics)
1 tonne oil = 1.5 t coal = 4.9 t lignite = 3.3 t peat = 1167 m3 natural gas = 12000 kWh (British Petroleum statistics)
1 tonne tropical topsoil @ 1.45% Cn = 14.5 kg carbon. 1 tonne loam soil @ 3-7% C = 30-70 kg C.
About 735 joules of energy are required to lift 15 kg of oil 5 meters out of the ground just to overcome gravity.
Energy conversion
Potential energy E = m x h x g
(J) where m = mass (kg) and h = height (m) and g=
9.81 = acceleration of gravity
Kinetic energy E = 0.5 x m x v x v
where m= mass and v = velocity
Converting mass to energy: E = m x c x c
where m = mass and c = speed of light
1 g of matter = 9E13 J = 25 GWh
1 atomic unit of mass = 1 u = 1.49E-10 J= 931 MeV
1 electron = 0.000549 u = 0.510 MeV
Electrical noise power P = k x T x B watt,
where k = Boltzman's constant, T = temperature ºK and
B
= bandwidth (hz)
To photosynthesise 1 kg of carbon, 4.77E8 J in potential energy is obtained,
= 1.14E8 cal.
per gram of carbohydrate: 15.9kJ= 3.8 kcal.
To electrolyse 1 mole of a substance, 96,500 Coulombs of electricity
are required for each of its valence.
e.g. 96,500 Coulombs to electrolyse 1 mole of copper
(Cu++) = 63.54 deposits 31.77 gram.
Heat
Heat is the energy passed from one substance to another. Heat capacity
= specific heat = heat storage (per kg per degree)
Heat of fusion of water (melting energy) at 0 ºC = 79.71 cal/g
= 333.52 J/g
Heat of vaporization of water (evaporation energy) at 100 ºC =
539.55 cal/g = 2256 j/g
Latent heat of evaporation at 10ºC ? = 2.5E6 J/kg
Specific heat of water = 1.000 = calories to warm 1 g by 1 ºC
= 1.000 cal = 4.184 J
Specific heat of sea water at 3.5% salinity = 0.932 cal = 3899 J/kg/ºC
(roughly 4000) [density = 1000kg/m3]
Specific heat of rock = 800 J/kg/ºC (about 5 times less
than water). [density is 3000kg/m3]
Specific heat of air = 1030 J/kg/ºC [density is 1.3 kg/m3]
Oceans exchange heat to a depth of 100m, whereas rocks don't. This
makes the ocean store 100 times more heat than the land.
Energy radiation
1 Gray (Gy) = 1 J/kg
1 rad = 10 mGy = 1E-7 J absorbed per gram of material.
Q = Quality factor: 1 for X-ray and gamma radiation; 10 for beta and
20 for alpha radiation
RBE = Relative Biological Effectiveness=
1 rem = 1 rad x Q (above). Maximum permissible human dosage = 0.1 -
0.2 rem/yr = 1 - 2 mSv/yr (??)
A sudden dose of 350 rem gives 50% mortality in 30 days.
1 Sievert = 1 Sv = 100 rem; 1 mSv = 0.1 rem.
1 Curie = 3.7E10 Becquerel (Bq) = 3.7E10 disintegrations/s = 1 gram
of pure radium
| Natural
radiation hazard
Average radiation exposure for a US resident: 3.6 mSv (higher in areas with radon emission) This is made up of: Radon 2 + food & water 0.4 + diagnostic X-rays 0.4 + cosmic radiation 0.26 (mSv). One flight from New York to HongKong = 0.1 mSv; Watching TV = 0.01 mSv/yr. Maximum occupational exposure per year: 50 mSv (equals 500 flights as above). Max for pregnant women: 5 mSv. Radiation hazard of 3.6 mSv equals a loss of life expectancy of 1.5 minutes or fewer than 2 cigarette puffs. (Source: Sci-Am Jan 2002 p 20) |
Decrease in internal energy = heat produced + work done: dE = Q + W
Second law, all forms of energy ultimately reduce to heat:
All
physical processes lead to a decrease in the availability of the energy
involved. Processes involving energy transformations will not occur
spontaneously unless there is a degradation of energy from a non-random
to a random form. All spontaneous (natural) events act to increase the
entropy within a system. Until a system reaches its maximum entropy, it
can do useful work. But as a system does work, its entropy increases
until the system can no longer perform work.
1) In any transformation of energy, some of the energy is degraded.Third law, concerns absolute zero temperature: It states that it is impossible to reduce the temperature of any system to absolute zero.
2) No process is possible with 100% efficiency in transformation of energy.
3) No process is possible through the flow of heat from a colder body to a hotter one.
4) Once enrgergy has been used by a process, it cannot be used again by the same process.
5) High order energy (low entropy) converts into lower order energy (high entropy), and never the other way.
6) Order (low entropy) naturally degrades to disorder (high entropy).
Ideal gases
An 'ideal' gas is a conceptual one, behaving contrary to the second
law, by not losing energy during expansion or compression.
The volume of one mole of a substance, produces 22.4 litres of an ideal
gas at OºC, 1 At, and 24.5 @ 25ºC
Thus 1 mole of oxygen, O2 = 2 x 16 = 32
g, produces 22.4 litres of gas with a density of 32/22,400 = 1.43E-3 g/cm3
@0ºC
which is 700 times lighter than water.
Air averages 28.96 g/mol = 1.29E-3 g/cm3 @0ºC = 773 times lighter
than water.
Boyle Gay-Lussac: pressure x volume / temperature (K) =
constant
The volume of a gas increases proportionally to absolute temperature;
The pressure of a gas increases proportionally as the volume decreases.
( P1 x V1 ) / T1 = ( P2
x V2 ) / T2 where situation (1) is before and situation
(2) after a change.
Heating 22.4 litres of an ideal gas
from 0º to 25ºC increases its volume to 22.4 x (273+25)/273 =
24.5 litres, see above.
To heat one mole of an ideal gas by one degree K, requires 8.3143 J.
Electronic charge = e = 1.6021917E-19 C
1 Ampere = 1 Coulomb/second.
Perfect gas constant, R = 8.3143 J/(g mol)/ºK. [Amount
of energy needed to heat a gas]
Avogadro's number, N = 6.022169E23 molecules/(g mol) [Number
of molecules in a mole]
Faraday constant, F = 9.648670E-4 C/mol
Stefan-Boltzmann constant, sigma = 5.6697E-8 W/m2/ºK4
Planck's constant, h = 6.6255E-34 Js [Amount of energy in an
electro-magnetic wave; quantum theory]
Boltzmann constant, k = 1.380622E-23 J/ºK. [Amount of radiated
energy of a black body; entropy]
Permeability of a vacuum, 4 x pi E-7 kg m /s/s/A/A
Plants
Dry weight (DM) of a crop is about 25% of wet weight.
Carbon content of dried matter (DM) = 45% (containing carbohydrates
CH2O chains)
Nitrogen content of DM is 1.1 - 1.6%
| Biomass calculations
The ratios shown are not by weight but by the numbers of atoms. Average composition of terrestrial life: H:O:C:N:P:S = 2960:1480:1480:16:1.8:1 (E S Deevey Jr) Average composition of land plants: H:O:C:N:P:S = 1600:800:800:9:5:1 Average composition of marine plants: H:O:C:N:P:S = 212:106:106:16:2:1 Average composition of plant biomass: C:H:O= 1:(1.3-1.8):(0.5-0.6) (McDermitt&Loomis 1981) Redfield ratio required for phytoplankton: C:N:P= 106:16:1 Silicon
requirement of diatoms: N:Si= 1:1
Carbohydrates = CH2O chains; glucose = C6H12O6: H:O:C = 12:6:6, or in
mass 1:6:8
1 kg dry organic matter (DM) = 0.45 kg C = 1.5 kg CO2 (with 15% variation)
= 4200 kcal energy
|
Animals
1 kg of beef requires 50,000 kg of water.
A general equation to estimate the food requirement of marine mammal
species (Innes et al 1987)
Daily food cunsumption (kg biomass) Y = 0.123 x M ^ 0.80 or log(Y)
= log(0.123) + 0.8 x log(M)
Biochemical productivity
Plant productivity increases 100% with 12ºC temperature increase
Soil [note that facts relating to soil are traditionally expressed
per hectare ha]
Natural erosion before farming: 9E9 tonnes worldwide. In 1984: 25E9
tonnes
Tennessee: losing 14 t/acre/yr = 35t/ha/yr.
Nature puts back 5 t/acre/yr= 10t/ha/yr: Loss= 25t/ha/yr = 15m3/10,000m2/yr
= 1.5mm /yr
Conservation farming reduced soil loss from 14 to 10 t/acre/yr
tropical rainforest = 180 t/acre in dry matter
sediment yield from erosion by water 20-2600 t/sqkm/yr avg 30-92 m3/sqkm/yr
=9 km3/yr particles + 9.4E9 ton dissolved = 6 cm/1000yr= 0.06
mm/yr (Last Frontier p367)
Natural rate of weathering = 0.1mm/yr = 0.1 x 0.001 x 10,000 m3/ha/yr = 1m3/ha/yr = 100 m3/km2/yr = 1.5t/ha/yr
Water
Capillary rise of height h in a tube with diameter d
: h = 0.3 / d (in cm) (approximately)
A hair-thin capillary of 0.1 mm =
0.01 cm causes water to rise by 30 cm.
Henry's law: at a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid (for small concentrations, not saturated).
Sea area in cable protection zones: 1500 km2
Sea area in ammunition dumps, mining & oil drilling: 1500 km2
Sea area in marine reserves around mainland: 150 km2 = 15,000 ha
Productivity of NZ coastal seas 2-8 t/km2 (D Pauly)
NZ soil erosion: 270Mt/yr = 1000 t/km2/yr = 10 t/ha/yr = 6 m3/ha/yr
is about six times the sustainable rate, which is severely underestimated.
But most erosion by far comes from the 13Mha of agricultural land (about
50% of the land), which makes erosion 12 times the sustainable rate. But
NZ has always had very low natural erosion and in recent years erosion
has accelerated due to more torrential rains. so, NZ erosion may well top
400Mt/yr or over 20 times of what was natural.
loss of Carbon by soil erosion, estimated at between 3 and 10 Mt C
per year (AgResearch)
