|
|
|
|
|
|
|---|---|---|---|---|---|
 |
 |
 |
 |
 |
 |
|---|---|---|---|---|---|
 |
 |
 |
 |
|---|---|---|---|
 |
 |
 |
 |
 |
|---|---|---|---|---|
 |
 |
 |
 |
 |
|---|---|---|---|---|
 |
 |
|---|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
Continue to the rest of the "scales of the universe exhibit"
 |
|---|
For a material, the "stiffness" is characterized by the "Tensile modulus". The stiffer a material, the more force it takes to stretch it.
 |
|---|
The plot shows the elastic energy per mass at the breaking point, divided by the density. Alloys are much stronger than pure metals. Kevlar is substantially stronger than metals.
Stiffness tends to go together with density.
 |
|---|
The following plot quantifies the elastic strength of materials.
Kevlar is stronger than metals.
Alloys are stronger than pure metals.
 |
|---|
The "Yield strength" is the tensile force/area required to break it.
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
 |
|---|
Dot size corresponds to atom size. For gases, the density at boiling point is used.
 |
 |
 |
 |
 |
 |
 |
|---|---|---|---|---|---|---|
Hydrogen forms molecules with all elements except the noble gases, osmium, iridium, promethium, francium, and radium. This makes it a benchmark for determining the number of bonds that each element forms, as well as the strength of each element's attraction for electrons.
 | |
|---|---|
Every atom attracts electrons and the electronegativity table shows the relative energy released when the atom captures an electron. The elements in the upper right are the most electron-hungry.
In the reaction H + H + O → H2O, The oxygen steals an electron from each of the two hydrogens. It is able to do this because the electrons are at a lower energy with oxygen than with hydrogen.
Most chemical reactions involve elements on the left side of the periodic table giving electrons to elements on the right side.
 |
 |
|---|---|
A molecule is organic if it contains carbon. Molecules are often depicted with the hydrogens excluded.
 |
 |
|
 |
|---|---|---|---|
An "Alkane" is a carbon chain with hydrocarbons attached. At standard temperature (300 K), alkanes are solid if they have more than 20 carbons. This is why lipids (long alkanes) are the optimal form of energy storage. Short alkanes are liquids or gases at STP and are hard to store.
 |
|---|
In the following table, the first section shows properties of alkanes and the second section shows properties of other energy sources.
Alkane Carbons Energy of Melt Boil Solid Liquid Gas Phase at
type combustion (K) (K) density density density 300 K
(MJ/kg) (g/cm^3) (g/cm^3) (g/cm^3)
Hydrogen 0 141.8 14.0 20.3 .07 .000090 Gas
Methane 1 55.5 90.7 111.7 .423 .00070 Gas
Ethane 2 51.9 90.4 184.6 .545 .0013 Gas
Propane 3 50.4 85.5 231.1 .60 .0020 Gas
Butane 4 49.5 136 274 .60 .0025 Gas
Pentane 5 48.6 143.5 309 .63 Liquid
Hexane 6 48.2 178 342 .65 Liquid
Heptane 7 48.0 182.6 371.5 .68 Liquid
Octane 8 47.8 216.3 398.7 .70 Liquid
Dodecain 12 46 263.5 489 .75 Liquid
Hexadecane 16 46 291 560 .77 Liquid
Icosane 20 46 310 616 .79 Solid
Alkane-30 30 46 339 723 .81 Solid
Alkane-40 40 46 355 798 .82 Solid
Alkane-50 50 46 364 848 .82 Solid
Alkane-60 60 46 373 898 .83 Solid
Gasoline ~ 8 47 .76 Liquid Mostly alkanes with ~ 8 carbons
Natural gas 54 91 112 Gas Mostly methane
Coal 32 - - Solid Mostly carbon
Wood 22 - - Solid Carbon, oxygen, hydrogen
Pure carbon 1 32.8 - - Solid Pure carbon, similar to coal
Methanol 1 175.6 337.8 .79 Liquid
Ethanol 2 159 351.5 .79 Liquid
Propanol 3 147 370 Liquid
An alkane with 7 or more carbons has a heat of combustion of 46 MJoules/kg.
A nitrogen molecule is more tightly bound than an oxygen molecule, making it impossible to extract energy from hydrocarbons with nitrogen. Few things burn in a nitrogen atmosphere, lithium and magnesium being examples.
A chain is "saturated" if it contains the maximum number of hydrogen atoms and "unsaturated" if it contains less. Examples of unsaturated carbon chains:
 |
 |
 |
 |
|---|---|---|---|
The hydrogens are required to stabilize the carbon chain.
 |
 |
 |
 |
|---|---|---|---|
If there is a double or triple bond then the electrons can be mobile and assume different states. The molecule exists in a quantum-mechanical resonance between the possible states.
 |
 |
 |
|---|---|---|
 |
 |
 |
 |
|---|---|---|---|
 |
 |
 |
|---|---|---|
Suppose we make a chain of atoms that is saturated in hydrogen. The following table gives the longest stable chain for each element, and the longest stable chain in an oxygen environment. Only carbon is capable of making long chains. We can expect that aliens will be carbon-based.
Stable Stable in an
oxygen environment
Lithium 1 1
Boron 0 0
Carbon ∞ ∞
Nitrogen 1 1
Oxygen 1 1
Aluminum 1 1
Silicon 2 0
Phosphorus 1 0
Sulfur 1 0
 |
 |
 |
 |
 |
|---|---|---|---|---|
 |
 |
|---|---|
Cyclohexane comes in different conformations with different energies.
 |
 |
|---|---|
 |
 |
 |
|---|---|---|
Benzine is a resonance molecule.
 |
 |
|---|---|
 |
|---|
 |
 |
 |
 |
 |
 |
|---|---|---|---|---|---|
Organic molecules are classified by their functional group. "R" stands for an arbitrary molecule.
 |
-skeletal.png) |
 |
 |
|---|---|---|---|
 |
 |
 |
 |
|---|---|---|---|
.png) |
 |
|---|---|
 |
|  |
 |
|---|---|---|---|
 |
 |
 |
 |
|---|---|---|---|
 |
 |
|---|---|
 |
|---|
MJoules/kg
Antimatter 90 billion
Hydrogen bomb 25000000 theoretical maximum yield
Hydrogen bomb 21700000 highest achieved yield
Uranium 20000000 as nuclear fuel
Hydrogen 143
Natural gas 53.6
Gasoline 47
Jet fuel 43
Fat 37
Coal 24
Carbohydrates & sugar 17
Protein 16.8
Wood 16
Lithium-air battery 9
TNT 4.6
Gunpowder 3
Lithium battery 1.3
Lithium-ion battery .72
Alkaline battery .59
Compressed air .5 300 atmospheres
Supercapacitor .1
Capacitor .00036
The chemical energy source with the highest energy/mass is hydrogen+oxygen, but
molecular hydrogen is difficult to harness. Hydrocarbons + oxygen is the next
best choice. Carbon offers a convenient and lightweight way to carry hydrogen
around.
Reacting hydrocarbons in an oxygen atmosphere yields the optimal power-to-weight ratio.
Given the enormous power required by brains, if intelligent life exists in the universe, it likely gets its energy from reacting hydrocarbons in an oxygen atmosphere. Most likely we would be able to eat their food.
MJ/kg Calories/gram
Sugar 16 5
Protein 17 5
Alcohol 25 7
Fat 38 9
Humans can metabolize a wide range of fats and sugars.
Life appeared on the Earth within a billion years of its formation. http://en.wikipedia.org/wiki/Timeline_of_evolutionary_history_of_life
Shortly after that, between 3500 and 3800 million years ago, the "Last Universal Common Ancestor" lived. http://en.wikipedia.org/wiki/Last_Universal_Common_Ancestor
The LUCA had the following properties:
Single-cellular with a bilipid cell wall.
ATP to power enzymes.
A DNA codon system with 4^3=64 options coding for 20 proteins.
This code hasn't changed since.
Abundance in Mass frac in
Crust (ppm) Human body
Oxygen 460000 .65
Carbon 1000 .18
Hydrogen 1500 .10
Nitrogen 20 .03
Calcium 45000 .014
Phosphorus 1100 .011
Potassium 20000 .0025
Sulfur 400 .0025
Sodium 25000 .0015
Chlorine 200 .0015
Magnesium 25000 .0005
Iron 60000 .00006
Fluorine 500 .000037
Zinc 75 .000032
Silicon 275000 .00002
Trace elements <.00001
Among the elements required for life, nitrogen is the scarcest.
The nitrogen in the first 250 km of the Earth's crust has the same mass as
the nitrogen in the atmosphere.
Used by Used by
humans bacteria
Hydrogen * *
Helium
Lithium
Beryllium
Boron * *
Carbon * *
Nitrogen * *
Oxygen * *
Fluorine *
Neon
Sodium * *
Magnesium * *
Aluminum
Silicon *
Phosphorus * *
Sulfur * *
Chlorine * *
Argon
Potassium * *
Calcium * *
Scandium
Titanium
Vanadium *
Chromium
Manganese * *
Iron * *
Cobalt * *
Nickel *
Copper * *
Zinc * *
Gallium
Germanium
Arsenic *
Selenium * *
Bromine * *
Krypton
Molybdenum *
Tellurium *
Iodine * *
Tungsten *
 |
|---|
Cell walls are formed from a double layer of lipids. They are elastic and they self-assemble.
Each lipid has a polar and a non-polar end. The polar end faces the water and the non-polar end faces another lipid.
* Video of the self-assembly of a bilipid layer
* Video of an amoeba
If life were to exist in a non-polar solvent it would have to find another way to make cell walls.
 |
 |
|---|
Enzymes use ATP as an energy source to power chemical reactions. ATP and ATP synthase are common to all Earth life.
* Video of the ATP synthase enzyme in action
 |
|---|
Amino acids have the above form, where R stands for an arbitrary molecule.
 |
|---|
 |
|---|
C-C-N-C-C-N-C-C-N-C-C-N-C-C-N
 |
 |
|---|
DNA codes a sequence of amino acids. The 64-element codon system is universal to Earth life.
 |
 |
|---|
The codon ATG both codes for methionine and serves as an initiation site: the first ATG in an mRNA's coding region is where translation into protein begins.
21 amino acids are used by eucaryote. More than 500 amino acids are known.
 |
|---|
A sugar generally has the formula CN H2N ON, where N = 2, 3, etc. The common sugars are hexoses with N=6.
Number of Number of
carbons sugars
Diose 2 1
Triose 3 2
Tetrose 4 3
Pentose 5 4
Hexose 6 12 At least 6 carbons are required to form a ring
Heptose 7 many Rarely observed in nature
Octose 8 many Unstable. Not observered in nature.
"Number of sugars" refers to the number of different types of sugar molecules for each
carbon number.
Each sugar molecule has two mirror-symmetric forms, the "D" and "L" form. Only the D forms are found in nature.
The following figures show all sugars up to 6 carbons. All can be metabolized by humans.
2 carbons:
 |
|---|
3 carbons:
 |
 |
|---|---|
4 carbons:
 |
 |
 |
|---|---|---|
5 carbons:
 |
 |
 |
 |
|---|---|---|---|
6 carbons:
|
 |
 |
 |
 |
 |
 |
 |
|---|---|---|---|---|---|---|---|
 |
 |
 |
 |
|---|---|---|---|
Energy Sweetness
Succrose 1.00 1.00 Benchmark
Glucose .74
Maltose .32
Galactose .32
Lactose .16
Allose
Altrose
Mannose
Fructose 1.73
Psichose .70
Tagatose .38 .92
Sorbose 1.0
Honey .97
Monosaccharde: 1 sugar molecule Disaccharide: 2 monosaccharides Polysaccharide: More than 2 monosaccharides, such as starch and cellulose
 |
 |
 |
 |
 |
|---|---|---|---|---|
Sucrose = Glucose + Fructose Maltose = Glucose + Glucose Lactose = Galactose + Glucose Lactulose = Galactoce + Fructose Trehalose = Glucose + Glucose Cellobiose = Glucose + Glucose Chitobiose = Glucosamine + GlucosamineStarch and cellulose are long chains of glucose molecules.
 |
 |
|---|---|
 |
 |
|---|---|
 |
|
 |
 |
 |
 |
|---|---|---|---|---|---|
Fatty acids and sugars are metabolized in the following stages, with each stage yielding energy.
Fatty acid → Acetyl → CO2 and H2O Sugar → Pyruvate → CO2 and H2O
Blood delivers fatty acids to cells.
The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2. Coenzyme-A carries the acetyl around.
A fat molecule is converted into a fatty acid by lipolysis, and then the fatty acid is converted into acetyl by beta oxydation, and then the acetyl is converted into H2O and CO2 by the citric acid cycle.
Beta oxidation cleaves 2 carbons from a fatty acid, which becomes acetyl. This process is repeated until te entire fatty acid has been converted into acetyls.
The steps of beta oxidation are:
 |
|---|
 |
|---|
 |
|---|
 |
|---|
Glycolysis converts a glucose molecule into 2 pyrovate molecules. A summary of the reaction showing only the starting and ending points is:
 |
|---|
The full reaction is:
 |
|---|
 |
|---|
 |
|---|
The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2.
Fat metabolism oxidizes a carbon chain so that the chain can be split into acetyl. The strategy of the citric acid cycle is to further oxidize the acetyl (now a part of citrate) so that the remaining carbon bonds in the acetyl can be broken.
An alcohol is a carbon chain with one OH attached.
 |
 |
 |
 |
 |
|---|---|---|---|---|
Carbons
Methanol 1 Toxic
Ethanol 2 Inebriating
Propanol 3 3 times more inebriating than ethanol
Isopropanol 3 Toxic
Butanol 4 6 times more inebriating than ethanol
 |
 |
|
|---|---|---|
Palmitic acid has 16 carbons and is the most common fatty acid found in food.
Carbons 1 2 Vinegar 3 4 Found in butter 8 Found in coconuts 10 Found in coconuts 12 Found in coconuts 16 Most common fatty acid. Found in palm oil 18 Found in chocolate 20 Found in peanut oil
 |
 |
 |
 |
|
|
 |
|---|---|---|---|---|---|---|
 |
|---|
LD50
(mg/kg)
CO Carbon monoxide
HCN 6.4 Hydrogen cyanide
CH2O Methanol
CH2O Formaldehyde
H2S Hydrogen sulfide
NO2 Nitrite
Cl2 Chlorine
Fl2 Fluorine
Ethanol 7060
Salt 3000
Caffeine 192
Aspirin 200
NaNO2 180 Sodium nitrite
Cobalt 80
NaF 52
Capsaicin 47 Chili pepper
Mercury 41
Arsenic 13
Nicotine .8
Bromine
C2N2
PH3
SiCl4
Almost anything with fluorine or bromine is toxic.
Weakly toxic:
C2H2 Acetylene. Inebriating C3H6 Propene. Inebriating
 |
|---|
Opsin Wavelength Humans
(nm)
RH1 500 White Black/White
RH2 600 Black/White. Extinct in mammals
OPN1LW 564 Red Once possessed by mammals, then lost by most
OPN1MW 534 Green All mammals
OPN1SW 440 Blue All mammals
SWS2 480 Extinct in mammals
VA 500 Vertebrates except mammals. Vertebrae ancient opsin.
Parapinopsin UV 365 Catfish
Parapinopsin Blue 470 Catfish and lamphrey
Pareitopsin 522 Lizards
Panopsin Cyan 500 Fish vision. Found in the brains of humans
Panopsin Blue 450 Fish vision. Found in the brains of humans
Neuropsin 380 Bird vision. Found in the brains of humans
Melanopsin 480 Found in the brains of humans
Retinal G Found in the brains of humans
 |
 |
|---|---|
Metals are held by a cofactor, which is held by a protein. Many cofactors are porphyrin rings conposed of 4 pyrroles. Examples of porphyrins:
 |
 |
 |
 |
|---|---|---|---|
 |
|---|
 |
|
 |
 |
|---|---|---|---|
 |
 |
 |
|---|---|---|
 |
|---|
Oxygen bonds to the iron in a heme molecule and becomes superoxide.
Hemoglobin is a set of 4 helix proteins that carry 4 iron ligands, and each
iron ligand carries 1 oxygen molecule.
Human hemoglobin is composed mostly of heme B.
The oxygen density of hemoglobin is 70 times the solubility of oxygen
in water.
Hemoglobin fraction of red blood cells = .96 (dry weight) Hemoglobin fraction of red blood cells = .35 (including water) Oxygen capacity of hemoglobin = 1.34 Liters of oxygen / kg hemoglobin Iron ligands per hemoglobin = 4 O2 molecules per ion ligand = 1
 |
 |
 |
|---|---|---|
 |
 |
 |
|---|---|---|
 |
 |
 |
|---|---|---|
All chlorophyll uses magnesium.
A Universal B Plants C1 Algae C2 Algae D Cyanobacteria F Cyanobacteria
 |
 |
 |
|---|---|---|
 |
 |
 |
|---|---|---|
Zinc stabilizes the proteins that manipulate DNA and RNA.
 |
|
|---|---|
Element Humans Cofactor Function
Hydrogen *
Helium No biological role
Lithium No biological role
Beryllium Toxic becauseit displaces magnesium in proteins
Boron * Plant cell walls. Metabolism of calcium in plants & animals
Magnesium * Chlorin Chlorophyll
Scandium No biological role
Titanium No biological role
Vanadium Found only in rare bacteria.
Chromium No biological role
Manganese * Superoxide dimutase. Converts superoxide to oxygen
Iron * Porphin Hemoglobin
Cobalt * Corrin Cobalamin (Vitamin B12)
Nickel Corphin Coenzyme F430 (Creates methane. Found only in archaea)
Copper * Heme Cytochrome C oxidase. Electron transport chain
Hemocyanin, an alternative to hemoglobin used by some animals
Hemoglobin carries 4 times as much oxygen as hemocyanin
Plastocyanin protein, used in photosynthesis
Sometimes used in superoxide dimutase
Zinc * Component of proteins that manipulate DNA and RNA (Zinc fingers)
Component of carbonic anhydrase, which interconverts CO2 and HCO3
Metallothionein proteins, which bind to metals such as
zinc, copper, selenium cadmium, mercury, silver, and arsenic
Molybdenum Nitrogen fixase. Convert N2 to NH3
Selenium * Component of the amino acide selenocysteine
Bromine * Limited role
Iodine * Component of thyroxine and triiodotyronine, which
regulate metabolic rate
Lead Toxic because it displaces calcium in bones
 |
 |
|---|---|
 |
 |
 |
|---|---|---|
 |
 |
|
|---|---|---|
Superoxide dimutase converts superoxide to oxygen or hydrogen peroxide.
The peroxidase enzyme decomposes hydrogen peroxide to water. Peroxidase contains the selenocysteine amino acid, which contains selenium.
 |
|---|
Nitrogen fixase uses an iron-molybdenum cofactor.
 |
|---|
Selenium is a component of the amino acid selenocysteine.
 |
 |
 |
|---|---|---|
The hemocyanin protein uses copper to carry oxygen. It has an oxygen density that is 1/4 of hemoglobin.
Plastocyanin is a copper-containing protein used in photosynthesis.
 |
|---|
 |
|---|
Lignin is the structural component of wood.
 |
 |
|---|---|
 |
|
|
 |
||
|---|---|---|---|---|---|
|
|
 |
 |
|---|---|---|---|
 |
 |
 |
|---|---|---|
 |
 |
 |
|---|---|---|
 |
 |
|---|---|
Gold and silver were known since antiquity because they occur naturally in pure form.
Gold mining started in 6000 BCE and silver smelting started in 4000 BCE.
Iron can occasionally be found as iron meteorites.
Copper was discovered around 7500 BCE by smelting copper minerals in a wood fire.
Around 3200 BCE it was found that copper is strenghened by tin, and this is bronze.
Around 2000 BCE it was found that copper is also strengthed by zinc, and this is brass.
The earliest metals were smeltable with a wood fire and they consist of copper,
lead, silver, tin, zinc, and mercury. They come from the following minerals:
The next metal to be discovered was iron (c. 1200 BC), which requires a bellows-fed coal
fire to smelt.
No new metals were discovered until cobalt in 1735.
Once cobalt was discovered, it was realized that
new minerals may have new metals, and the race was on to find new minerals. This gave
nickel, chromium, manganese, molybdenum, and tungsten.
Chromium is lighter and stronger than steel and was discovered in 1797. It
satisfies the properties of mithril from "Lord of the Rings" and Valyrian steel
from "Game of Thrones".
There's no reason chromium couldn't have
been discovered earlier.
Coal smelting can't produce the metals lighter than chromium. These need
electrolysis. The battery was invented in 1799, enabling electrolysis, and
the lighter metals were discovered shortly after. These include aluminum, magnesium, titanium,
and beryllium. Once you have
Carbon fiber eclipses metals. The present age could be called the carbon age. The carbon age became
mature in 1987 when Jimmy Connors switched from a wood to a carbon racket.
The plot shows the strength of materials.
Wood rivals alloys for strength.
Gold was the densest element known until the discovery of platinun in 1735. It
was useful as an uncounterfeitable currency until the discovery of tungsten in
1783, which has the same density as gold. Today, we could use iridium,
platinum, or rhenium as an uncounterfeitable currency.
Prior to 1800, metals were obtained by smelting minerals, and the known metals
were gold, silver, copper, iron, tin, zinc, mercury, cobalt, manganese,
chromium, molybdenum, and tungsten. Elements to the left of chromium titanium
and scandium cant's be obtained by smelting, and neither can aluminum,
magnesium, and beryllium. They require electrolysis, which was enabled by
Volta's invention of the battery in 1799.
Prior to 1800, few elements were known in pure form. Electrolyis enabled the
isolation of most of the rest of the elements. The periodic table then became
obvious and was discovered by Mendeleev 1871. The battery launched modern
chemistry, and the battery could potentially have been invented much earlier.
Electrolysis enabled the isolation of sodium and potassium in 1807, and these were used
to smelt metals that can't be smelted with carbon.
For a metal, the stiffness is characterized by the "shear strength" and the
sword worthiness is characterized by the shear strength over the density
(the "strength to weight ratio"). For example for iron,
This plot includes all metals with a strength/density at least as large as lead,
plus mercury.
Beryllium is beyond the top of the plot.
In prehistoric times iron meteorites were the only source of metallic iron.
They consist of 90% iron and 10% nickel.
New alloys have been discovered that are stronger and ligher than diamond. These alloys have an
amorphous structure rather than the crystalline structure of conventional alloys.
A crystaline alloy tends to be weak at the boundaries between crystals and this limits
its strength. Amorphous alloys don't have these weaknesses and can be stronger.
Pure metals and alloys consisting of 2 or 3 different metals tend to be crystaline while alloys
with 5 or more metals tend to be amorphous. The new superalloys are mixes of at least 5 different
metals.
A material's strength is characterized by the "yield strength" and the quality is
the ratio of the yield strength to the density. This is often referred to as the "strength to weight ratio".
Most alloys weaken with increasing temperature except for a small subset called
"superalloys" that strengthen with temperature, such as Ni3Al and
Co3Al. This is called the "yield strength anomaly".
Nickel alloys in jet engines have a surface temperature of 1150 Celsius
and a bulk temperature of 980 Celsius. This is the limiting element for
jet engine performance. Half the mass of a jet engine is superalloy.
Current engines use Nickel superalloys and Cobalt superalloys are under
development that will perform even better.
Yield strength in GPa as a function of Celsius temperature.
Bells and cymbals are made from bell bronze, 4 parts copper and 1 part tin.
The "atomization energy" is the energy required to extract an atom
from an element in its raw form. For example,
The atomization energy of H2O is -971 kJ/mole.
Most metals are in oxidized form. The only metals that can be found in
pure form are gold, silver, copper, platinum, palladium, osmium, and iridium.
Smelting is a process for removing the oxygen to produce pure metal.
The ore is heated in a coal furnace and the carbon seizes the oxygen from
the metal. For copper,
For iron, the oxidation state is reduced in 3 stages until the
pure iron is left behind.
The following table gives the temperature required to smelt each element with
carbon.
The farther to the right on the periodic table, the lower the smelting
temperature, a consequence of "electronegativity".
The battery was invented in 1800, launching the field of electrochemistry
and enabling the the isolation of non-carbon-smeltable elements.
Davy used electrolysis in 1807 to isolate sodium and potassium and then he used
these metals to smelt other metals. To smelt beryllium with potassium,
BeO + 2 K ↔ Be + K2O.
Titanium can't be carbon smelted because it forms the carbide Ti3C.
For an expanded discussion of smelting physics, see jaymaron.com/metallurgy.html.
Thermite is smelting with aluminum. For example, to smelt iron with aluminum,
The following table shows reactions that change the oxidation state of a metal.
"M" stands for an arbitrary metal and the magnitudes are scaled to one mole of
O2. The last two columns give the oxidation state of the metal on
the left and right side of the reaction. An oxidation state of "0" is the pure
metal and "M2O" has an oxidation state of "1".
These elements are not necessarily on the Science Olympiad list.
We list minerals by element, with the most abundant mineral for each element listed first.
The composition of a typical opium poppy is:
High explosives have a large shock velocity.
The best oxidizer is liquid oxygen, and the exhaust speed for various fuels when
burned with oxygen is:
We use kerosene as a standard fuel and show the rocket speed for various oxidizers.
Some of the oxidizers can be used by themselves as monopropellants.
Above 550 Celsius, potassium nitrate decomposes. 2 KNO3 ↔ 2 KNO2 + O2.
The safety match was invented in 1844 by Pasch. The match head cannot ignite by
itself. Ignitition is achieved by striking it on a rough surface that contains
red phosphorus. When the match is struck, potassium chlorate in the match head
mixes with red phosphorus in the abrasive to produce a mixture that is easily ignited
by friction. Antimony trisulfide is added to increase the burn rate.
Before the invention of iron, fires were started by striking flint (quartz)
with pyrite to generate sparks. Flintlock rifles work by striking
flint with iron. With the discovery of cerium, ferrocerium replaced iron
and modern butane lighters use ferrocerium, which is still referred to as "flint".
Nitrous oxide is stored as a cryogenic liquid and injected along with gaoline
into the combustion chamber. Upon heating to 300 Celsius the nitrous oxide
decomposes into nitrogen and oxygen gas and releases energy.
The oxygen fraction in this gas is higher than that in air (1/3 vs. .21) and the
higher faction allows for more fuel to be consumed per cylinder firing.
Hydroquinone and peroxide are stored in 2 separate compartments are pumped into
the reaction chamber where they explode with the help of protein catalysts.
The explosion vaporizes 1/5 of the liquid and expels the rest as a boiling drop
of water, and the p-quinone in the liquid damages the foe's eyes. The energy
of expulsion pumps new material into the reaction chamber and the process
repeats at a rate of 500 pulses per second and a total of 70 pulses. The
beetle has enough ammunition for 20 barrages.
A turbojet engine compresses air before burning it to increase the flame speed
and make it burn explosively. A ramjet engine moving supersonically doesn't need
a turbine to achieve compression.
If the pressure front moves supersonically then the front forms a discontinuous
shock, where the pressure makes a sudden jump as the shock passes.
Metal powder is often included with explosives.
An oxygen candle is a mixture of sodium chlorate and iron powder,
which when ignited smolders at 600 Celsius and produces oxygen at a rate
of 6.5 man-hours of oxygen per kilogram of mixture. Thermal decomposition releases
the oxygen and the burning iron provides the heat. The products of the reaction are
NaCl and iron oxide.
The energy distribution for a 7.62 mm Hawk bullet is
The muzzle break at the end of the barrel deflects gas sideways to reduce recoil.
Corundum is a crystalline form of aluminium oxide (Al2O3). It is transparent in
its pure form and can have different colors when metal impurities are
present.
Lignin comprises 30 percent of wood and it is the principal structural element.
A string ideally has both large strength and large strain, which favors
Vectran.
Suppose Batman has a rope made out of Zylon, the strongest known polymer.
Valyrian steel is a fictional substance from "Game of Thrones" that is
stronger, lighter, and harder than steel. The only elements that qualify are
beryllium, titanium, and vanadium, none of which were known in Earth history
until the 18th century. Valyrian steel could be of these elements,
an alloy, or a magical substance. According to George Martin, magic is
involved.
The fact that it is less dense than steel means that it can't be a fancy form
of steel such as Damascus steel or Wootz steel. Also, fancy steel loses its
special properties if melted and hence cannot be reforged, whereas Valyrian steel
swords can be reforged.
In Earth history, the first metal discovered since iron was cobalt in 1735.
This launched a frenzy to smelt all known minerals and most of the smeltable
metals were discovered by 1800. Then the battery and electrochemstry were
discovered in 1800 and these were used to obtain the unsmeltable metals, which
are lithium, beryllium, magnesium, aluminum, titanium, vanadium, niobium, and
Uranium. Almost all of the strong alloys use these metals, and so the Valyrians
must have used either electrochemistry or magic to make Valyrian steel.
The following metals and alloys are both stronger and lighter than steel and
could hypothetically be Valyrian steel.
Petyr Baelish: Nothing holds an edge like Valyrian steel.
Tyrion Lannister: Valyrian steel blades were scarce and costly, yet thousands
remained in the world, perhaps two hundred in the Seven Kingdoms alone.
George Martin: Valyrian steel is a fantasy metal. Which means it has magical
characteristics, and magic plays a role in its forging.
George Martin: Valyrian steel was always costly, but it became considerably
more so when there was no more Valyria, and the secret of its making were lost.
Ned Stark's stord "Ice" is melted down and reforged into two smaller swords,
"Oathkeeper" and "Widow's Wail". This rules out Valyrian steel being Wootz steel
because Wootz steel loses its special properties when reforged.
Appearances of Valyrian steel in Game of Thrones:
The burn rate of gasoline is limited by the supply of oxygen.
Copper burns with a green flame. Adding copper powder to the explosive adds
energy to the blast.
Three types of incendiaries are:
The reason air heats when compressed is because it is composed of atoms. You
can see this in action with the "Gas" simulation at phet.colorado.edu. You can
also see how atoms in a gas can carry a sound wave, and why the sound speed
has the same order-of-magnitude as the thermal velocity of the atoms.
An alien civilization could easily build a rocket that travels at 1/10 the speed of light,
which would take 1 million years to cross the galaxy. The aliens have plenty of time
to get here.
A spine
Humans have the most complex wrists and hands in the animal kingdom.
Bruce Lee: There is only one type of body, 2 arms, 2 legs, etc that make up the
human body. Therefore, there can only be one style of fighting. If the other
guy had 4 arms and 2 legs, there might have to be a different one. Forget the
belief that one style is better than the other, the point of someone that does
not just believe in tradition, but actually wants to know how to fight is to
take what you need from every martial art and incorporate it into your
own. Make it effective and very powerful, but don't worry if you are taking
moves from many different arts, that is a good thing.
Define one "Earth Atmosphere Oxygen Mass" (EAOM) as the mass of the oxygen in
the Earth's atmosphere, equal to 1.4*10^18 kg.
Early in the Earth's history, oxygen produced by photosynthesis was absorbed by
iron dissolved in the oceans, creating "banded iron formations". Once photosynthesis
overwhelmed the ocean's iron, an oxygen atmosphere became possible.
A desert planet like Tatooine would have a hard time generating an oxygen atmosphere.
This diagram of the fast carbon cycle shows the motion of carbon between
land, atmosphere, and oceans, in billions of tons of carbon per year. Yellow
numbers are natural fluxes, red are human contributions in billions of tons of
carbon per year. White numbers indicate stored carbon.
Carbon content of the Earth, with the atmosphere normalized to 1
Photosynthesis moves carbon from the atmosphere to plants, and the carbon
returns to the atmosphere through plant respiration and through microbial
decomposition of dead plants. Given the global rate of photosynthesis, it
takes photosynthesis ~ 7 years to cycle through the atmosphere's carbon.
Before the Earth had oxygen and ozone, the continents were uninhabitable
and the only place photosynthesis could take place was underwater.
Water is more transparent to visible light than to ultraviolet light.
Cyanobacteria can fix 1.8 kg of nitrogen per hectare per day.
Nitrogen can be fixed in the ocean at twice the rate than what is possible on land.
Aerobic organisms have an energy advantage over anaerobic organisms.
Oxygen is usually toxic to anaerobic organisms.
Anaerobic organisms produce H2S and CS2, which is toxic to most aerobic organisms.
Before the Earth had an oxygen atmosphere, sulfur-reducing bacteria ruled the
Earth. When oxygen appeared, aerobic organisms took over because of the energy
advantage. Sulfur-reducing bacteria retreated underground where there is no
oxygen. On occasion the sulfur bacteria make a comeback, such as during the
runaway global warming event 251 million years ago. During this episode, the
atmosphere became flooded with H2S, causing a mass extinction of aerobic
species.
Peter Ward's book "The Medea Hypothesis" has a nice discussion of the rivalry
between aerobic and anaerobic organisms, and of the interaction between the
Earth's geology and biology.
In the film "Avatar", the atmosphere of Pandora is toxic to humans because of
H2S.
Oxygen is more electronegative than sulfur, which is why reacting hydrocarbons with
oxygen yields more energy than by reacting them with sulfur.
The only element that rivals oxygen's electronegativity is fluorine, but fluorine gas is
highly reactive and HF is a strong acid.
The human brain consumes 20 Watts.
Even though the brain is a power-hungry organ, organisms take the trouble to develop large brains.
Reacting hydrocarbons in an oxygen atmosphere yields the optimal power-to-weight ratio.
Given the enormous power required by brains, if intelligent life exists in the universe,
it likely gets its energy from reacting hydrocarbons in an oxygen atmosphere.
Most likely we would be able to eat their food.
Bruce Lee: When the opponent expands I contract, when he contracts I expand,
and when there is an opportunity, I do not hit, it hits all by itself.
The diaphragm creates pressure in the abdomen, which expands the ribcage and creates
negative pressure for inhalation. Any air-breathing alien has to find a
way to generate negative pressure. The ribcage expansion also puts tension energy into
the rib muscles, which can be released in a sudden pulse to launch motion of the limbs.
Breathing is coordinated with skeletal motion to minimize energy expenditure.
Motion cycles between the following two columns.
When you are relaxing, your breathing adjusts to minimize energy, coordinate
cycles, and smooth transitions.
Tetrapod limbs have 2 long bones. A limb with only one long bone is obviously insufficient
and 2 long bones are sufficient to support 3D motion of the hand. 3 long bones is probably
unnecessary.
There is 1 bone in the upper limb and 2 bones in the lower limb, with a
universal joint at the shoulder/hip, a locking joint at the knee/elbow, and a
universal joint at the wrist/ankle. The shoulder/hip universal joints can be
realistically supported because the torso has abundant muscle mass and torque.
The locking joint is harder to support because the upper limb has less muscles
and torque than the torso. This is why the lower limb has 2 bones, to help
with torque and to stabilize the hand.
The hand is small enough that it can be supported by a univeral joint (the wrist).
The length of limbs is limited by the ability of the torso to deliver force and
torque to the hands and feet.
Humans have the most complex wrists in the animal kingdom. Only humans can fully exploit the
universal joint of the wrist.
Humans are one of the only animals capable of good balance while on one foot.
In your forearm, the ulna is the large bone and the radius is the small bone.
The forearm should ideally rotate around the large bone.
The ulna connects to your hand on the pinky side and the radius connects to the
thumb side. Your hand should rotate about the pivot point where your ulna connects
to your wrist.
In your lower leg the tibia is the large bone and the fibula is the small bone.
The tibia connects to your foot at the big toe side and the fibula connects at the
little toe site.
The lower limbs are connected directly to the spine so that the can deliver force from the
ground to the spine. The upper limbs are not directly connected to the spine so that they
can absorb shock and move with precision. If an organism has no collarbone then there is no
skeletal connection between the limbs and spine at all. If an organism has a colarbone
then the connection sequences is:
"Lapse" is the adiabatic lapse rate.
"Max height" is the maximum elevation.
"Min height" is the minimum elevation.
The atmosphere of Titan is non-toxic and there is enough atmospheric pressure
that you don't need a pressure suit. You can roam around Titan with a ski suit and
scuba gear. Gravity is so low that human-powered flight is easy.
80% of the Earth's heat is from radioactivity and 20% is from accretion.
The radioactive heating rate 3 billion years ago is twice that of today.
The Earth's core temperature is ~ 7000 K.
Io is heated by tidal forces from Jupiter.
Goldreich & Tremaine (1980): "We present an illustrative application of our
results to the interaction between Jupiter and the plantary disk. The angular
momentum transfer is shown to be so rapid that substantial changes in both the
structure of the disk and the orbit of Jupiter must have taken place on a time
scale of a few thousand years."
This is a plot of all known planetary systems with at least 3 planets.
Each row corresponds to a planetary system and the solar system is 2/3 of the
way down.
Horizontal cyan lines indicate the range between the planet's perigee and apogee.
Horizontal green lines correspond to 6 times the planet's Hill radius, a measure of the
planet's zone of gravitational dominance.
Vertical blue lines indicate the planet's orbital inclination.
Same as above except for:
The Earth has been beset by asteroids, supervolcanoes, global ice ages, runaway
global warming, supernovae, gamma ray bursts, and the industrial age.
Molecules are often depicted with the hydrogens excluded.
Metals are held by a cofactor, which is held by a protein. Many cofactors
are porphyrin rings conposed of 4 pyrroles. Examples of porphyrins:
Oxygen bonds to the iron in a heme molecule and becomes superoxide.
All chlorophyll uses magnesium.
Zinc stabilizes the proteins that manipulate DNA and RNA.
Superoxide dimutase converts superoxide to oxygen or hydrogen peroxide.
The peroxidase enzyme decomposes hydrogen peroxide to water. Peroxidase contains
the selenocysteine amino acid, which contains selenium.
Nitrogen fixase uses an iron-molybdenum cofactor.
Selenium is a component of the amino acid selenocysteine.
The hemocyanin protein uses copper to carry oxygen. It has an oxygen density that is
1/4 of hemoglobin.
Plastocyanin is a copper-containing protein used in photosynthesis.
Lignin is the structural component of wood.
Audax: Lives underground, eats rock, and gets its energy from molecules generated
by radioactivity. It can colonize a planet from scratch.
Conan: Survives radioactivity, outer space, acid, and freezing.
It has four independent sets of chromosomes with active repair mechanisms.
Tardigrade (water bear): Survives temperatures from absolute zero to 161 C.
Survives outer space. Found everywhere on the Earth from Mount Everest to
the bottom of the ocean.
The colossal squid is up to 14 meters long, has eyes up to 27 cm in diameter,
and inhabits the ocean at depths of up to 2 km.
The eyes of a Mantis shrimp have 12 color channels, including UV, and they are
sensitive to linear and circular polarization. Each eye is trinocular, giving
it a total of 6 channels for depth perception.
The Mantis shrimp has two clubs for striking.
Top speed of 33 meters/second
Fastest bird. Top horizontal speed of 45 meters/second.
Mass of up to 15 kg
Mass of 75 kg
Edward Lasker: While the Baroque rules of Chess could only have been created by
humans, the rules of Go are so elegant, organic, and rigorously logical that if
intelligent life forms exist elsewhere in the universe, they almost certainly
play Go.
Just tuning is based on integer ratios and equal tuning is based on logarithms,
and there is no direct connection between them. Fortuitously, 12-tone equal
tuning gives a set of notes that are nearly identical to those for just tuning.
The correspondence is close, but not exact, and violinists use a compromise
between just and equal tuning that is situation dependent.
The synthesis of just and equal tuning offers rich contrapuntal possibilities,
as was explored during the Baroque age by composers such as Vivaldi, Bach, and
Handel.
exp(Index/12)
Equal tuning is based on equal frequency ratios. Just tuning adjusts the
frequencies to correspond to the nearest convenient integer ratio. For example,
in equal tuning, the frequency ratio of a fifth is 1.498. Just tuning changes it
to 1.500 = 3/2.
The 12-tone scale is ubiquitous in Earth music and it arises from elegant
mathematics. If alien life plays music, they likely use the 12-tone scale.
The major and minor scales select 8 notes from the 12 note scale, favoring notes that
have nice integer ratios.
In the 6th century BCE, Pythagoras developed a 12-tone scale based on the
ratios 2/1 and 3/2. This tuning was widely used until the 16th century CE.
Pythagoriean tuning gives good results for fourths and fifths but poor results
for thirds.
In the baroque age, violinists played with a pure, vibratoless tune, using bow
speed rather than vibrato for expressivity. After the baroque age, an epidemic
of vibrato emerged and is still with us, especially at Juilliard and Lincoln
Center. Vibrato obstructs the resonances of just intonation.
"There are performers who tremble consistently on each note as if they had the permanent fever"
- Leopold Mozart, 1756
The violinist and teacher Leopold Auer, in his book "Violin Playing as I Teach
It" (1920), advised violinists to practise playing completely without vibrato,
and to stop playing for a few minutes as soon as they noticed themselves
playing with vibrato in order for them to gain complete control over their
technique.
From the Wikipedia page on Yehudi Menuhin:
After building early success, he experienced considerable physical and artistic
difficulties caused by overwork during the war as well as unfocused and
unstructured early training (reportedly he said "I watched myself on film and
realized that for 30 years I'd been holding the bow wrong").
Careful practice and study combined with meditation and yoga helped him
overcome many of these problems. When he finally resumed recording, he was
known for practising by analyzing music phrases one note at a time.
The Atlas-Skull joint controls pitch and the Axis-Atlas joint controls yaw.
Alexander Technique emphasizes gaining an awareness of these motions.
Visual information passes through the motor cortex before being combined at the rear of
the brain. The brain and body are an image stabilization system for the eyes.
The muscles of the back are continuously connected between the shoulder blades
and the hips, to coordinate motion of the limbs.
Bruce Lee: "Balance is the all-important factor in a fighter's attitude or stance.
Without balance at all times, he can never be effective."
Jascha Heifetz masterclass
In this clip, at time=5:45-6:15, Heifetz emphasizes the importance of balance and
posture.
* Marie Daniels illustrates the importance of balance for playing the viola.
Balance flows from a stance with knees in and heels out.
* Gordon Liu demonstrates the wire style at time=4:37
Bruce Lee: "One should seek good balance in motion and not in stillness."
Bruce Lee: "Balance is the control of one's center of gravity plus the control and utilization of body slants
and unstable equilibrium, hence gravity pull to facilitate movement. So, balance might mean being able
to throw one's center of gravity beyond the base of support, chase it, and never let it get away."
* Jet Li and the Drunken Sword. Try this with a viola bow.
Bruce Lee: "The center of gravity kept under delicate and rapid motion are characteristic habbits of athletes
in games that require sudden and frequent changes of direction."
Bruce Lee: "The short step and the glide, as contrasted with the hop or cross step, are devices to keep
the center of gravity. When it is necessary to move rapidly, a good man takes small enough steps
so that his center of gravity is rarely out of control."
Bruce Lee: "In general for athletic contests, a preparatory stance a coiled, or
semicrouched posture and a lowered, forward center of gravity. with the
bending of the forward knee, the center of gravity moves forward a little. For
general readiness, the lead heal usually remains just touching even after the
knees bend. Slight ground contact of the heel aids in balance and decreases
tension."
Bruce Lee: Experiments indicate that auditory cues, when occurring close to the
athlete, are responded to more quickly than visual ones. Make use of auditory
clues together with visual clues, if possible. Remember, however, the focus of
attention on general movement produces faster action than focus on hearing or
seeing the cue.
Time in milliseconds:
Oxygen atmosphere
If a planet is close enough to a star it becomes tidally locked to the star.
Mercury is just barely close enough for this and it orbits such that
3 * Orbit period = 2 * Spin period
If it were any closer it would be forced into a lock such that
Orbit period = Spin period
All of the solar system's moons are locked to their planets in this way. None
of the planets are locked to their moons except Pluto.
For a low-mass star, the habitable zone is closer to the star than it is for
the sun. If the star is sufficiently small, a planet in the habitable zone
will be close enough to be locked to the star and will experience extreme
weather.
Let L = Luminosity of a star / Luminosity of the sun (Watts).
If a star is such that the habitable zone is at Mercury's orbit, what is L?
What stellar mass corresponds to this luminosity?
Among the elements required for life, nitrogen is the scarcest.
The nitrogen in the first 250 km of the Earth's crust has the same mass as
the nitrogen in the atmosphere.
The elements that are abundant in the crust and never used by life are aluminum and titanium.
All elements necessary for life are abundant in either the crust, the ocean, or the atmosphere.
Enzymes use ATP as an energy source to power chemical reactions. ATP and ATP
synthase are common to all Earth life.
* Video of the ATP synthase enzyme in action
Cell walls are formed from a double layer of lipids. They are elastic and they
self-assemble.
Each lipid has a polar and a non-polar end. The polar end faces the water
and the non-polar end faces another lipid.
* Video of the self-assembly of a bilipid layer
If life were to exist in a non-polar solvent it would have to find another way
to make cell walls.
Amino acids have the above form, where R stands for an arbitrary molecule.
DNA codes a sequence of amino acids. The 64-element codon system is universal to
Earth life.
The codon ATG both codes for methionine and serves as an initiation site: the
first ATG in an mRNA's coding region is where translation into protein begins.
21 amino acids are used by eucaryote. More than 500 amino acids are known.
Hydrocarbons have good energy/mass and are good for energy storage. Sugars and fats
are convenient hydrocarbons to metabolize, and humans can metabolize most of them.
An "Alkane" is a carbon chain with hydrocarbons attached. At standard
temperature (300 K), alkanes are solid if they have more than 20 carbons. This
is why lipids (long alkanes) are the optimal form of energy storage. Short
alkanes are liquids or gases at STP and are hard to store.
In the following table, the first section shows properties of alkanes and the second section
shows properties of other energy sources.
An alkane with 7 or more carbons has a heat of combustion of 46 MJoules/kg.
A nitrogen molecule is more tightly bound than an oxygen molecule, making it impossible
to extract energy from hydrocarbons with nitrogen. Few things burn in a nitrogen atmosphere,
lithium and magnesium being examples.
A sugar generally has the formula CN H2N ON, where
N = 2, 3, etc. The common sugars are hexoses with N=6.
Each sugar molecule has two mirror-symmetric forms, the "D" and "L" form. Only the D forms
are found in nature.
The following figures show all sugars up to 6 carbons. All can be metabolized by humans.
2 carbons:
3 carbons:
4 carbons:
5 carbons:
6 carbons:
Fatty acids and sugars are metabolized in the following stages, with each stage yielding energy.
Blood delivers fatty acids to cells.
The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2.
Coenzyme-A carries the acetyl around.
A fat molecule is converted into a fatty acid by lipolysis, and then the fatty acid is converted
into acetyl by beta oxydation, and then the acetyl is converted into H2O and CO2
by the citric acid cycle.
Beta oxidation cleaves 2 carbons from a fatty acid, which becomes acetyl. This process is repeated
until te entire fatty acid has been converted into acetyls.
The steps of beta oxidation are:
Glycolysis converts a glucose molecule into 2 pyrovate molecules. A summary of the reaction showing only
the starting and ending points is:
The full reaction is:
The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2.
Fat metabolism oxidizes a carbon chain so that the chain can be split into acetyl.
The strategy of the citric acid cycle is to further oxidize the acetyl (now a part of citrate)
so that the remaining carbon bonds in the acetyl can be broken.
An alcohol is a carbon chain with one OH attached.
Palmitic acid has 16 carbons and is the most common fatty acid found in food.
Weakly toxic:
For a rod under tension,
Tensile strain is stretching, and is measured as a fractional change in length. For a rod under strain,
The tensile modulus is resistance to strain, and can be thought of as
stiffness. This is a
form of Hooke's law. For a rod under stress,
A material's "tensile strength" is the maximum tensile stress it can take before
breaking.
A material's "tensile yield strength" is the maximum stress it can take before
deforming irreversibly. For metals, the yield strength is usually 3/4 of the
tensile strength, and for wood, the yield strength is only slightly less than the
tensile strength.
For engineering, we focus on yield strength rather than tensile strength.
A material's "tensile yield strain" is the maximum strain it can take before yielding.
For metals, the value varies widely.
Alloying a metal doesn't change the tensile modulus, but it improves yield strain.
The table shows the "strong metals", the metals with good strength/density.
For bridges, what counts is strength/density.
For wood and for the strong metals,
Beryllium is an exception, with a value of 137 MJoules/kg.
The plot shows the tensile modulus divided by density.
For many applications, the measure of the quality of a material is the elastic
energy/mass it can take before yielding. For this, a material should have a large tensile
modulus and a large yield strain.
The best materials are polymers such as Kevlar.
Alloys outperform pure metals. The best alloy is titanium alloy.
The types of deformation are tension, shear, and bulk compression.
A wire shortens when stretched and widens when compressed.
For an isotropic material, the tensile, shear, and bulk moduli are related
through the dimensionless Poisson ratio.
For beams, the types of stresses are:
Tensile strength relates to the strength of wires.
For bending, the yield force of a beam is determined by the shear yield strength.
Z matters more than Y. If you have a beam with a 2x4 cross section, it's best
to align the beam so that Z=4 and Y=2, rather than with Z=2 and Y=4.
Short columns fail by crushing and long columns fail by buckling.
Crushing strength is determined by bulk yield strength.
Long columns fail by buckling, and strength is determined by
tensile yield strength.
For a column that is cylindrical and hollow,
If a column's buckling limit is equal to its squashing limit, and if r=0,
For beams and columns, the lower the density, the better.
For a square beam with Y=Z,
At fixed length and mass, the measure of quality is t/ρ3/2.
For a cylindrical column,
At fixed length and mass, the measure of quality is t ρ-2.
The measure of merit depends on the application. If force/mass is what counts, then the measure of merit is
For many applications, the measure of merit for a material is energy/mass, where "energy" is the maximum
elastic energy the material can take before breaking. This applies to things like racquets, aircraft,
and swords. The cases are:
The strongest woods are:
For most woods, t/ρ has a similar value. For t/ρ2,
balsa wins. We plot t/ρ, t/ρ3/2, and t/ρ2.
To compare wood to other materials,
For a vertical tree trunk, "longitudinal" is the vertical direction. "Radial"
is the direction from the tree center axis, going outward in the horizonal
plane. "Tangential" is the direction along a tree ring, in the horizontal
plane.
Poisson numbers:
The strongest direction is the longitudinal direction and the weakest direction is the radial
direction. For a beam under bending stress, you should align the longitudinal grain with the
long axis of the beam, and you should align the tangential grain with the direction of the
force.
A hollow beam is weaker than a solid beam, but it has a better
stength/mass ratio. This is the point of a truss. A truss consists of a set of upper and lower
beams connected by struts. The struts deliver forces between the beams and they resist warp.
Struts are arranged as triangles because triangles resist warp better than squares.
In a Pratt truss, diagonal beams are under tension and vertical beams are under compression.
A Howe truss is like a Pratt truss except that the diagonals slant the opposite way.
In a Howe truss, diagonal beams are under compression and vertical beams are under tension.
Beams under compression should be wider than beams under tension. Compression is harder than tension.
Bridges from centuries ago tended to use wood for compression elements and steel rods for tension elements.
.jpg)
Alloys can be much stronger than pure metals.
Discovery Method of Source
(year) discovery
Carbon Ancient Naturally occuring
Gold Ancient Naturally occuring
Silver Ancient Naturally occuring
Sulfur Ancient Naturally occuring
Lead -6500 Smelt with carbon Galena PbS
Copper -5000 Smelt with carbon Chalcocite Cu2S
Bronze (As) -4200 Copper + Arsenic Realgar As4S4
Tin -3200 Smelt with carbon Calamine ZnCO3
Bronze (Sn) -3200 Copper + Tin
Brass -2000 Copper + Zinc Sphalerite ZnS
Mercury -2000 Heat the sulfide Cinnabar HgS
Iron -1200 Smelt with carbon Hematite Fe2O3
Arsenic 1250 Heat the sulfide Orpiment As2S3
Zinc 1300 Smelt with wool Calamine ZnCO3 (smithsonite) & Zn4Si2O7(OH)2·H2O (hemimorphite)
Antimony 1540 Smelt with iron Stibnite Sb2S3
Phosphorus 1669 Heat NaPO3 Excrement
Cobalt 1735 Smelt with carbon Cobaltite CoAsS
Platinum 1735 Naturally occuring
Nickel 1751 Smelt with carbon Nickeline NiAs
Bismuth 1753 Isolated from lead
Hydrogen 1766 Hot iron + steam Water
Oxygen 1771 Heat HgO
Nitrogen 1772 Isolated from air
Manganese 1774 Smelt with carbon Pyrolusite MnO2
Molybdenum 1781 Smelt with carbon Molybdenite MoS2
Tungsten 1783 Smelt with carbon Wolframite (Fe,Mn)WO4
Chromium 1797 Smelt with carbon Crocoite PbCrO4
Palladium 1802 Isolated from Pt
Osmium 1803 Isolated from Pt
Iridium 1803 Isolated from Pt
Rhodium 1804 Isolated from Pt
Sodium 1807 Electrolysis
Potassium 1807 Electrolysis
Magnesium 1808 Electrolysis Magnesia MgCO3
Cadmium 1817 Isolated from zinc
Lithium 1821 Electrolysis of LiO2 Petalite LiAlSi4O10
Zirconium 1824 Smelt with potassium Zircon ZrSiO4
Aluminum 1827 Smelt with potassium
Silicon 1823 Smelt with potassium
Beryllium 1828 Smelt with potassium Beryl Be3Al2Si6O18
Thorium 1929 Smelt with potassium Gadolinite (Ce,La,Nd,Y)2FeBe2Si2O10
Vanadium 1831 Smelt VCl2 with H2 Vanadinite Pb5(VO4)3Cl
Uranium 1841 Smelt with potassium Uranite UO2
Ruthenium 1844 Isolated from Pt
Tantalum 1864 Smelt with hydrogen Tantalite [(Fe,Mn)Ta2O6]
Niobium 1864 Smelt with hydrogen Tantalite [(Fe,Mn)Ta2O6]
Fluorine 1886 Electrolysis
Helium 1895 From uranium ore
Titanium 1910 Smelt with sodium Ilmenite FeTiO3
Hafnium 1924 Isolated from zirconium
Rhenium 1928 Isolated from Pt
Scandium 1937 Electrolysis Gadolinite FeTiO3
-384 -322 Aristotle. Wrote "Meteorology"
-370 -285 Theophrastus. Wrote "De Mineralibus"
77 Pliny the Elder publishes "Natural History"
973 1050 Al Biruni. Published "Gems"
1546 Georgius Agricola publishes "On the Nature of Rocks"
1556 Georgius Agricola publishes "On Metals"
1609 de Boodt publishes a catalog of minerals
1669 Brand: Discovery of phosphorus
1714 John Woodward publishes "Naturalis historia telluris illustrata & aucta", a mineral catalog
1735 Brandt: Discovery of cobalt
1777 Lavoisier: Discovery of sulfur
1778 Lavoisier: Discovery of oxygen and prediction of silicon
1783 Lavoisier: Discovery of hydrogen
1784 T. Olof Bergman publishes "Manuel du mineralogiste, ou sciagraphie du regne mineral",
and founds analytical chemistry
1778 Lavoisier: Discovery of oxygen
1801 Rene Just Huay publishes "Traite de Mineralogie", founding crystallography
1811 Avogadro publishes "Avogadro's law"
1860 The Karlsruhe Congress publishes a table of atomic weights
1869 Mendeleev publishes the periodic table
Shear modulus = S = 82 GJoules/meter3
Density = D = 7900 kg/meter3
Sword worthiness = Q = S/D = 10.4 MJoules/kg
-600 Wootz steel developed in India and is renowned as the finest steel in the world.
1700 The technique for making Wootz steel is lost.
1790 Wootz steel begins to be studied by the British Royal Society.
1838 Anosov replicates Wootz steel.
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon),
and cementite (iron carbide, Fe, 6.7% carbon).
Yield strength = Y (Pascals)
Density = D (kg/meter3)
Quality = Q = Y/D (Joules/kg)
The strongest allyos are:
Yield strength Density Quality
(GPa) (g/cm3) (MJoule/kg)
Magnesium + Lithium .14 1.43 98
Magnesium + Y2O3 .31 1.76 177
Aluminum + Beryllium .41 2.27 181
Amorphous LiMgAlScTi 1.97 2.67 738
Diamond 1.6 3.5 457
Titanium + AlVCrMo 1.3 4.6 261
Amorphous AlCrFeCoNiTi 2.26 6.5 377
Steel + Cobalt, Nickel 2.07 8.6 241
Amorphous VNbMoTaW 1.22 12.3 99
Molybdenum+ Tungsten, Hafnium 1.8 14.3 126
The strongest pure metals are weaker than the strongest alloys.
Yield strength Density Quality
(GPa) (g/cm3) (MJoule/kg)
Magnesium .10 1.74 57
Beryllium .34 1.85 184
Aluminum .02 2.70 7
Titanium .22 4.51 49
Chromium .14 7.15 20
Iron .10 7.87 13
Cobalt .48 8.90 54
Molybdenum .25 10.28 24
Tungsten .95 19.25 49
Beryllium + Li → Doesn't exist. The atoms don't mix
Beryllium + Al → Improves strength
Magnesium + Li → Weaker and lighter than pure Mg. Lightest existing alloy
Magnesium + Be → Only tiny amounts of beryllium can be added to magnesium
Magnesium + Carbon tubes → Improves strength, with an optimal tube fraction of 1%
Aluminum + Li,Mg,Be,Sc → Stronger and lighter than aluminum
Titanium + Li,Mg,Sc → Stronger and lighter than titanium
Steel + Cr,Mo → Stronger and more uncorrodable than steel. "Chromoly"
Copper + Be → Stronger than beryllium and is unsparkable
Melting point (Celsius)
Tungsten 3422
Rhenium 3186
Osmium 3033
Tantalum 3017
Molybdenum 2623
Niobium 2477
Iridium 2446
Ruthenium 2334
Hafnium 2233
Technetium 2157
Rhodium 1964
Vanadium 1910
Chromium 1907
20 600 800 900 1000 1100 1200 1400 1600 1800 1900 Celsius
VNbMoTaW 1.22 .84 .82 .75 .66 .48 .4
AlMohNbTahTiZr 2.0 1.87 1.60 1.2 .74 .7 .25
Nickel superalloy 1.05 1.20 .90 .60 .38 .15
Tungsten .95 .42 .39 .34 .31 .28 .25 .10 .08 .04
Below 1100 Celsius AlMohNbTahTiZr has the best strength-to-mass ratio and above
this VNbMoTaW has the best ratio. Both alloys supersede nickel superalloy
and both outperform tungsten, the metal with the highest melting point.
Data:
Entropy, nickel superalloy
Yield strength (GPa)
Copper .27
Brass .41 30% zinc
Bronze .30 5% tin
Phosphor bronze .69 10% tin, .25% phosphorus
Copper + beryllium 1.2 2% beryllium, .3% cobalt
Copper + nickel + zinc .48 18% nickel, 17% zinc
Copper + nickel .40 10% nickel, 1.25% iron, .4% manganese
Copper + aluminum .17 8% aluminum
Atom Form of Atomization energy
raw element kJoules/mole
H H2 218
He He 0 Noble elements are already atomized
Be Metal 159
Li Metal 324
B Boron solid 563
C Graphite 717
N N2 473
O O2 249
F F2 79
Ne Ne 0
Na Metal 107
Mg Metal 146
Al Metal 326
Si Crystal 456
P Solid 315
S Solid 279
Cl Cl2 122
Fe Metal 415
Pressure = P
Volume = V
Entropy = S
Temperature = T
Internal energy = E
Enthalpy = H = E + P V
Gibbs energy = G = E + P V - T S
Helmholtz energy = A = E - T S
The Gibbs energy is the energy required to assemble a molecule from raw
elements at standard temperatue (298.2 Kelvin) and pressure (1 bar). The Gibbs energy
of raw elements is defined as zero.
Energy = E Joules
Electron volt = e = 1.602e-19 Joules = 96.47 kJoules/mole
Avogadro number = A = 6.0221e23 particles/mole
Atomic mass unit = m = 1.6605e-27 kg
Boltzmann constant = k = 1.3806e-23 Joules/Kelvin
H2O → H2 + ½ O2 - 286 kJ/mole
→ 2 H + O - 286 - 2*218 - 249 kJ/mole
→ 2 H + O - 971 kJ/mole
Gibbs Enthalpy Entropy Atomize
kJ/mole kJ/mole kJ/mole/K kJ/mole
H2 0 0 .131 -436
C graphite 0 0 .00574 -717
N2 0 0 .1915 -946
O2 0 0 .2050 -498
H2O -237.24 -285.83 .06995 -716 -286 - 2*218 - 249
CO2 -394.4 -393.5 .214 -1609 -394 - 717 - 498
CH4 -74.87 .1862 -1664 -75 - 717 - 872
C2H6 -83.7
C3H8 -104.6
C4H10 -125.5
C5H12 -146.9
C6H14 -167.4
C7H16 -187.9
C8H18 -208.4
C12H26 -352.1 .4907
C16H34 -456.3 .5862
Gunpowder has oxygen in the mixture in the form of
KNO3 which makes it burn faster.
eV kJoules/mole
H - H
HO - H 493.4
O - H 424.4
CH3 - H 4.52 435
CH2 - H 444
CH - H 444
C - H 339
C2H5 - H 423
C2H - H 556
C6H5 - H 473
CH3 - CH3 3.64 351
CH2 = CH2 622
CH ≡ CH 837
C2H3 - H 464
CH2CHCH2 - H 372
Gibbs Enthalpy Entropy
kJoule/mole kJoule/mole kJoule/mole/K
H2 0 0 .131
C graphite 0 0 .00574
C diamond 2.90 1.90 .00238
N2 0 0 .1915
O2 0 0 .2050
Ne 0 0 .1464
Na 0 0 .0512
Mg 0 0 .0327
Al 0 0 .0283
Al 0 0 .0283
Si 0 0 .0188
P4 0 0 .1644
S 0 0 .0318
Cl2 0 0 .223
K 0 0 .0642
Ca 0 0 .0414
Ar 0 0 .155
Cr 0 0 .0238
Mn 0 0 .0327
Fe 0 0 .0273
Ni 0 0 .0299
Cu 0 0 .0332
Zn 0 0 .0416
Ag 0 0 .0426
Sn 0 0 .0516
Hg 0 0 .0760
Pb 0 0 .0648
H2O -237.24 -285.83 .06995
CH4 -74.87 .1862 Combustion = -890.7
C2H6 -83.7 Combustion = -1561
C3H8 -104.6
C4H10 -125.5
C5H12 -146.9
C6H14 -167.4
C7H16 -187.9
C8H18 -208.4
C12H26 -352.1 .4907 Combustion =-7901.7
C16H34 -456.3 .5862 Combustion =-10699
N2O 82.05 .2200
H2O2 -187.80
N2O4 9.16 .3043
N2H4 50.63 .1215
NH4NO3
NH4ClO4
HNO3 -207 .146
Li2O -561.9 -20.01 .03789
C4H8N8O8 HMX explosive
BeO -579.1
B2O3 -1184
CO2 -394.4 -393.5 .214
CO -137.2 -110.5 .198
NO 90.2 .211
NO2 33.2 .240
Na2O -377
MgO -596.3 -601.6 .0269
Al2O3 -1582.3 -1675.7 .0509
SiO2 -856.6 -910.9 .0418 Quartz
P2O5
SO2 -296.8 .2481
SO3 -395.7 .2567
K2O -322.2
CaO -533.0 -634.9 .0398
TiO2 -852.7
Ti2O3 -1448
VO -404.2
V2O3 -1139.3
V2O4 -1318.4
Cr2O3 -1053.1 -1139.7 .0812
MnO2 -465.2
MnO -362.9 -385.2 .0597
MnO2 -520.0 .0530
Fe2O3 -741.0 -824.2 .0874
Fe3O4 -1014 -1118.4 .0146
CoO -214.2
Co3O4 -795.0
NiO -211.7 -239.7 .0380
CuO -129.7 -157.3 .0426
Cu2O -146.0 -168.6 .0931
ZnO -318.2 -350.5 .0436
MoO2 -533.0
MoO3 -668.0
Ag2O -11.2
PdO
SnO2 -577.6 .0523
CdO -228.4
WO2 -533.9
WO3 -764.1
HgO -58.5 -90.8 .0703
PbO -219.0 .0665
PbO2 -219.0 -277.4 .0686
UO2
CuS -53.1 .0665
Cu2S -79.5 .1209
ZnS2 -206.0 .0577
CaCO3 -1128 -1207 .090
H+ (aq) 0 0 0
OH- (aq) -157.2 -230.0 -.0108
H2O (l) -237.2 -285.8 .0699
H2O (g) -228.6 -241.8 .1888
Cu+ 71.7 .0406
Cu+2 64.8 -.0996
Ca+2 -543.0 -.0531
Ag+ (aq) 105.8 .0727
Al+3 (aq) -538.4 -.3217
CO3-2 -675.2 -.0569
NH3 (g) -16.4 -46.1
NaCl (s) -384.1 -411.2 .0721
Gibbs Enthalpy Entropy
kJoule/mole kJoule/mole kJoule/mole/K
Target Molecule Bonds Bond 1st 2nd 3rd 4th
atom energy bond bond bond bond
(eV) (eV) (eV) (eV) (eV)
H H2 1 4.52 4.52
He - 0 - -
Li LiH 1 2.56 2.56
Be BeH2 2 ? 2.35 ?
B BH3 3 ? 3.43 ? ?
C CH4 4 4.31 3.52 4.61 4.61 4.52
N NH3 3 3.90 3.26 3.91 4.52
O H2O 2 4.76 4.41 5.12
F HF 1 5.90 4.90
Ne - 0 - -
Na NaH 1 2.09 2.09
Mg MgH2 2 ? 2.04 ?
Al AlH3 3 ? 2.96 ? ?
Si SiH4 4 ? 3.10 ? ? 4.08
P PH3 3 ? 3.56 ? ?
S H2S 2 3.76 3.57 3.95
Cl HCl 1 4.48 4.48
Ar - 0 - -
K KH i 1.90 1.90
Ca CaH2 i ? 1.74 ?
Ga ? ? ? ?
Ge ? 3.36 ? ? ?
As ? 2.82 ? ?
Se SeH2 2 ? 3.17 ?
Br HBr 1 3.80 3.80
Kr - 0 - -
In ? ? ? ?
Sn ? 2.77 ? ? ?
Sb ? ? ? ?
Te TeH2 2 ? 2.78 ?
I HI 1 3.10 3.10
Xe - 0 - -
Single Double Triple Quadruple
B B 3.04
B C 3.69
B O 5.56
C C 3.65 6.45 8.68 6.32
C N 3.19 6.38 9.19
C O 3.73 7.7 11.11
C Si 3.30
C P 2.74
C S 2.82 5.94
N N 1.76 4.33 9.79
N O 2.08 6.29
N Si 3.70
N P
N S
O O 1.50 5.15
O Si 4.69
O P 3.47 5.64
O S 5.41
Si Si 2.30
Si S 3.04
Si P
P P 2.08
P S 3.47
S S 2.34 4.41
H H 4.52
H C 4.25
H N 4.05
H O 3.79
H F 5.89
H Si 3.30
H P 3.34
H S 3.76
H Cl 4.48
Enthalpy
kJ/mole
H2O -285.83
Li2O -20.01
BeO -609.4
CO2 -393.5
MgO -601.6
Al2O3 -1675.7
Fe2O3 -824.2
Enthalpy Entropy Boil Density
kJ/mole kJ/mole Kelvin
O2 0 .2050
O3 142.67 .2389 161
H2O2 -187.80
NO 90.2 .211
NO2 33.2 .240
HNO3 -207 .146 356 1.51
N2O3 91.20 .3146 277 1.45
N2O4 9.16
N2O5 -43.1 .1782 320 1.64 solid
N2O 82.05 .2200
SO2 -296.8 .2481 265
SO3 -395.7 .2567
N2H4 50.63 .1215
NH4NO3 -365.6 483 1.72
NH4ClO4 -295.77 .1842
C4H8N8O8 296.16 HMX explosive
NH3OHNO3
Cu2O + C → 2 Cu + CO
At low temperature copper stays in the form of Cu2O and at high
temperature it gives the oxygen to carbon and becomes pure copper.
3 Fe2O3 + C → 2 Fe3O4 + CO
Fe3O4 + C → 3 FeO + CO
FeO + C → Fe + CO
Oxidation state = Number of electrons each iron atom gives to oxygen
Oxidation state
CuO 2
Cu2O 1
Cu 0
Fe2O3 3
Fe3O4 8/3
FeO 2
Fe 0
Smelt Method Year Abundance
(C) (ppm)
Gold <0 * Ancient .0031
Silver <0 * Ancient .08
Platinum <0 * 1735 .0037
Mercury <0 heat -2000 .067
Palladium <0 chem 1802 .0063
Copper 80 C -5000 68
Sulfur 200 * Ancient 420
Lead 350 C -6500 10
Nickel 500 C 1751 90
Cadmium 500 C 1817 .15
Cobalt 525 ? 1735 30
Tin 725 C -3200 2.2
Iron 750 C -1000 63000
Phosphorus 750 heat 1669 10000
Tungsten 850 C 1783 1100
Potassium 850 e- 1807 15000
Zinc 975 C 1746 79
Sodium 1000 e- 1807 23000
Chromium 1250 C 1797 140
Niobium 1300 H 1864 17
Manganese 1450 C 1774 1120
Vanadium 1550 ? 1831 190
Silicon 1575 K 1823 270000
Titanium 1650 Na 1910 66000
Magnesium 1875 e- 1808 29000
Lithium 1900 e- 1821 17
Aluminum 2000 K 1827 82000
Uranium 2000 K 1841 1.8
Beryllium 2350 K 1828 1.9
Smelt: Temperature required to smelt with carbon
Method: Method used to purify the metal when it was first discovered
*: The element occurs in its pure form naturally
C: Smelt with carbon
K: Smelt with potassium
Na: Smelt with sodium
H: Smelt with hydrogen
e-: Electrolysis
heat: Heat causes the oxide to decompose into pure metal. No carbon required.
chem: Chemical separation
Discovery: Year the element was first obtained in pure form
Abundance: Abundance in the Earth's crust in parts per million
Elements with a low carbon smelting temperature were discovered in ancient
times unless the element was rare. Cobalt was discovered in 1735, the first new
metal since antiquity, and this inspired scientists to smelt every known
mineral in the hope that it would yield a new metal. By 1800 all the rare
elements that were carbon smeltable were discovered.
Fe2O3 + 2 Al → 2 Fe + Al2O3
Oxidation state Oxidation state
at left at right
2 M2O ↔ 4 M + O2 1 0
4 MO ↔ 2 M2O + O2 2 1
2 M3O4 ↔ 6 MO + O2 8/3 2
6 M2O3 ↔ 4 M3O4 + O2 3 8/3
2 M2O3 ↔ 4 MO + O2 3 2
2 MO ↔ 2 M + O2 2 0
2/3 M2O3 ↔ 4/3 M + O2 3 0
1 MO2 ↔ 1 M + O2 4 0
2 MO2 ↔ 2 MO + O2 4 2
.jpg)
2(OH)6.jpg)
_.jpg)
.jpg)
_3.jpg)
-178918.jpg)
Hydrogen White
Carbon Black
Nitrogen Blue
Oxygen Red
Sulfur Yellow
Scoville scale (relative capsaicin content)
Ghost pepper 1000000
Trinidad 1000000 Trinidad moruga scorpion
Naga Morich 1000000
Habanero 250000
Cayenne pepper 40000
Malagueta pepper 40000
Tabasco 40000
Jalapeno 5000
Guajillo pepper 5000
Cubanelle 500
Banana pepper 500
Bell pepper 50
Pimento 50
Molecule Relative hotness
Rresiniferatoxin 16000
Tinyatoxin 5300
Capsaicin 16 Chili pepper
Nonivamide 9.2 Chili pepper
Shogaol .16 Ginger
Piperine .1 Black pepper
Gingerol .06 Ginger
Capsiate .016 Chili pepper
Strength Half life Dose
hours mg
Carfentanil 30000 7.7 .0003
Ohmefentanil 6300
Dihydroetorphine 4000 .03
Etorphine 2000 .006
Sufentanil 750 4.4 .015
Ocfentanil 180 .06
Fentanyl 75 .04 .1
Oxymorphone 7 8 10
Hydromorphone 5 2.5 1.5 Dilaudid
Heroine 4.5 <.6 2.2 Diamorphine
Methadone 3.5 30 35
Oxycodone 1.5 4 6.7
Morphine 1 2.5 10
Hydrocodone 1 5 10 Vicodin
Codeine .1 2.8 180
Naproxen .0072 18 1380
Ibuprofen .0045 2 2220
Aspirin .0028 6 3600
% First isolated
Morphine 10 1817 Used to produce heroine
Codeine 2 1832
Thebaine 8 Used to produce hydrocodone and hydromorphone
Papaverine 14 1848 Not psychoactive
Noscapine 5 1820 Not psychoactive
Other alkaloiods .1
MJoules Rocket Shock Density Boil
/kg km/s km/s g/cm3 Kelvin
Beryllium+ O2 23.2 5.3
Aluminum + O2 15.5
Magnesium+ O2 14.8
Hydrogen + O2 13.2 4.56 .07 20
Kerosene + O3 12.9
Octanitrocubane 11.2 10.6 1.95
Methane + O2 11.1 3.80 .42 112 CH4
Octane + O2 10.4 .70 399 C8H18
Kerosene + O2 10.3 3.52 .80 410 C12H26
Dinitrodiazeno. 9.2 10.0 1.98
C6H6N12O12 9.1 1.96 China Lake compound
Kerosene + H2O2 8.1 3.2
Kerosene + N2O4 8.0 2.62
HMX (Octogen) 8.0 3.05 9.1 1.86
RDX (Hexagen) 7.5 2.5 8.7 1.78
Al + NH4NO3 6.9
Nitroglycerine 7.2 8.1 1.59 Unstable
PLX 6.5 1.14 95% CH3NO2 + 5% C2H4(NH2)2
Composition 4 6.3 8.04 1.59 91% RDX. "Plastic explosive"
Kerosene + N2O 6.18
Dynamite 5.9 7.2 1.48 75% Nitroglycerine + stabilizer
PETN 5.8 8.35 1.77
Smokeless powder 5.2 6.4 1.4 Used after 1884. Nitrocellulose
TNT 4.7 6.9 1.65 Trinitrotoluene
Al + Fe2O3 4.0 Thermite
H2O2 2.7 1.59 1.45 423 Hydrogen peroxide
Black powder 2.6 .6 1.65 Used before 1884
Al + NH4ClO4 2.6
NH4ClO4 2.5
N2O 1.86 1.76
N2H4 1.6 2.2 1.02 387 Hydrazine
Bombardier beetle .4 Hydroquinone + H2O2 + protein catalyst
N2O4 .10 1.45 294
Rocket: Rocket exhaust speed
Shock: Shock speed
MJoules Shock Density
/kg km/s g/cm3
Octanitrocubane 11.2 10.6 1.95
Dinitrodiazeno. 9.2 10.0 1.98
C6H6N12O12 9.1 1.96 China Lake compound
HMX (Octogen) 8.0 9.1 1.86
RDX (Hexagen) 7.5 8.7 1.78
PLX 6.5 1.14 95% CH3NO2 + 5% C2H4(NH2)2
Composition 4 6.3 8.04 1.59 91% RDX. "Plastic explosive"
Dynamite 5.9 7.2 1.48 75% Nitroglycerine + stabilizer
PETN 5.8 8.35 1.77
Exhaust Energy Density of fuel + oxidizer
speed /mass
km/s MJ/kg g/cm3
Hydrogen H2 4.46 13.2 .32
Methane CH4 3.80 11.1 .83
Ethane C2H6 3.58 10.5 .9
Kerosene C12H26 3.52 10.3 1.03
Hydrazine N2H4 3.46 1.07
Liquid hydrogen is usually not used for the ground stage of rockets because of
its low density.
Energy/Mass Energy/Mass Rocket Rocket Boil Density
with kerosene as monopropellant with kerosene as monopropellant Kelvin g/cm3
MJoule/kg MJoule/kg km/s km/s
O3 12.9 2.97 161
O2 10.3 0 3.52 0 110 1.14
H2O2 8.1 2.7 3.2 1.6 423 1.45
N2O4 8.00 .10 2.62 294 1.44
N2O 6.18 1.86 1.76 185
N2H4 - 1.58 2.2 387 1.02
MJoules Rocket Density
/kg km/s g/cm3
C6H6N12O12 9.1 1.96 China Lake compound
HMX (Octogen) 8.0 3.05 1.86
RDX (Hexagen) 7.5 2.5 1.78
Al + NH4ClO4 2.6
NH4ClO4 2.5
NH3OHNO3 2.5 1.84 Hydrxyammonium nitrate
Al + NH4NO3 6.9
NH4NO3 1.4 2.0 1.12 Ammonium nitrate
~808 Qing Xuzi publishes a formula resembling gunpower, consisting of
6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850 Incendiary property of gunpower discovered
1132 "Fire lances" used in the siege of De'an, China
1220 al-Rammah of Syria publishes "Military Horsemanship and Ingenious War
Devices", describes the purification of potassium nitrate by
adding potassium carbonate with boiling water, to precipitate out
magnesium carbonate and calcium carbonate.
1241 Mongols use firearms at the Battle of Mohi, Hungary
1338 Battle of Arnemuiden. First naval battle involving cannons.
1346 Cannons used in the Siege of Calais and the Battle of Crecy
1540 Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1610 First flintlock rifle
1661 Boyle publishes "The Sceptical Chymist", a treatise on the
distinction between chemistry and alchemy. It contains some of the
earliest modern ideas of atoms, molecules, and chemical reaction,
and marks the beginning of the history of modern chemistry.
1669 Phosphorus discovered
1774 Lavoisier appointed to develop the French gunpowder program. By 1788
French gunpowder was the best in the world.
1832 Braconnot synthesizes the first nitrocellulose (guncotton)
1846 Nitrocellulose published
1847 Sobrero discovers nitroglycerine
1862 LeConte publishes simple recipes for producing potassium nitrate.
1865 Abel develops a safe synthesis of nitrocellulose
1867 Nobel develops dynamite, the first explosive more powerful than black powder
It uses diatomaceous earth to stabilize nitroglycerine
1884 Vieille invents smokeless gunpowder (nitrocellulose), which is 3 times
more powerful than black powder and less of a nuisance on the battlefield.
1902 TNT first used in the military. TNT is much safer than dynamite
1930 RDX appears in military applications
1942 Napalm developed
1949 Discovery that HMX can be synthesized from RDX
1956 C-4 explosive developed (based on RDX)
1999 Eaton and Zhang synthesize octanitrocubane and heptanitrocubane
Black powder = .75 KNO3 + .19 Carbon + .06 Sulfur
Potassium nitrate KNO3 75% (Saltpeter)
Charcoal C7H4O 15%
Sulfur S 10%
Oversimplified equation: 2 KNO3 + 3 C + S → K2S + N2 + 3 CO2
Realistic equation: 6 KNO3 + C7H4O + 2 S → KCO3 + K2SO4 + K2S + 4 CO2 + 2 CO + 2 H2O + 3 N2
Nitrite (NO3) is the oxidizer and sulfur lowers the ignition temperature.
MJoules
/kg
Hydrogen + Oxygen 13.16
Gasoline + Oxygen 10.4
Mass Energy Energy/Mass
kg MJ MJ/kg
MOAB 9800 46000 4.7 8500 kg of fuel
Form Ignition Density
(Celsius)
White 30 1.83
Red 240 1.88
Violet 300 2.36
Black 2.69
Red phosphorus is formed by heating white phosphorus to 250 Celsius or by
exposing it to sunlight. Violet phosphorus is formed by heating red phosphorus
to 550 Celsius. Black phosphorus is formed by heating white phosphorus at a
pressure of 12000 atmospheres. Black phosphorus is least reactive form and it
is stable below 550 Celsius.
Match head Fraction Striking surface Fraction
Potassium chlorate KClO3 .50 Red phosphorus .5
Silicon filler Si .4 Abrasive .25
Sulfur S small Binder .16
Antimony3 trisulfide Sb2S3 small Neutralizer .05
Neutralizer small Carbon .04
Glue small
A "strike anywhere" match has phosphorus in the match head in the form of
phosphorus sesquisulfide (P4S3) and doesn't need red
phosphorus in the striking surface. P4S3 has an ignition
temperature of 100 Celsius.
.jpg)
Cerium .38 Ignition temperature of 165 Celsius
Lanthanum .22
Iron .19
Neodymium2 .04
Praseodymium .04
Magnesium .04
Air density = .00122 g/cm3
Nitrous oxide gas density = .00198 g/cm3
Diesel density = .832 g/cm3
Gasoline density = .745 g/cm3
Diesel energy/mass = 43.1 MJoules/kg
Gasoline energy/mass = 43.2 MJoules/kg
Nitrous oxide boiling point = -88.5 Celsius
Air oxygen fraction = .21
Nitrous oxide oxygen fraction= .33
Nitrous oxide decompose temp = 300 Celsius
Nitrous oxide liquid pressure= 52.4 Bars Pressure required to liquefy N2O at room temperature
2 H2O2 → 2 H2O + O2 (with protein catalyst)
C6H4(OH)2 → C6H4O2 + H2 (with protein catalyst)
O2 + 2 H2 → 2 H2O
Firing rate = 500 pulses/second
Number of pulses in one barrage = 70
Firing time = .14 seconds
Number of barrages = 20
Airbus A350 compression ratio = 52
Air density at sea level = 1 bar
Air density at 15 km altitude = .25 bar
Air density in A350 engine = 13 bar
From the thermal flame theory of Mallard and Le Chatelier,
Temperature of burnt material = Tb
Temperature of unburnt material = Tu
Temperature of ignition = Ti
Fuel density = Dfuel
Oxygen density = Doxygen
Reaction coefficient = C
Reaction rate = R = C Dfuel Doxygen
Thermal diffusivity = Q = 1.9⋅10-5 m2/s
Flame speed = V
V2 = Q C Dfuel Doxygen (Tb - Ti) / (Ti - Tu)
Energy/mass Energy/mass
not including including
oxygen oxygen
(MJoule/kg) (MJoule/kg)
Hydrogen 113.4 12.7
Gasoline 46.0 10.2
Beryllium 64.3 23.2
Aluminum 29.3 15.5
Magnesium 24.5 14.8
Carbon 12.0 3.3
Lithium 6.9 3.2
Iron 6.6 4.6
Copper 2.0 1.6
Bullet Bullet Speed Energy Barrel Gun Fire Vehicle Cartridge
diam mass rate mass
mm kg m/s kJoule meters kg Hertz tons
Swiss Mini Gun 2.3 .00013 122 .00097 .0018 .020
Chiappa 17 4.4 .0010 560 .16 .121 .17 PMC/Aguila
Chiappa 17 4.4 .0010 640 .20 .121 .17 HM2
SPP-1 4.5 .0128 245 .38 .95 4.5x40mmR
Heckler Koch MP7 4.6 .0020 735 .54 .180 1.9 HK 4.6x30mm
Walther PPK 5.6 .0020 530 .281 .083 .560
Walther PPK 5.6 .0030 370 .141 .083 .560
Walther PPK/S 7.65 .0050 318 .240 .083 .630
Walther PPK/E 9.0 .0065 323 .338 .083 .665
Luger 9mm 9.0 .0081 354 .102
Winchester 9x23 9.0 .0081 442
Colt 45 11.4 .0100 262 .127
Magnum 44 11.2 .0156 448 .165
Smith Wesson 460 11.5 .019 630 3.77 .213 .460 SW Magnum
Magnum DesertEagle 12.7 .019 470 .254 1.996 .50 Action Express
Smith Wesson 50mag 12.7 .026 550 .267 2.26
Smith Wesson 50mag 12.7 .029 520 3.92 .267 2.26
Smith Wesson 50mag 12.7 .032 434 3.01 .267 2.26 .500 SW Magnum
MagnumResearch BFR 12.7 .026 550 3.93 .254 2.40 .50 Beowulf
Ruger 96 4.4 .0013 720 .34 .47 2.38 .17 HMR
Ruger M77 5.2 .0026 1200 1.83 .61 3.74 .204 Ruger
CMMG MK47 Mutant 5.6 .0036 975 Remmington 22
Remmington 9mm 9.0 .0091 975
M4 Carbine 5.56 .0041 936 1.80 .370 2.88 15.8
FN SCAR-H Rifle 7.62 .011 790 3.51 .400 3.58 10.4 20 round magazine
Barrett M82 13.0 .045 908 18.9 .74 14.0 10 round magazine
Hannibal 14.9 .049 750 13.8
CZ-550 15.2 .065 914 27.2 .600 Overkill
Vidhwansak 20 .13 720 33.7 1.0 26 20x81 mm. 3 round magazine
RT-20 20 .13 850 47 .92 19.2 1 round magazine
M621 cannon 20 .102 1005 51.5 45.5 13.3 20x102 mm
M61 Vulcan 20 .102 1050 56.2 92 110 20x102. 6 barrels
Oerlikon KBA 25 .184 1335 164 2.888 112 10
M242 Bushmaster 25 .184 1100 111 2.175 119 8.3 27.6 M2 Bradley
GAU-12 Equalizer 25 .184 1040 99.5 122 70 6.3 Harrier 2. 5 barrels
M230 chain gun 30 .395 805 128 55.9 10.4 5.2 Apache. 30x113 mm
Mk44 Bushmaster 2 30 .395 1080 230 2.41 160 3.3 27.6 M2 Bradley. 30x173 mm
GAU-8 Avenger 30 .395 1070 226 2.30 281 70 11.3 A-10 Warthog. 30x173 mm. 7 barrels
Bushmaster III 35 1180 218 3.3 35x228 mm
Bushmaster IV 40 1.08 198 3.3 40x365 mm
Rheinmetall 120 120 8.350 1750 12800 6.6 4500 .1 62 M1 Abrams tank
M777 Howitzer 155 48 827 16400 5.08 4200 .083
Iowa Battleship 406 862 820 290000 20.3 121500 .033 45000
2 bore rifle 33.7 .225 460 23.7 .711 4.5 Historical big-game rifle
Cannonball 6 lb 87 2.72 438 261 2.4
Cannonball 9 lb 96 4.08 440 395 2.7
Cannonball 12 lb 110 5.44 453 558 2.4
Cannonball 18 lb 125 8.16 524 1120 2.6 2060
Cannonball 24 lb 138 10.89 524 1495 3.0 2500
Cannonball 32 lb 152 14.5 518 1945 3.4 2540
Cannonball 36 lb 158 16.33 450 1653 2.9 3250
Cannonball diameters are calculated from the mass assuming a density of 7.9
g/cm3.
For a pistol or rifle, the "vehicle mass" is the mass of the person wielding it. We
use the mass of a typical person.
The "Metal Storm" gun has 36 barrels, 5 bullets per barrel, and fires all bullets
in .01 seconds. The bullets are stacked in the barrel end-to-end and fired sequentially.
Bullet energy .32
Hot gas .34
Barrel heat .30
Barrel friction .02
Unburnt powder .01
To estimate the velocity of a bullet,
Energy efficiency = e = .32 (Efficiency for converting powder energy to bullet enery)
Bullet mass = M
Powder mass = m
Powder energy/mass = Q = 5.2 MJoules/kg
Bullet velocity = V
Bullet energy = E = ½ M V2 = e Q m (Kinetic energy = Efficiency * Powder energy)
V = (2 e Q m / M)2 = 1820 (m/M)½ meters/second
Color Colorant carat ($)
Painite 55000 CaZrAl9O15(BO3)
Diamond Clear 1400 C
Ruby Red Chromium 15000 Al2O3
Sapphire Blue Iron 650 Al2O3
Sapphire yellow Titanium Al2O3
Sapphire Orange Copper Al2O3
Sapphire Green Magnesium Al2O3
Emerald Green Chromium Be3Al2(SiO3)6
Beryl Aqua Iron Be3Al2(SiO3)6 AKA "aquamarine"
Morganite Orange Manganese 300 Be3Al2(SiO3)6
Topaz Topaz Al2SiO4(F,OH)2
Spinel Red Red MgAl2O4
Quartz Clear SiO2
Amethyst Purple Iron SiO2
Citrine Yellow SiO2
Zircon Red ZrSiO4
Garnet Orange [Mg,Fe,Mn]3Al2(SiO4)3 & Ca3[Cr,Al,Fe]2(SiO4)3
Garnet Blue 1500 [Mg,Fe,Mn]3Al2(SiO4)3 & Ca3[Cr,Al,Fe]2(SiO4)3
Opal SiO2·nH2O
Opal Black 11000 SiO2·nH2O
Jet Black Lignite
Peridot Green (Mg,Fe)2SiO4
Pearl White CaCO3
Jade Green NaAlSi2O6
Amber Orange Resin
.gif)
Year Young Tensile Strain Density Common
(GPa) strength (g/cm3) name
(GPa)
Gut Ancient .2
Cotton Ancient .1 1.5
Hemp Ancient 10 .3 .023
Duct tape .015
Gorilla tape .030
Polyamide 1939 5 1.0 .2 1.14 Nylon, Perlon
Polyethylene 1939 117 1.4 Dacron
Polyester 1941 15 1.0 .067 1.38
Polypropylene 1957 .91
Carbon fiber 1968 3.0 1.75
Aramid 1973 135 3.0 .022 1.43 Kevlar
HMPE 1975 100 2.4 .024 .97 Dyneema, Spectra
PBO 1985 280 5.8 .021 1.52 Zylon
LCAP 1990 65 3.8 .058 1.4 Vectran
Vectran HT 75 3.2 .043 1.41 Vectran
Vectran NT 52 1.1 .021 1.41 Vectran
Vectran UM 103 3.0 .029 1.41 Vectran
Nanorope ~1000 3.6 .0036 1.3
Nanotube 1000 63 .063 1.34
Graphene 1050 160 .152 1.0
Strain = Strength / Young
Carbon fiber is not useful as a rope.
Batman mass = M = 100 kg (includes suit and gear)
Gravity constant = g = 10 meters/second2
Batman weight = F = 1000 Newtons
Zylon density = D = 1520 kg/meter3
Zylon tensile strength = Pz = 5.8⋅109 Newtons/meter2
Rope load = P = 1.0⋅109 Newtons/meter2 (safety margin)
Rope length = L 100 meters
Rope cross section = A = F/P =1.0⋅10-6 meters2
Rope radius = R =(A/π)½= .56 mm
Rope mass = Mr = DAL = .15 kg
Density Tensile Young
strength
(g/cm^3) (Gpa) (Gpa)
Balsa .12 .020 3.7
Corkwood .21
Cedar .32 .046 5.7 Northern white
Poplar .33 .048 7.2 Balsam
Cedar .34 .054 8.2 Western red
Pine .37 .063 9.0 Eastern white
Buckeye .38 .054 8.3 Yellow
Butternut .40 .057 8.3
Basswood .40 .061 10.3
Spruce, red .41 .072 10.7
Aspen .41 .064 10.0
Fir, silver .42 .067 10.8
Hemlock .43 .061 8.5 Eastern
Redwood .44 .076 9.6
Ash, black .53 .090 11.3
Birch, gray .55 .069 8.0
Walnut, black .56 .104 11.8
Ash, green .61 .100 11.7
Ash, white .64 .110 12.5
Oak, red .66 .100 12.7
Elm, rock .66 .106 10.9
Beech .66 .102 11.8
Birch, yellow .67 .119
Mahogany .67 .124 10.8 West Africa
Locust .71 .136 14.5 Black or Yellow
Persimmon .78 .127 14.4
Oak, swamp .79 .124 14.5 Swamp white
Gum, blue .80 .118 16.8
Hickory .81 .144 15.2 Shagbark
Eucalyptus .83 .122 18.8
Bamboo .85 .169 20.0
Oak, live .98 .130 13.8
Ironwood 1.1 .181 21.0
Lignum Vitae 1.26 .127 14.1
Data #1
Data #2
Density Tensile Young
strength
(g/cm^3) (Gpa) (Gpa)
Polyamide .11 4.5
Polyimide .085 2.5
Acrylic .07 3.2
Polycarbonate .07 2.6
Acetyl copoly .06 2.7
ABS .04 2.3
Polypropylene .91 .04 1.9
Polystyrene .04 3.0
Polyethylene .95 .015 .8
Yield Density Strength/Density
strength (g/cm3) (GJoule/kg)
(GPascal)
Beryllium .34 1.85 .186
Aluminum + Be .41 2.27 .181
LiMgAlScTi 1.97 2.67 .738
Titanium .22 4.51 .050
Titanium + AlVCrMo 1.20 4.6 .261
Vanadium .53 6.0 .076
AlCrFeCoNiTi 2.26 6.5 .377
AlCrFeCoNiMo 2.76 7.1 .394
Steel .25 7.9 .032 Iron plus carbon
Copper .12 9.0 .013
"Yield strength" is the maximum pressure a material can sustain before
deforming. "Strength/Density" is the strength-to-weight ratio.
Steel is stronger and lighter than copper.
Name Owner
Sword Longclaw Jon Snow
Sword Heartsbane Samwell Tarly
Dagger Arya
Sword Ice Eddard Stark Reforged into Oathkeeper and Widow's Wail
Sword Oathkeeper Brienne of Tarth
Sword Widow's Wail The Crown
Sword Lady Forlorn Ser Lyn Corbray
Sword Nightfall Ser Harras Harlow
Sword Red Rain Lord Dunstan Drumm
Arakh Caggo
Armor Euron Greyjoy
Horn Dragonbinder The Citadel of The Maesters
Some Maesters carry links of Valyrian steel, a symbol of mastery of the highest arts.
C8H18 + 12.5 O2 → 8 CO2 + 9 H2O
3 C + S + 2 KNO3 → K2S + N2 + 3 CO2
We know that wildfire contains an oxidizer otherwise it wouldn't be able to
explode as it did on the show. Wildfire is made from manure, which contains
KNO3.
Gasoline: Flame spreads slowly. Needs oxygen from the air.
Gunpowder: Contains oxygen. Buns faster than gasoline. Subsonic pressure wave.
Plastic explosive: Pressure wave spreads supersonically as a shock.
~808 Qing Xuzi publishes a formula resembling gunpower, consisting of
6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850 Incendiary property of gunpower discovered
1540 Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1661 Boyle publishes "The Sceptical Chymist", a treatise on the
distinction between chemistry and alchemy. It contains some of the
earliest modern ideas of atoms, molecules, and chemical reaction,
and marks the beginning of the history of modern chemistry.
1662 Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
1663 Guericke invents the first electrostatic generator, which uses
mechanical work to separate charge. Generators were refined until
they were superceded by the battery.
1671 Boyle discovers that combining iron filings and acid produces hydrogen gas.
1754 Black isolates CO2
1758 Black formulates the concept of latent heat to explain phase transitions
1766 Cavendish identifies hydrogen as a colorless, odourless gas that burns
in air.
1772 Scheele produces pure oxygen gas by heating HgO.
1774 Priestly produces pure oxygen gas by focusing sunlight on HgO.
He noted that it is combustible and that it gives energy when breathed.
1745 von Kleist invents the capacitor, a device for storing charge generated
by an electrostatic generator.
1746 van Musschenbroek refines the capacitor, which comes to be known as a
"Leyden jar".
1777 Lavoisier finds that in the reaction tin+oxygen, mass is conserved.
He also finds that oxygen is not the only component of air, that air also
consists of something else.
1780 Galvani observes that when a frog leg is touched by an iron scalpel,
it twitches. This was the inspiration for Volta to invent the battery.
1781 Cavendish finds that buring hydrogen + oxygen produces water.
1787 Charles finds that for air at constant pressure,
Volume = Constant * Temperature
He also finds that this applies for O2, N2, H2, and CO2.
1789 Lavoisier publishes "Traite Elementaire de Chimie", the first modern
chemistry textbook. It is a complete survey of (at that time) modern
chemistry, the law of conservation of mass.
1791 Volta develops the first electrochemical cell, consisting of two different
metals separated by a moist intermediary.
1797 Proust proposes the law of definite proportions, that elements
combine in small whole number ratios to form compounds.
1800 Volta constructs the first "battery" by connecting multiple electrochemical
cells in parallel, increasing the output power and voltage.
1801 Dalton publishes the law of partial pressures.
The pressure of a mix of gases is equal to the sum of the pressures
of the components. He also finds that when a light and heavy gas are mixed,
the heavy gas does not drift to the bottom but rather fills the space
uniformly.
1805 Gay-Lussac and Humboldt find that water is formed of two volumes of
hydrogen gas and one volume of oxygen gas.
1809 Gay-Lussac finds that for an ideal gas at constant volume,
Pressure = Constant * Temperature
1811 Avogadro finds that equal volumes of different gases have the same number
of particles. At constant temperature and pressure,
Volume = Constant * NumberOfParticles
1811 Avogadro arrives at the correct interpretation of water's composition,
based on what is now called Avogadro's law and the assumption of diatomic
elemental molecules
1840 Hess finds that energy is conserved in chemical reactions
1848 Lord Kelvin establishes concept of absolute zero, the temperature at
which all molecular motion ceases.
1860 Cannizzaro publishes a table of atomic weights of the known elements
1864 Gulberg and Waage propose the law of mass action
1869 Mendeleev publishes a periodic table containing the 66 known elements
1876 Gibbs publishes the concept of "Gibbs free energy"
1877 Boltzmann defines entropy and develops thermodynamics
1877 Pictet freezes CO2 and liquefies oxygen.
Liquification enables the purification of gases.
1894 Ramsay discovers the noble gases, filling a large and unexpected gap in
the periodic table
1635 Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660 Viviani and Borelli produce the first accurate measurement of the speed of
sound, giving a value of 350 m/s.
1660 Hooke's law published. The force on a spring is proportional to the change
in length.
1662 Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
Hence, air obey's Hooke's law
1687 Newton publishes the Principia Mathematica, which contains the first analytic
calculation of the speed of sound. The calculated value was 290 m/s
and the true value is 342 m/s (at 20 Celsius).
Newton's result was the first solid evidence for the existence of atoms. His
result differed from the correct value because it had not yet been discovered
that air heats when compressed. If you add this effect you get the right
value.
1789 Lavoisier publishes "Traite Elementaire de Chimie", the first modern
chemistry textbook. It is a complete survey of (at that time) modern
chemistry, the law of conservation of mass.
1797 Proust proposes the law of definite proportions, that elements
combine in small whole number ratios to form compounds.
1801 Dalton publishes the law of partial pressures.
The pressure of a mix of gases is equal to the sum of the pressures
of the components. He also finds that when a light and heavy gas are mixed,
the heavy gas does not drift to the bottom but rather fills the space
uniformly.
1805 Gay-Lussac and Humboldt find that water is formed of two volumes of
hydrogen gas and one volume of oxygen gas.
1809 Gay-Lussac finds that for an ideal gas at constant volume,
Pressure = Constant * Temperature
1811 Avogadro finds that equal volumes of different gases have the same number
of particles. At constant temperature and pressure,
Volume = Constant * NumberOfParticles
1811 Avogadro arrives at the correct interpretation of water's composition,
based on what is now called Avogadro's law and the assumption of diatomic
elemental molecules
1860 Cannizzaro publishes a table of atomic weights of the known elements
1869 Mendeleev publishes a periodic table containing the 66 known elements
1877 Boltzmann defines entropy and develops thermodynamics
All of these results support the hypothesis that matter is composed of atoms,
but there was no known experiment sensitive enough to measure the size and mass
of an individual atom.
Wavelength of violet light = 4e-7 meters
Diameter of an iron atom = 2e-10 meters
Violet photons are much larger than atoms and so you can't see atoms in an optical
microscope.
1905 Einstein publishes a method for measuring the mass of an atom using
Brownian motion
1908 Perrin uses Einstein's method to produce the first measurement of the mass of
an atom. This is equivalent to measuring the value of Avogadro's number.
Minutephysics atoms
© Jason Maron, all rights reserved.
Data from Wikipedia unless otherwise specified.
Millions of years ago
Big bang 13700
First planets formed 13000
Earth formed 4500
Photosynthesis 3000
Oxygen atmosphere 600
Multicellular life 600
Vertebrates 480
Tetrapod vertebrates 400
Mammals 170
Dinosaur extinction 66
Cats 25
Cheetahs 6
Tigers 1.8
Humans 1
Lions .9
Agriculture .01
Civilization .005
Calculus .0004
An alien planet could conceivably have formed as early as 1 billion years after the
big bang, meaning that there are likely aliens with a head start on us by billions of
years.
-> Reptiles -> Dinosaurs -> Birds
/
Vertebrates -> Tetrapod vertebrates --
\
-> Mammals
A tetrapod is a vertebrate with four limbs. Reptiles, dinosaurs, birds and
mammals all evolved from tetrapods, and the essential elements of the tetrapod
design haven't changed since its emergence. Elements of the tetrapod design
include:
A skull
A ribcage
Four limbs
One bone in the upper limb and two bones in the lower limb.
Oxygen Mass Flux Half life
Reservoir (EAOM) (EAOM/year)
Atmosphere 1 .000214 4500 years
Biosphere .0114 .000214 50 years
Lithosphere 207 4.3*10^-7 400 million years
Land photosynthesis = .000118 EAOM/year = 165*10^12 kg Oxygen / year
Ocean photosynthesis = .000096 EAOM/year = 135*10^12 kg Oxygen / year
The time required by photosynthesis to generate one EAOM is 4700 years.
Atmosphere 1.00
Biomass .62
Surface ocean 1.25
Deep ocean 46.2
Ocean sediment 7.5
Soil 2.88
Fossil carbon 12.5
Given the global rate of fossil fuel burning, it would take ~ 89 years to double
the atmosphere's carbon.
Ozone production from solar radiation = 400 million tons / day
Ozone loss from combining with oxygen radicals = 400 million tons / day
Total atmospheric ozone = 3000 million tons
The Sun produces 12% of the ozone layer each day.
Atmosphere temperature rise= .017 Kelvin/year (.9 Kelvin since 1800)
Sea level rise = 2.8 mm/year (225 mm since 1800)
Atmosphere CO2 frac = .0035 (.0027 in 1800)
Atmosphere carbon =720 Gtons
Photosynthesis of carbon =120 Gtons/year
Human carbon emissions = 9 Gtons/year = 1240 kg/person/year
Energy produced = .57 ZJoules/year = 78.6 GJoules/person/year
Electricity produced = .067 ZJoules/year = 9.2 GJoules/person/year
Food = .027 ZJoules/year = 3.7 GJoules/person/year = 2500 Cal/person/day
Sunlight energy =3850 ZJoules/year
Wind energy = 2.25 ZJoules/year
Photosynthesis of biomass = 3.00 ZJoules/year
Ocean heat gain = 7.5 ZJoules/year
World power = 18 TWatts = 4500 Watts/person
Energy cost = 16 T$/year = 2210 $/person/year (27.8 $/GJoule)
Population = 7.254 billion
Food = 1.58 Tkg/year = 218 kg/person/year (As carbs)
Earth land area =148.9 Mkm2 = 2.0 Hectares/person
Rainfall over land =107000 km3/year = 14.8 tons/person/year
River flow = 37300 km3/year = 5140 tons/person/year
Water total use = 9700 km3/year = 1390 tons/person/year
Water for agriculture = 1526 km3/year = 218 tons/person/year
Water for home use = 776 km3/year = 111 tons/person/year
Water desalinated = 36 km3/year = 5 tons/person/year
Contribution to Half life in the atmosphere
greenhouse warming
H2O 36-72%
CO2 9-26% 90 years
CH4 4-9% 12 years
Ozone 3-7% 1 week
Chuck Sulfur-reducing bacteria
(Oxygen Clan) (Sulfur Clan)
Mass 100 kg single-cellular
Power source Hydrocarbons + oxygen Hydrocarbons + sulfur
ATP per glucose 30 2
Resting power 100 Watts tiny
Peak power kilowatts tiny
Peak power/weight 10 Watts/kg tiny
Strength Kilonewtons tiny
Computation 10^14 synapses -
Brain power 20 Watts -
Achilles heel H2S Oxygen
Aerobic respiration: Glucose + Oxygen --> H2O + 30 ATP of energy
Anaerobic respiration: Glucose + Sulfur --> H2S + 2 ATP of energy
Aerobic organisms also have a weight advantage over anaerobic organisms.
Aerobic organisms can get oxygen from the air whereas anaerobic organisms have
to carry their oxidizer.
For the reaction
Hydrocarbons + Oxygen --> H2O + CO2 + energy
Mass of oxygen / Mass of hydrocarbons ~ 8
These two factors give aerobic organisms an overwhelming energy advantage over
anaerobic ones, and this is the reason why nearly all multi-cellular organisms
are aerobic.
Brain Total Brain/
mass mass body
(kg) (kg)
Sperm whale 8
Orca whale 6
Elephant 5 2800 .0018
Blue whale 4
Bottlenose dolphin 1.7
Neanderthal 1.9
Human 1.6 64 .025
Gorilla .6
Chimpanzee .4
Orangutan .4
Horse .4 235 .0017
Pig .20
Dog .10 12 .0080
Cat .04 4 .0091
Squirrel .009 1.4 .0067
Mouse .001 .04 .025
Shrew .0002 .002 .1
Bat .0001
Frog .0058
Small bird .071
Shark .0004
Ant .14
"The body cannot exist without the mind" - Morpheus
MJoules/kg
Antimatter 90 billion
Hydrogen bomb 25000000 theoretical maximum yield
Hydrogen bomb 21700000 highest achieved yield
Uranium 20000000 as nuclear fuel
Hydrogen 143
Natural gas 53.6
Gasoline 47
Jet fuel 43
Fat 37
Coal 24
Carbohydrates & sugar 17
Protein 16.8
Wood 16
Lithium-air battery 9
TNT 4.6
Gunpowder 3
Lithium battery 1.3
Lithium-ion battery .72
Alkaline battery .59
Compressed air .5 300 atmospheres
Supercapacitor .1
Capacitor .00036
The chemical energy source with the highest energy/mass is hydrogen+oxygen, but
molecular hydrogen is difficult to harness. Hydrocarbons + oxygen is the next
best choice. Carbon offers a convenient and lightweight way to carry hydrogen
around.
MJ/kg Calories/gram
Sugar 16 5
Protein 17 5
Alcohol 25 7
Fat 38 9
Breathe in Breathe out
Diaphram contracts Diaphram expands
Ribcage expands Ribcage contracts
Spine muscles contract Spine muscles release
Arms rotate out Arms rotate in
Elbows rotate out Elbows rotate in
Thumbs rotate out Thumbs rotate in
Head rises Head descends
Lower back arches Lower back sags
Legs rotate out Legs rotate in
Gut squashed by diaphram Gut expands
Daydream Focus
Rebalance Exertion
Arms out Arms in
High moment of inertia Low moment of inertia
Discard angular momentum Discard pressure
When you are in action, your breathing adjusts to support the timing of your
skeletal motion, and if it has any spare time, it sucks in as much air as
possible.
Spine - Ribs - Breatbone - Collarbone - Shoulder blade - Humerus
The function of the spine is to smooth out angular momentum generated by the limbs.
Density Pressure Escape Gravity N2 O2 N2 CO2 Ar H2 H3 CH4 Temp
kg/m^3 (Bar) km/s m/s^2 kg/m^3 frac frac frac frac frac frac frac (K)
Venus 67 92.1 10.36 8.87 2.34 .035 .965 735
Titan 5.3 1.46 2.64 1.35 5.22 .984 .014 94
Earth 1.2 1 11.2 9.78 .94 .209 .781 .00039 .0093 287
Mars .020 .0063 .64 5.03 3.8 .00054 .0013 .027 .953 .016 210
Gravity H2 He CH4 Escape
m/s^2 frac frac frac speed (km/s)
Sun 279.4 .735 .248 617.7
Jupiter 24.79 .90 .10 .003 59.5
Saturn 10.44 .96 .03 .004 35.5
Uranus 8.69 .83 .15 .023 21.3
Neptune 11.15 .80 .19 .015 23.5
Titan is the smallest object with an atmosphere and Mercury is the largest object without an atmosphere.
Atmos Atmos Max Min
Density Pressure Gravity N2 O2 N2 CO2 Temp Lapse Height height Height
kg/m^3 (Bar) m/s^2 kg/m^3 frac frac frac (K) (K/km) (km) (km)
Mars .020 .0063 3.71 .00054 .0013 .027 .953 210 4.5 15 22 -7.15
Titan 5.3 1.46 1.35 5.22 .984 94 1.3 14 .5 -2
Venus 67 92.1 8.87 2.34 .035 .965 735 10.5 7 11
Earth 1.28 1.0 9.78 .94 .209 .781 .00039 287 9.8 9 8.8 -0.8
Moon 0 0 1.62 220 8 -6
Ceres 0 0 .27 168
"Atmospheric height" is the height at which the atmosphere density is exp(-1) times the
density at sea level.
Watts/kg half life mantle Watts/kg
of isotope (years) abundance of mantle
uranium-238 9.46e-5 4.47e9 30.8 e-9 2.91 e-12
uranium-235 56.9 e-5 .70e9 .22e-9 .125e-12
thorium-232 2.64e-5 14.0 e9 124 e-9 3.27 e-12
potassium-40 2.92e-5 1.25e9 36.9 e-9 1.08 e-12
The Earth loses heat at a rate of .087 Watts/m^2, for a global heat los
of 4.42e13 Watts.
Dipole Field at Magnetopause Axis Rotation Volcanic
moment equator (planet angle (days)
(Earth=1) (Gauss) radii) (degrees)
Sun 5 million 25.0
Mercury .0007 .003 1.5 14 58.6 No
Venus <.0004 <.00003 - - 243.0 Yes
Earth 1 .305 10 10.8 1.00 Yes
Mars <.0002 <.0003 - - 1.03 No
Jupiter 20000 4.28 80 9.6 .41
Saturn 600 .22 20 <1 .44
Uranus 50 .23 20 58.6 .72
Neptune 25 .14 25 47 .67
Io Yes
Europa .0016 .0072 4.5
.tif.jpg)
Dot size = (Planet Mass)^(1/3)
Dot X coordinate = Log(distance from star)
Yellow dot = Planets orbit a star with high metallicity
Red dot = Plaents orbit a star with low metallicity
The magenta dot indicates the location of the Goldilocks zone. For a given star,
Radius of Goldilocks zone ~ (1 AU) * (Star luminosity / Sun luminosity)^(-1/2)
Horizontal yellow line = Range from perigee to apogee
Horizontal red line = 6 times the planet's Hill radius
The planets of the solar system are smaller and more widely spaced than what is
typical for exoplanetary systems. In the Galactic Museum of Natural History,
the solar system might be classified as a "Dwarf planetary system".
Planet property If too little If too much
Mass Cannot capture atmosphere Becomes gas giant
No volcanism
Cannot generate a magnetic field
Distance from Too hot Too cold for surface water
star Inside the snow line
Atmospheric Cosmic rays reach the surface Blocks too much sunlight
thickness Atmosphere loses heat at night for photosynthesis
Water content If you don't have oceans then you No dry land
don't have enough photosynthesis
to generate an oxygen atmosphere
Planet spin Does not generate a large-scale
magnetic field
Planet spin tilt Extreme seasons
Star temperature Not enough blue light for Too much UV light
photosynthesis
Star metallicity Small planets Too many gas giants
Star mass Planet is so close to the star that it
is tidally locked to the star
Moon mass Planet tilt becomes unstable, causing
extreme seasons
A moon of a gas giant can potentially be protected from the solar wind by the
gas giant's magnetic field. It can also potentially have volcanism from tidal
heating by the gas giant.
Millions of
years ago
66 Cretaceous–Paleogene extinction, caused by a 10 km asteroid.
Dinosaurs become extinct.
201 Triassic-Jurassic extinction. Cause unknown.
252 Permian-Triassic extinction. Runaway global warming
370 Late-Devonian extinction. Cause unknown.
445 Ordovician-Silurian extinction events. Global glaciation.
Functional Organic
group molecule
C-H3 Alkane (lipid)
C-H2OH Alcohol
C-OOH Fatty acid (carboxylic acid)
C=O Carbonyl group. Aldehyde if at end, ketone if not at end
Humans can metabolize just about any chain hydrocarbon and any sugar.
Opsin Wavelength Humans Notes
(nm)
Parapinopsin UV 365 Catfish
Neuropsin 380 Bird vision. Found in the brains of humans
OPN1SW 440 Blue All mammals
Panopsin Blue 450 Fish vision. Found in the brains of humans
Parapinopsin Blue 470 Catfish and lamphrey
SWS2 480 Extinct in mammals
Melanopsin 480 Found in the brains of humans
VA 500 Vertebrates except mammals. Vertebrae ancient opsin.
RH1 500 White Black/White
Panopsin Cyan 500 Fish vision. Found in the brains of humans
Pareitopsin 522 Lizards
OPN1MW 534 Green All mammals
OPN1LW 564 Red Once possessed by mammals, then lost by most
RH2 600 Black/White. Extinct in mammals
NeoR 690 Fungus
Retinal G Found in the brains of humans
Porphin is an aromatic molecule because it is flat and because it resonates between
different electronic states.
Hemoglobin is a set of 4 helix proteins that carry 4 iron ligands, and each
iron ligand carries 1 oxygen molecule.
Human hemoglobin is composed mostly of heme B.
The oxygen density of hemoglobin is 70 times the solubility of oxygen
in water.
Hemoglobin fraction of red blood cells = .96 (dry weight)
Hemoglobin fraction of red blood cells = .35 (including water)
Oxygen capacity of hemoglobin = 1.34 Liters of oxygen / kg hemoglobin
Iron ligands per hemoglobin = 4
O2 molecules per ion ligand = 1
A Universal
B Plants
C1 Algae
C2 Algae
D Cyanobacteria
F Cyanobacteria
Element Humans Cofactor Function
Hydrogen *
Helium No biological role
Lithium No biological role
Beryllium Toxic becauseit displaces magnesium in proteins
Boron * Plant cell walls. Metabolism of calcium in plants & animals
Magnesium * Chlorin Chlorophyll
Scandium No biological role
Titanium No biological role
Vanadium Found only in rare bacteria.
Chromium No biological role
Manganese * Superoxide dimutase. Converts superoxide to oxygen
Iron * Porphin Hemoglobin
Cobalt * Corrin Cobalamin (Vitamin B12)
Nickel Corphin Coenzyme F430 (Creates methane. Found only in archaea)
Copper * Heme Cytochrome C oxidase. Electron transport chain
Hemocyanin, an alternative to hemoglobin used by some animals
Hemoglobin carries 4 times as much oxygen as hemocyanin
Plastocyanin protein, used in photosynthesis
Sometimes used in superoxide dimutase
Zinc * Component of proteins that manipulate DNA and RNA (Zinc fingers)
Component of carbonic anhydrase, which interconverts CO2 and HCO3
Metallothionein proteins, which bind to metals such as
zinc, copper, selenium cadmium, mercury, silver, and arsenic
Molybdenum Nitrogen fixase. Convert N2 to NH3
Selenium * Component of the amino acide selenocysteine
Bromine * Limited role
Iodine * Component of thyroxine and triiodotyronine, which
regulate metabolic rate
Lead Toxic because it displaces calcium in bones
OH-
CO3--
NO3-
NO2-
SiO4----
PO4---
SO4--
Iron(III) Oxide Fe2O3 Ferric oxide. Most common form
Iron(II) Oxide FeO Rare
Iron(II,III) Oxide Fe3O4 Magnetite
Copper(I) Oxide Cu2O Cuprous oxide
Copper(II) Oxide CuO Cupric oxide
Copper(III) Oxide Cu2O3
Impact speed = 23 m/s
Acceleration = 10400 g (similar to a .22 calibre bullet)
Impact force = 1500 Newtons
The strike produces cavitation bubbles that add to the damage.
Accelerates from 0 to 28 meters/second in 3 seconds
Wingspan of up to 3.1 meters
Wingspan of 7 meters
Wing loading of 85 Newtons/meter^2
Wing area of 8.1 meters^2
Extinct
Just and equal tuning
Note Index Interval Equal Just tuning Major Minor Pythagorean
tuning scale scale tuning
A 0 Unison 1.000 1.000 = 1/1 * * 1/1
Bflat 1 Minor second 1.059 256/243
B 2 Major second 1.122 1.125 = 9/8 * * 9/8
C 3 Minor third 1.189 1.200 = 6/5 * 32/27
C# 4 Major third 1.260 1.250 = 5/4 * 81/64
D 5 Fourth 1.335 1.333 = 4/3 * * 4/3
Eflat 6 Tritone 1.414 729/512
E 7 Fifth 1.498 1.500 = 3/2 * * 3/2
F 8 Minor sixth 1.587 * 128/81
F# 9 Sixth 1.682 1.667 = 5/3 * 27/16
G 10 Minor seventh 1.782 * 16/9
Aflat 11 Major seventh 1.888 * 243/128
A 12 Octave 2.000 2.000 = 2/1 * * 2/1
In equal tuning, the frequency ratio of an interval is
1572 Bombelli publishes complex numbers
1523 Pietro Anon introduced "meantone tuning" to fix the thirds, using a
frequency ratio of 5/4 for major thirds. His treatise "Thoscanello de la
musica" expanded the possibilities for chords and harmony.
1555 Andrea Amati develops the four-string violin.
1584 "Equal tuning" introduced. Equal tuning divides the octave logarithmically.
The first known examples of equal tuning were:
Vincenzo Galilei in 1584 (Father of Galileo Galilei)
Zhu Zaiyu in 1584
Simon Stevens in 1585
1585 Simon Stevin introduces decimal numbers (For example, writing 1/8 as 0.125).
This greatly expanded the calculational power of numbers.
1586 Simon Stevin drops objects of varying mass from a church tower to demonstrate that
they accelerate uniformly.
1604 Galileo publishes a mathematical description of acceleration.
1614 Logarithms invented by John Napier, making possible precise calculations
of equal tuning ratios. Stevin's calculations were mathematically sound but
the frequencies couldn't be calculated with precision until logarithms were
developed.
1637 Cartesian geometry developed by Fermat and Descartes
1684 Leibniz publishes The Calculus
1687 Newton publishes the "Principia Mathematica"
1722 Bach publishes the "Well Tempered Clavier"
Until ~ 1650, most keyboards used meantone tuning. This tuning gives good results if you
confine yourself to a small number of keys and use few accidentals but it can't be made
to work for all keys.
J.S. Bach tuned his own harpsichords and clavichords and he customized the tuning to
work in all 24 keys ("well temperament"). He demonstrated its effectiveness
in "The Well Tempered Clavier".
1821 Cauchy publishes the "Cours d'Analyse", introducing rigor to mathematics.
.000003 Time for light to cross a 10 meter orchestra
.2 Electric synapse. These synapses are 2-way and they do not amplify signals
2 Chemical synapse. These synapses are 1-way and they can amplify signals
1 Time for a neural signal to travel 10 cm, the size of a brain
10 Time for a neural signal to travel from your fingers to your brain
3 Time for sound to travel 1 meter, the distance to an adjacent musician
7 Period of a 130 Hertz wave. This is the frequency of the viola C string
30 Time for sound to travel across a 10 meter orchestra.
62 Time between notes in "Flight of the Bumblebee"
For an orchestra to have good timing it must use visual cues. Sound isn't fast enough.
This is especially true at the rear of the viola section amidst the cacophony
of winds and brass.
-776 First Olympic games
-648 The sport of "Pankration" is introduced in the Olympic Games. Similar to MMA.
-536 -520 Milo of Croton dominates Olympic wrestling
-450 Gautama Buddha develops the art of meditation
464 Batuo, a monk from India, founds the Shaolin Temple
500 Bodhidharma, a Buddhist monk, teaches at the Shaolin temple
1600 Emergence of sumo in Japan
~1700 Shaolin temple destroyed by the Chinese Emperor.
The monks who escaped spread Shaolin kung fu throughout China. These monks were:
Ji Sin - Developed Tiger Crane style
Ng Mui - Developed Wing Chun
Bak Mei - Known as "Pai Mei" in kung fu films. Appears in "Kill Bill"
~1700 Fong Sai Yuk. Portrayed by Jet Li in the "Fong Sai Yuk" film series.
1847 1924 Wong Fei Hung. Master of Hung Gar style. Portrayed by Jet Li in
the "Once Upon a Time in China" film series.
1860 1938 Jigoro Kano. Developed Judo and taught it to Mitsuyo Maeda and Moshe Feldenkrais
1868 1910 Huo Yuanjia. Portrayed by Jet Li in the film "Fearless"
1869 1955 F.M. Alexander. Developed "Alexander Technique"
1893 1972 Yip Man. Practitioner of Wing Chun. Teacher of Bruce Lee
1904 1984 Moshe Feldenkrais. Developed "Feldenkrais Technique"
1917 Mitsuyo Maeda teaches Judo to the Gracie family.
Helio Gracie subsequently develops Brasilian Jiu Jitsu
1933 Jigoro Kano trains Feldenkrais in Judo
1940 1973 Bruce Lee
1940 Chuck Norris
1951 Masahiko Kimura vs. Helio Gracie
1952 Sammo Hung
1954 Jackie Chan
1955 Gordon Liu
1963 Jet Li
1963 Michelle Yeoh
1963 Donnie Yen
1970 Shaw Brothers Studios begins mass-producing kung fu films
1993 Age of Mixed Martial Arts begins when Royce Gracie wins a tournament
consisting of fighers with diverse styles.
2000 Kazushi Sakuraba vs. Royce Gracie
2009- Ben Askren dominates MMA with wrestling
2012 Miesha Tate vs. Ronda Rousey
2013 Ben Askren signs with One FC. UFC declines in significance
Interviewer: Other than wrestling what would you say the best base to be a
successful MMA fighter would be?
Ben Askren: Wrestling
_-_The_Alien.jpg)
Rocket propulsion system Exhaust speed
(km/s)
Hydrogen+oxygen rocket 4.4
Chang-Diaz ion drive 50 VASIMR design
Nuclear thermal rocket, H2 exhaust 9
Orion fusion rocket 10000
Antimatter rocket 1/2 C
All of these rockets are possible with current technology except for the
antimatter rocket.
Distance to Alpha Centauri, the nearest star 4.3 light years
Milky Way diameter 0.1 million light years
Distance to Andromeda 2.5 million light years
Distance to the Virgo Supercluster 54 million light years
Light travel time during age of universe 13750 million light years
Age of the universe ~ 13.75 billion years
Age of the Earth ~ 4.54 billion years
An alien civilization in the Virgo Supercluster with a 1 billion year head start on us
has plenty of time to get here.
1 2 3 4 3 2 1 0
Hydrogen Helium
Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon
Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon
To be a part of a chain, an atom needs at least 2 valence sites and it needs to
be able to form strong bonds.
Single Double Triple Quadruple
B B 3.04
B C 3.69
B O 5.56
C C 3.65 6.45 8.68 6.32
C N 3.19 6.38 9.19
C O 3.73 7.7 11.11
C Si 3.30
C P 2.74
C S 2.82 5.94
N N 1.76 4.33 9.79
N O 2.08 6.29
N Si 3.70
N P
N S
O O 1.50 5.15
O Si 4.69
O P 3.47 5.64
O S 5.41
Si Si 2.30
Si S 3.04
Si P
P P 2.08
P S 3.47
S S 2.34 4.41
H H 4.52
H C 4.25
H N 4.05
H O 3.79
H F 5.89
H Si 3.30
H P 3.34
H S 3.76
H Cl 4.48
96.47 kJoules/mol = 1 eV
Fats and sugars for fuel
We'll be able to eat each other's food
As large as or larger than us
Flight is likely
Come from a small planet
Star is less hot than the sun
The planet is volcanic
The planet has a magnetic field
The planet has high metallicity
Minimum Used by Used Human Crust Ocean Atmosphere
for life humans by life ppt ppt ppt ppt
Hydrogen * * * .10 1.5 108 .00055
Helium .000008 .0052
Lithium .02
Beryllium .0028
Boron * * .0000007 .01
Carbon * * * .18 1.0 .028 .407
Nitrogen * * * .03 .02 780
Oxygen * * * .65 460 858 210
Fluorine * .5
Neon .0000051 .018
Sodium * * * .0015 25 10.8
Magnesium * * * .0005 25 1.3
Aluminum 82
Silicon * 275
Phosphorus * * * .011 1.1
Sulfur * * * .0025 .4 .91
Chlorine * * * .0015 .2 19
Argon .0035 9.3
Potassium * * * .0025 20 .4
Calcium * * * .014 45 .4
Scandium .022
Titanium 5.6
Vanadium * .12
Chromium .10
Manganese * * .00000017 .95
Iron * * .00006 60
Cobalt * * .000000021 .025
Nickel * .084
Copper * * .000001 .06
Krypton .0011
Zinc * * .000032 .075
Gallium .019
Germanium .0015
Arsenic * .0018
Selenium * * .00000019 .00005
Bromine * * .0000029 .0024 .067
Molybdenum * .0012
Tellurium * .000001
Iodine * * .00000016 .00045
Tungsten * .0012
* Video of an amoeba
Synthesis of two amino acids. Proteins are chains of animo acids with a backbone of
the form:
C-C-N-C-C-N-C-C-N-C-C-N-C-C-N
MJoule/kg Calories/gram
Sugar 17 5
Protein 17 5
Alcohol 25 7
Fat 38 9
ATP .057
Phosphocreatine .137
Hydrogen 143
Natural gas 53.6
Gasoline 47
Coal 24
Wood 16
Li-ion battery .6
Alkane Carbons Energy of Melt Boil Solid Liquid Gas Phase at
type combustion (K) (K) density density density 300 K
(MJ/kg) (g/cm^3) (g/cm^3) (g/cm^3)
Hydrogen 0 141.8 14.0 20.3 .07 .000090 Gas
Methane 1 55.5 90.7 111.7 .423 .00070 Gas
Ethane 2 51.9 90.4 184.6 .545 .0013 Gas
Propane 3 50.4 85.5 231.1 .60 .0020 Gas
Butane 4 49.5 136 274 .60 .0025 Gas
Pentane 5 48.6 143.5 309 .63 Liquid
Hexane 6 48.2 178 342 .65 Liquid
Heptane 7 48.0 182.6 371.5 .68 Liquid
Octane 8 47.8 216.3 398.7 .70 Liquid
Dodecain 12 46 263.5 489 .75 Liquid
Hexadecane 16 46 291 560 .77 Liquid
Icosane 20 46 310 616 .79 Solid
Alkane-30 30 46 339 723 .81 Solid
Alkane-40 40 46 355 798 .82 Solid
Alkane-50 50 46 364 848 .82 Solid
Alkane-60 60 46 373 898 .83 Solid
Gasoline ~ 8 47 .76 Liquid Mostly alkanes with ~ 8 carbons
Natural gas 54 91 112 Gas Mostly methane
Coal 32 - - Solid Mostly carbon
Wood 22 - - Solid Carbon, oxygen, hydrogen
Pure carbon 1 32.8 - - Solid Pure carbon, similar to coal
Methanol 1 175.6 337.8 .79 Liquid
Ethanol 2 159 351.5 .79 Liquid
Propanol 3 147 370 Liquid
Number of Number of
carbons sugars
Diose 2 1
Triose 3 2
Tetrose 4 3
Pentose 5 4
Hexose 6 12 At least 6 carbons are required to form a ring
Heptose 7 many Rarely observed in nature
Octose 8 many Unstable. Not observered in nature.
"Number of sugars" refers to the number of different types of sugar molecules for each
carbon number.
Energy Sweetness
Succrose 1.00 1.00 Benchmark
Glucose .74
Maltose .32
Galactose .32
Lactose .16
Allose
Altrose
Mannose
Fructose 1.73
Psichose .70
Tagatose .38 .92
Sorbose 1.0
Honey .97
Monosaccharde: 1 sugar molecule
Disaccharide: 2 monosaccharides
Polysaccharide: More than 2 monosaccharides, such as starch and cellulose
Sucrose = Glucose + Fructose
Maltose = Glucose + Glucose
Lactose = Galactose + Glucose
Lactulose = Galactoce + Fructose
Trehalose = Glucose + Glucose
Cellobiose = Glucose + Glucose
Chitobiose = Glucosamine + Glucosamine
Starch and cellulose are long chains of glucose molecules.
Fatty acid -> Acetyl -> CO2 and H2O
Sugar -> Pyruvate -> CO2 and H2O
Carbons
Methanol 1 Toxic
Ethanol 2 Inebriating
Propanol 3 3 times more inebriating than ethanol
Isopropanol 3 Toxic
Butanol 4 6 times more inebriating than ethanol
Carbons
1
2 Vinegar
3
4 Found in butter
8 Found in coconuts
10 Found in coconuts
12 Found in coconuts
16 Most common fatty acid. Found in palm oil
18 Found in chocolate
20 Found in peanut oil
LD50
(mg/kg)
CO Carbon monoxide
HCN 6.4 Hydrogen cyanide
CH2O Methanol
CH2O Formaldehyde
H2S Hydrogen sulfide
NO2 Nitrite
Cl2 Chlorine
Fl2 Fluorine
Ethanol 7060
Salt 3000
Caffeine 192
Aspirin 200
NaNO2 180 Sodium nitrite
Cobalt 80
NaF 52
Capsaicin 47 Chili pepper
Mercury 41
Arsenic 13
Nicotine .8
Bromine
C2N2
PH3
SiCl4
Almost anything with fluorine or bromine is toxic.
C2H2 Acetylene. Inebriating
C3H6 Propene. Inebriating
Hydrogen White
Carbon Black
Nitrogen Blue
Oxygen Red
Sulfur Yellow
Scoville scale (relative capsaicin content)
Ghost pepper 1000000
Trinidad 1000000 Trinidad moruga scorpion
Naga Morich 1000000
Habanero 250000
Cayenne pepper 40000
Malagueta pepper 40000
Tabasco 40000
Jalapeno 5000
Guajillo pepper 5000
Cubanelle 500
Banana pepper 500
Bell pepper 50
Pimento 50
Molecule Relative hotness
Rresiniferatoxin 16000
Tinyatoxin 5300
Capsaicin 16 Chili pepper
Nonivamide 9.2 Chili pepper
Shogaol .16 Ginger
Piperine .1 Black pepper
Gingerol .06 Ginger
Capsiate .016 Chili pepper
Rod cross-sectional area = A meter2
Tensile force = F Meter
Tensile stress = P = F/A Pascal
Rod length = X Meter
Rod change in length = x Meter
Strain = s = x/X Dimensionless
Stress on the rod = P Pascals
Rod tensile modulus = T Pascals
Rod strain = s = P/T Dimensionless
Tensile strength = tbreak Newton/meter2 (Pascals)
Cross-sectional area = A meter2
Breaking force = Fbreak = tbreak A Newton
Yield strength = t Pascals
Tensile modulus = T Pascals
Yield strain = S = t/T Dimensionless
Density = ρ kg/meter2
Cross-sectional area = A meter2
Force = F Newton
Tensile stress = P = F/A Pascals
Tensile modulus = T Pascals
Tensile yield stress = t Pascals
Tensile breaking stress= tbreak Pascals
Strain = s = P/T Dimensionless
Tensile yield strain = S = t/T Dimensionless
Tensile energy/volume = evol = ½ T s2 Joule/meter3
Tensile energy/mass = e = ½ T s2/ρ Joule/kg
Tensile modulus / Density ~ 25 MJoules/kg
Tensile modulus = T
Tensile yield strength = t
Tensile yield strain = S
Density = ρ
Tensile energy/volume = evol = ½ T S2 Joule/meter3
Tensile energy/mass = e = ½ T S2/ρ Joule/kg
dX = Fractional increase in length of the wire
dY = Fractional decrease in diameter of the wire
PoissonRatio = dY / dX
Tensile modulus = T Pascals
Shear modulus = Tshear Pascals
Bulk modulus = Tbulk Pascals
Poisson ratio = U dimensionless
T = 2 (1 + U) Tshear = 3 (1 - 2U) Tbulk
Tensile yield strength = t Newton/meter2 (Pascals)
Cross-sectional area = A meter2
Yield force = F = tA Newton
Beam length = X meter
Beam width = Y meter
Beam height = Z meter The force is in the Z direction
Beam yield force = f Newton
Tensile yield strength = t Pascal
Poisson ratio = U dimensionless
Shear yield strength = tshear = ½ t / (1+U) Pascal
Bending yield force = f = ⅔ tshear Y Z2 / X
Bulk yield strength = tbulk Newton/meter2 (Pascals)
Cross-sectional area = A meter2
Crushing force = F = bbulkA Newton
Column length = L
Column outer radius = R
Column inner radius = r
Column boundary factor = K dimensionless
= .5 if both ends are fixed
= 2 if one end is fixed and the other end is free to move laterally
= 1 if both ends are pinned (hinged and free to rotate)
= .699 if one end is fixed and the other is pinned
Tensile yield strength = t
Buckling force = f = ½ π3 t (R4-r4) / (K L)2
R/L = (K/π) (tbulk/t)1/2
Beam length = L
Beam radius = R
Beam tension strength ~ R2
Beam bending strength ~ R3/L
Beam buckling strength ~ R4/L2
Density = ρ
Mass = M = X Y Z ρ
Beam yield force = F = ⅔ s Y Z2 / X = ⅔ S M3/2 ρ-3/2 / X5/2
Density = ρ
Mass = M = π R2 L ρ
Column effective length= K = 1/2 dimensionless For a column that's fixed at both ends
Column buckling force = F = ½ π3 t R4 / (K L)2 = ½ π3 t M2 ρ-2 / (K2 L4)
Tensile yield strength / Density Beam under tension
Tensile yield strength / Density3/2 Beam under shear
Tensile yield strength / Density2 Beam under compression
Case Measure of merit
Tension Energy / Mass
Shear Energy / Mass / Density1/2
Compression Energy / Mass / Density
Density Tensile Tensile Hardness
strength modulus
gram/cm3 GPascal GPascal kNewton
Balsa .12 .020 3.7 .31
Cedar, white .32 .046 5.7
Cedar, red .34 .054 8.2
Pine, white .37 .063 9.0 1.9
Spruce, red .41 .072 11.7
Redwood .44 .076 9.6
Ash, black .53 .090 11.3
Walnut, black .56 .104 11.8 4.5
Ash, white .64 .110 12.5 5.9
Mahogany .67 .124 10.8
Locust, black .71 .136 14.5 7.6
Hickory .81 .144 15.2
Bamboo .85 .15 20.0 7.2
Oak, live .98 .13 13.8
Ironwood 1.1 .181 21.0 14.5
Verawood 1.19 .178 15.7 16.5
Quebracho 1.24 .14 16.6 20.3
Lignum vitae 1.26 .127 14.1 19.5
Ironwood, black 1.36 .125 20.5 16.3
Tensile yield strength = t Pascal
Density = ρ kg/meter3
Longitudinal Radial Tangential
Wood, low density .4 .25 .2
Wood, high density .43 .35 .18
Triangles are stronger than squares. A structure needs triangles to resist warping.
 |
 |
 |
 |
|---|---|---|---|
 |
 |
|
|---|---|---|
Tension is easy. If you can use pure tension, do it.
 |
 |
 |
|---|---|---|
 |
 |
|---|---|
 |
 |
 |
|---|---|---|
A cable hangs as a catenary, and the ideal form for an arch is a catenary.
A hanging catenary transforms the load into pure tension.
An arch transforms the load into pure compression.
For a suspension bridge supporting a road, if the cable is heavier than the road, then the cable hangs as a catenary. If the road is heavier than the cable, the cable hangs as a parabola.
If you want height, use a concave catenary. If you want volume, use a convex catenary.
 |
 |
|---|---|
 |
 |
.jpg) |
 |
|---|---|---|---|
The arch can go above or below.
 |
 |
|---|---|
You can combine an arch and a truss.
 |
 |
 |
 |
 |
|---|---|---|---|---|
 |
|---|
 |
 |
 |
 |
|---|---|---|---|
|
|
|---|---|
Concrete and ceramics typically have much higher compressive strengths than tensile strengths. Concrete is typically mixed with steel bars to improve tensile strength.
 |
 |
 |
 |
 |
|---|---|---|---|---|
 |
 |
.png) |
|---|---|---|
Brinell = A measure of a material's resistance to dents, measured in Pascals Mohs = A dimensionless measure of a material's resistance to dentsThe Mohs scale of mineral hardness reflect's a material's ability to resist scratching. If two materials are scraped together then the material with the lower Mohs value will be scratched more. Diamond has the largest Mohs value of any material.
Mohs
Diamond 10
RhB2 9.5
Silicon carbide 9.5
Corundum 9
Tungsten carbide 9
Chromium 8.5
Emerald 8
Topaz 8
Tungsten 8
Hardened steel 8
Quartz 7
Osmium 7
Rhenium 7
Vanadium 7
If a material has a large Brinell hardness then it has a large Mohs hardness. The reverse is not necessarily true. Materials exist with a large Mohs hardness and a small Brinell hardness.
 |
|---|
The Brinell hardness is related to the tensile modulus and tensile strength.
 |
|---|
For tension, what usually matters is tensile strength divided by density. Materials with a high value include:
Young's Yield Tensile Tensile Strength/ Tough/ Density
modulus stress strengh strain density density
GPa Gpa GPa MNewton/kg kJ/kg g/cm^3
Graphene 1050 160 .152 160 12190 1.0
Nanotube 1000 63 .063 48 1480 1.34 Carbon nanotube
Colossal tube 1000 7 .116 Carbon nanotube with large radius
Zylon 270 5.8 .010 3.7 1.56
Kevlar 155 3.76 .023 2.6 1.44
Vectran UM 103 3.0 .029 1.4
Vectran HT 75 3.2 .043 1.4
Vectran NT 52 1.1 .021 1.4
Diamond 1220 1.6 2.8 .0023 .80 .92 3.5
Sapphire 345 .4 1.9 .0055 .48 1.315 3.98
Carbon fiber 181 1.6 .0088 .91 4.04 1.75
Rubber, butyl .007 .020 2.86 .92
Balsa 3.7 .020 .12
Pine, white 9 .063 .37
Bamboo 20 .15 .85
Ironwood 21 .181 .181 .0086 .65 1.1
Beryllium 287 .345 .448 .0016 .189 1.85
Magnesium + Li 45 .14 1.43
Magnesium + Y2O3 45 .31 1.76
Magnesium alloy 45 .100 .232 .0052 .344 1.74
Aluminum + Be 70 .41 2.27
Aluminum alloy 70 .414 .483 .0069 .595 2.8
Titanium 120 .225 .37 .0031 .054 4.51
Steel + Co, Ni 220 2.07 .0094 8.6
Moly + W, Hf 1.8 14.3
Aluminum amorphous 70 1.97 2.67 LiMgAlScTi
Titanium amorphous 120 1.20 4.6 Titanium + AlVCrMo
Chromium amorphous 2.26 6.5 AlCrFeCoNiTi
Molybden amorphous 1.22 12.3 VNbMoTaW
Molybdenum + W, Hf 1.8 14.3
|
|
|
|
|---|---|---|---|
|
|
|
|---|---|---|
|
|
|---|---|
Lignin comprises 30 percent of wood and it is the principal structural element.
Year Young Tensile Strain Density Common
(GPa) strength (g/cm3) name
(GPa)
Gut Ancient .2
Cotton Ancient .1 1.5
Hemp Ancient 10 .3 .023
Duct tape .015
Gorilla tape .030
Polyamide 1939 5 1.0 .2 1.14 Nylon, Perlon
Polyethylene 1939 117 1.4 Dacron
Polyester 1941 15 1.0 .067 1.38
Polypropylene 1957 .91
Carbon fiber 1968 3.0 1.75
Aramid 1973 135 3.0 .022 1.43 Kevlar
HMPE 1975 100 2.4 .024 .97 Dyneema, Spectra
PBO 1985 280 5.8 .021 1.52 Zylon
LCAP 1990 65 3.8 .058 1.4 Vectran
Vectran HT 75 3.2 .043 1.41 Vectran
Vectran NT 52 1.1 .021 1.41 Vectran
Vectran UM 103 3.0 .029 1.41 Vectran
Nanorope ~1000 3.6 .0036 1.3
Nanotube 1000 63 .063 1.34
Graphene 1050 160 .152 1.0
Strain = Strength / Young
Carbon fiber is not useful as a rope.
A string ideally has both large strength and large strain, which favors Vectran.
Suppose Batman has a rope made out of Zylon, the strongest known polymer.
Batman mass = M = 100 kg (includes suit and gear) Gravity constant = g = 10 meters/second2 Batman weight = F = 1000 Newtons Zylon density = D = 1520 kg/meter3 Zylon tensile strength = Pz = 5.8⋅109 Newtons/meter2 Rope load = P = 1.0⋅109 Newtons/meter2 (safety margin) Rope length = L 100 meters Rope cross section = A = F/P =1.0⋅10-6 meters2 Rope radius = R =(A/π)½= .56 mm Rope mass = Mr = DAL = .15 kg
Density Tensile Young
strength
(g/cm^3) (Gpa) (Gpa)
Balsa .12 .020 3.7
Corkwood .21
Cedar .32 .046 5.7 Northern white
Poplar .33 .048 7.2 Balsam
Cedar .34 .054 8.2 Western red
Pine .37 .063 9.0 Eastern white
Buckeye .38 .054 8.3 Yellow
Butternut .40 .057 8.3
Basswood .40 .061 10.3
Spruce, red .41 .072 10.7
Aspen .41 .064 10.0
Fir, silver .42 .067 10.8
Hemlock .43 .061 8.5 Eastern
Redwood .44 .076 9.6
Ash, black .53 .090 11.3
Birch, gray .55 .069 8.0
Walnut, black .56 .104 11.8
Ash, green .61 .100 11.7
Ash, white .64 .110 12.5
Oak, red .66 .100 12.7
Elm, rock .66 .106 10.9
Beech .66 .102 11.8
Birch, yellow .67 .119
Mahogany .67 .124 10.8 West Africa
Locust .71 .136 14.5 Black or Yellow
Persimmon .78 .127 14.4
Oak, swamp .79 .124 14.5 Swamp white
Gum, blue .80 .118 16.8
Hickory .81 .144 15.2 Shagbark
Eucalyptus .83 .122 18.8
Bamboo .85 .169 20.0
Oak, live .98 .130 13.8
Ironwood 1.1 .181 21.0
Lignum Vitae 1.26 .127 14.1
Data #1
Data #2
Density Tensile Young
strength
(g/cm^3) (Gpa) (Gpa)
Polyamide .11 4.5
Polyimide .085 2.5
Acrylic .07 3.2
Polycarbonate .07 2.6
Acetyl copoly .06 2.7
ABS .04 2.3
Polypropylene .91 .04 1.9
Polystyrene .04 3.0
Polyethylene .95 .015 .8
|
|
|
|---|---|---|
|
|
|
|---|---|---|
|
|---|
New alloys have been discovered that are stronger and ligher than diamond. These alloys have an amorphous structure rather than the crystalline structure of conventional alloys. A crystaline alloy tends to be weak at the boundaries between crystals and this limits its strength. Amorphous alloys don't have these weaknesses and can be stronger.
Pure metals and alloys consisting of 2 or 3 different metals tend to be crystaline while alloys with 5 or more metals tend to be amorphous. The new superalloys are mixes of at least 5 different metals.
A material's strength is characterized by the "yield strength" and the quality is the ratio of the yield strength to the density. This is often referred to as the "strength to weight ratio".
Yield strength = Y (Pascals) Density = D (kg/meter3) Quality = Q = Y/D (Joules/kg)The strongest allyos are:
Yield strength Density Quality
(GPa) (g/cm3) (MJoule/kg)
Magnesium + Lithium .14 1.43 98
Magnesium + Y2O3 .31 1.76 177
Aluminum + Beryllium .41 2.27 181
Amorphous LiMgAlScTi 1.97 2.67 738
Diamond 1.6 3.5 457
Titanium + AlVCrMo 1.3 4.6 261
Amorphous AlCrFeCoNiTi 2.26 6.5 377
Steel + Cobalt, Nickel 2.07 8.6 241
Amorphous VNbMoTaW 1.22 12.3 99
Molybdenum+ Tungsten, Hafnium 1.8 14.3 126
The strongest pure metals are weaker than the strongest alloys.
Yield strength Density Quality
(GPa) (g/cm3) (MJoule/kg)
Magnesium .10 1.74 57
Beryllium .34 1.85 184
Aluminum .02 2.70 7
Titanium .22 4.51 49
Chromium .14 7.15 20
Iron .10 7.87 13
Cobalt .48 8.90 54
Molybdenum .25 10.28 24
Tungsten .95 19.25 49
Beryllium + Li → Doesn't exist. The atoms don't mix Beryllium + Al → Improves strength Magnesium + Li → Weaker and lighter than pure Mg. Lightest existing alloy Magnesium + Be → Only tiny amounts of beryllium can be added to magnesium Magnesium + Carbon tubes → Improves strength, with an optimal tube fraction of 1% Aluminum + Li,Mg,Be,Sc → Stronger and lighter than aluminum Titanium + Li,Mg,Sc → Stronger and lighter than titanium Steel + Cr,Mo → Stronger and more uncorrodable than steel. "Chromoly" Copper + Be → Stronger than beryllium and is unsparkable
Melting point (Celsius)
Tungsten 3422
Rhenium 3186
Osmium 3033
Tantalum 3017
Molybdenum 2623
Niobium 2477
Iridium 2446
Ruthenium 2334
Hafnium 2233
Technetium 2157
Rhodium 1964
Vanadium 1910
Chromium 1907
Most alloys weaken with increasing temperature except for a small subset called "superalloys" that strengthen with temperature, such as Ni3Al and Co3Al. This is called the "yield strength anomaly".
Nickel alloys in jet engines have a surface temperature of 1150 Celsius and a bulk temperature of 980 Celsius. This is the limiting element for jet engine performance. Half the mass of a jet engine is superalloy.
Current engines use Nickel superalloys and Cobalt superalloys are under development that will perform even better.
Yield strength in GPa as a function of Celsius temperature.
20 600 800 900 1000 1100 1200 1400 1600 1800 1900 Celsius
VNbMoTaW 1.22 .84 .82 .75 .66 .48 .4
AlMohNbTahTiZr 2.0 1.87 1.60 1.2 .74 .7 .25
Nickel superalloy 1.05 1.20 .90 .60 .38 .15
Tungsten .95 .42 .39 .34 .31 .28 .25 .10 .08 .04
Below 1100 Celsius AlMohNbTahTiZr has the best strength-to-mass ratio and above
this VNbMoTaW has the best ratio. Both alloys supersede nickel superalloy
and both outperform tungsten, the metal with the highest melting point.
Data:
Entropy, nickel superalloy
Yield strength (GPa)
Copper .27
Brass .41 30% zinc
Bronze .30 5% tin
Phosphor bronze .69 10% tin, .25% phosphorus
Copper + beryllium 1.2 2% beryllium, .3% cobalt
Copper + nickel + zinc .48 18% nickel, 17% zinc
Copper + nickel .40 10% nickel, 1.25% iron, .4% manganese
Copper + aluminum .17 8% aluminum
|
|
|
|
|---|---|---|---|
Bells and cymbals are made from bell bronze, 4 parts copper and 1 part tin.
|
|
|
|
|
|---|---|---|---|---|
|
|
|
|
|---|---|---|---|
|
|
|
|
|---|---|---|---|
 |
|---|
Young's Tensile Hardness Max temp Density Toughness Price/kg
modulus strength /density
GPa MPa Shore D Celsius g/cm3 kJoule/kg $/kg
PVA 1.5 78 72 64 1.23 1650 75
PC Polycarbonate 2.2 65 82 112 1.23 58
PLA 3.2 65 84 56 1.32
PLA Tough 2.8 46 84 56 1.32
PAHT CF15 5.2 66 72 127 1.10
Nylon 1.8 60 81 88 1.15 45
ASA 2 55 110 95 1.07 39
PETG 2.0 50 71 70 1.27 40
TPU .2 40 48 110 1.45
Carbon fiber filled 4 46 52 1.3
Flexible .2 37 10 67 1.21 50
ABS 1.9 40 76 95 1.07
HIPS 4 32 77 100 1.04 28
PP Polypropylene 1 30 42 90 .9 90
PP GF30 2.6 42 42 126 .9
Metal filled 4 25 52 3 85
PA .4 35 73 100 1.00
Diamond 1220 1600 3.5 300
Graphene 1050 160000 1.0
Kevlar 112 3620 170 1.44 40600 Aramid
Zylon 270 5800 1.56 PBO, Polyoxazole
Vectran 11.5 140 1.40
Rubber, butyl .004 17 1.25 28900
Carbon fiber 228 3500 88 1.8 16000
Balsa 3.7 20 4.9 .2
Bamboo 20 150 70 .85
Ironwood 21 181 90 1.1
Beryllium alloy 287 500 2.1
Magnesium alloy 45 260 1.74
Aluminum alloy 70 590 2.7
Titanium alloy 116 1100 4.51 1160
Iron alloy 211 1500 7.9
Tungsten alloy 441 2100 19.25
.png) |
 |
 |
 |
 |
|---|---|---|---|---|
 |
 |
 |
|---|---|---|
Gold and silver were known since antiquity because they occur naturally in pure form.
Gold mining started in 6000 BCE and silver smelting started in 4000 BCE.
Iron can occasionally be found as iron meteorites.
Copper was discovered around 7500 BCE by smelting copper minerals in a wood fire.
Around 3200 BCE it was found that copper is strenghened by tin, and this is bronze.
Around 2000 BCE it was found that copper is also strengthed by zinc, and this is brass.
The earliest metals were smeltable with a wood fire and they consist of copper,
lead, silver, tin, zinc, and mercury. They come from the following minerals:
The next metal to be discovered was iron (c. 1200 BC), which requires a bellows-fed coal
fire to smelt.
No new metals were discovered until cobalt in 1735.
Once cobalt was discovered, it was realized that
new minerals may have new metals, and the race was on to find new minerals. This gave
nickel, chromium, manganese, molybdenum, and tungsten.
Chromium is lighter and stronger than steel and was discovered in 1797. It
satisfies the properties of mithril from "Lord of the Rings" and Valyrian steel
from "Game of Thrones".
There's no reason chromium couldn't have
been discovered earlier.
Coal smelting can't produce the metals lighter than chromium. These need
electrolysis. The battery was invented in 1799, enabling electrolysis, and
the lighter metals were discovered shortly after. These include aluminum, magnesium, titanium,
and beryllium. Once you have
Carbon fiber eclipses metals. The present age could be called the carbon age. The carbon age became
mature in 1987 when Jimmy Connors switched from a wood to a carbon racket.
The plot shows the strength of materials.
Wood rivals alloys for strength.
Gold was the densest element known until the discovery of platinun in 1735. It
was useful as an uncounterfeitable currency until the discovery of tungsten in
1783, which has the same density as gold. Today, we could use iridium,
platinum, or rhenium as an uncounterfeitable currency.
Prior to 1800, metals were obtained by smelting minerals, and the known metals
were gold, silver, copper, iron, tin, zinc, mercury, cobalt, manganese,
chromium, molybdenum, and tungsten. Elements to the left of chromium titanium
and scandium cant's be obtained by smelting, and neither can aluminum,
magnesium, and beryllium. They require electrolysis, which was enabled by
Volta's invention of the battery in 1799.
Prior to 1800, few elements were known in pure form. Electrolyis enabled the
isolation of most of the rest of the elements. The periodic table then became
obvious and was discovered by Mendeleev 1871. The battery launched modern
chemistry, and the battery could potentially have been invented much earlier.
Electrolysis enabled the isolation of sodium and potassium in 1807, and these were used
to smelt metals that can't be smelted with carbon.
For a metal, the stiffness is characterized by the "shear strength" and the
sword worthiness is characterized by the shear strength over the density
(the "strength to weight ratio"). For example for iron,
This plot includes all metals with a strength/density at least as large as lead,
plus mercury.
Beryllium is beyond the top of the plot.
In prehistoric times iron meteorites were the only source of metallic iron.
They consist of 90% iron and 10% nickel.
Most metals are in oxidized form. The only metals that can be found in
pure form are gold, silver, copper, platinum, palladium, osmium, and iridium.
Smelting is a process for removing the oxygen to produce pure metal.
The ore is heated in a coal furnace and the carbon seizes the oxygen from
the metal. For copper,
For iron, the oxidation state is reduced in 3 stages until the
pure iron is left behind.
The following table gives the temperature required to smelt each element with
carbon.
The farther to the right on the periodic table, the lower the smelting
temperature, a consequence of "electronegativity".
The battery was invented in 1800, launching the field of electrochemistry
and enabling the the isolation of non-carbon-smeltable elements.
Davy used electrolysis in 1807 to isolate sodium and potassium and then he used
these metals to smelt other metals. To smelt beryllium with potassium,
BeO + 2 K ↔ Be + K2O.
Titanium can't be carbon smelted because it forms the carbide Ti3C.
For an expanded discussion of smelting physics, see jaymaron.com/metallurgy.html.
Thermite is smelting with aluminum. For example, to smelt iron with aluminum,
The following table shows reactions that change the oxidation state of a metal.
"M" stands for an arbitrary metal and the magnitudes are scaled to one mole of
O2. The last two columns give the oxidation state of the metal on
the left and right side of the reaction. An oxidation state of "0" is the pure
metal and "M2O" has an oxidation state of "1".
These elements are not necessarily on the Science Olympiad list.
We list minerals by element, with the most abundant mineral for each element listed first.
Corundum is a crystalline form of aluminium oxide (Al2O3). It is transparent in
its pure form and can have different colors when metal impurities are
present.
The critical electric field for electric breakdown for the following materials is:
Relative permittivity is the factor by which the electric field between
charges is decreased relative to vacuum. Relative permittivity is dimensionless.
Large permittivity is desirable for capacitors.
A ferromagnetic material amplifies a magnetic field by a factor called the "relative
permeability".
Resistivity in 10^-9 Ohm Meters
All superconductors are described by the BCS theory unless stated otherwise.
Titan has a temperature of 94 Kelvin, allowing for superconducting equipment.
The temperature of Mars is too high at 210 Kelvin.
For a system in thermodynamic equilibrium each degree of freedom has
a mean energy of ½ k T. This is the definition of temperature.
The sound speed is proportional to the thermal speed of gas molecules. The
thermal speed of a gas molecule is defined in terms of the mean energy per
molecule.
For air, γ = 7/5 and
We can change the sound speed by using a gas with a different value of M.
In a gas, some of the energy is in motion of the molecule and some is in
rotations and vibrations. This determines the adiabatic constant.
The fact that Newton's calculation differed from the measured speed is due to
the fact that air consists of diatomic molecules (nitrogen and oxygen). This
was the first solid clue for the existence of atoms, and it also contained a
clue for quantum mechanics.
In Newton's time it was not known that changing the volume of a gas changes its
temperature, which modifies the relationship between density and pressure.
This was discovered by Charles in 1802 (Charles' law).
Carbon dioxide doesn't have a liquid state at standard temperature and pressure.
It sublimes directly from a solid to a vapor.
For an object to have an atmosphere, the thermal energy must be much less than the
escape energy.
The threshold for capturing an atmosphere appears to be around Z = 1/25, or
When an object collapses by gravity, its temperature increases such that
For an ideal gas,
The Earth's core is composed chiefly of iron. What is the temperature of an iron
atom moving at the Earth's escape speed?
We first derive the law for a 1D gas and then extend it to 3D.
Suppose a gas molecule bounces back and forth between two walls separated
by a distance L.
Time between collisions = 2 L / V
The average force on a wall is
A typical globular cluster consists of millions of stars.
If you measure the total gravitational and kinetic energy of the stars, you will
find that
Suppose a system consists of a set of objects interacting by a potential. If
the system has reached a long-term equilibrium then the above statement about
energies is true, no matter how chaotic the orbits of the objects. This is the
"Virial theorem". It also applies if additional forces are involved. For
example, the protons in the sun interact by both gravity and collisions and the
virial theorem holds.
For a gas,
For a diatomic gas there are also two rotational degrees of freedom. In this
case d=5.
In general,
The fact that Gamma=7/5 for air was a clue for the existence of both atoms,
molecules, and quantum mechanics.
For dark energy,
As a substance expands it does work on its surroundings according to its pressure.
Dark matter consists of pointlike particles but they rarely interact with other
particles and so they exert no pressure.
Valyrian steel is a fictional substance from "Game of Thrones" that is
stronger, lighter, and harder than steel. The only elements that qualify are
beryllium, titanium, and vanadium, none of which were known in Earth history
until the 18th century. Valyrian steel could be of these elements,
an alloy, or a magical substance. According to George Martin, magic is
involved.
The fact that it is less dense than steel means that it can't be a fancy form
of steel such as Damascus steel or Wootz steel. Also, fancy steel loses its
special properties if melted and hence cannot be reforged, whereas Valyrian steel
swords can be reforged.
In Earth history, the first metal discovered since iron was cobalt in 1735.
This launched a frenzy to smelt all known minerals and most of the smeltable
metals were discovered by 1800. Then the battery and electrochemstry were
discovered in 1800 and these were used to obtain the unsmeltable metals, which
are lithium, beryllium, magnesium, aluminum, titanium, vanadium, niobium, and
Uranium. Almost all of the strong alloys use these metals, and so the Valyrians
must have used either electrochemistry or magic to make Valyrian steel.
The following metals and alloys are both stronger and lighter than steel and
could hypothetically be Valyrian steel.
Petyr Baelish: Nothing holds an edge like Valyrian steel.
Tyrion Lannister: Valyrian steel blades were scarce and costly, yet thousands
remained in the world, perhaps two hundred in the Seven Kingdoms alone.
George Martin: Valyrian steel is a fantasy metal. Which means it has magical
characteristics, and magic plays a role in its forging.
George Martin: Valyrian steel was always costly, but it became considerably
more so when there was no more Valyria, and the secret of its making were lost.
Ned Stark's stord "Ice" is melted down and reforged into two smaller swords,
"Oathkeeper" and "Widow's Wail". This rules out Valyrian steel being Wootz steel
because Wootz steel loses its special properties when reforged.
Appearances of Valyrian steel in Game of Thrones:
Vantablack is the blackest known substance, composed of carbon nanotubes and
invented in 2014. "Vanta" stands for Vertically Aligned Nano tube Arrays.
Viscosity is analogous to electrical conductivity and thermal conductivity.
For a given instrument there is a characteristic ideal tension for the strings.
If the tension is too low or high the string becomes unplayable. The tension can
be varied to suit the performer's taste but it can't be changed by an extreme
degree.
The height of the string is the distance from the fingerboard, at the end of the fingerboard.
The frequency of a string and the speed of a wave on the string are
related by:
The speed of a wave on a string is
The larger the radius the more difficult the string is to play and the more
impure the overtones. The radius can be minimized by using a material with a
high density. This is why cello, bass, and bass guitar strings are often made of
tungsten.
High-density strings are only appropriate for low-frequency strings because
they have a low wavespeed. High-frequency strings require a material with low
density.
String manufacturers almost never state the density and radius of the string.
You can infer the density from the type of metal used, with numbers given the
table below.
The speed of sound in air has an analogous form as the speed of a wave on a string.
If the tension force on a string exceeds the "Tensile strength" then the string
breaks.
A space elevator requires a material with Z > 100.
Gut was usually used in the Baroque age because steel alloys hadn't been
perfected. A-strings were tuned to a frequency of around 420 Hertz.
Modern steel made possible the 660 Hertz E-string and the high-frequency strings
on a piano.
You can use zylon to make a bass sound like a violin.
Tungsten is a high-density metal that can be used to make low-frequency strings
("Darth Vader" strings). You can make a violin sound like a bass.
The larger the diameter of a string the more difficult it is to play. Diameter
sets the lower limit of the frequency of a string.
If a string is made of tungsten with a density of 19.25 g/cm^3 then the
diameter of the lowest string on each instrument is
The "Tungsten" lines are string diameters for tungsten and the "Zylon" lines
are string diameters for zylon. Tungsten diameters assume a density of 19.3
g/cm^3 and zylon diameters assume a density of 1.5 g/cm^3. The zylon lines cut
off at the right at the frequency where the string breaks.
The price is for strings made of gold with a density 19.3 g/cm^3, the same
as for tungsten.
If the strings are made from iridium or osmium then the metal price is half this.
For tungsten strings the price of the tungsten is negligible.
Even though iridium is half the price of gold, gold wire may be cheaper because
gold is easier to forge.
When a beam is bent it exerts a restoring force. If a string is too stiff it
acts like a beam and becomes impossible to play. The stiffness is inversely
proportional to the Young's modulus. This is why metal strings are usually
wound around a flexible core.
Examples of beam vibrations.
Strings typically have a flexible core with a low Young's modulus and a high-density
metallic winding.
The overtones of an ideal string are exact integer ratios.
If the string is non-ideal then the overtones can change.
The principal source of non-ideality is the finite thickness of the string.
String stiffness also contributes non-ideality.
Plucked strings exhibit inharmonicity. Bowed strings are "mode-locked" so that
the harmonics are exact integer ratios. Reed instruments and the human voice
are also mode locked.
The coefficient of inharmonicity can be expressed in terms of density as
Low strings are more inharmonic than high strings.
The higher the note you play on a string, the smaller the effective string length
and the more inharmonic the note. This is what prevents you from playing notes
of arbitrarily high frequency.
The following is a table of inharmonicity coefficients for various instruments.
We have assumed standard values for the string tension and we assume the string
has the density of steel.
The lower the frequency of a string, the more inharmonic it is. Low-frequency
strings typically consist of a synthetic core (for
elasticity) and an outer metallic winding (for density).
You can't use metal for the entire string because metal is too stiff (the Young's
modulus is too high.
An ideal core material has a high tensile strengh, so that you can use a small
core diameter, and a low Young's modulus, to minimize inharmonicity. The
synthetic material that is best suited for this is Vectran (see the table
above).
For constant string length the ideal force doesn't depend on frequency.
If "r" is too large compared to "R" then the string loses density. We assume that
r is is a fixed fraction of R and that r/R ~ 2/5.
Using
Let
The following table shows a set of example parameters for low-frequency strings.
We assume a core of Vectran (density=1400 kg/m^3) and a winding of
osmium (density=22600 kg/m^3).
Elements are built from protons, neutrons, and electrons.
The identity of an element is determined by the proton number.
The heaviest naturally-occuring element is uranium with 92 protons.
If two atoms of hydrogen encounter each other they combine into a diatomic
molecule, releasing energy. All elements that are gases at room temperature are
diatomic.
Alloys can be much stronger than pure metals.
Discovery Method of Source
(year) discovery
Carbon Ancient Naturally occuring
Gold Ancient Naturally occuring
Silver Ancient Naturally occuring
Sulfur Ancient Naturally occuring
Lead -6500 Smelt with carbon Galena PbS
Copper -5000 Smelt with carbon Chalcocite Cu2S
Bronze (As) -4200 Copper + Arsenic Realgar As4S4
Tin -3200 Smelt with carbon Calamine ZnCO3
Bronze (Sn) -3200 Copper + Tin
Brass -2000 Copper + Zinc Sphalerite ZnS
Mercury -2000 Heat the sulfide Cinnabar HgS
Iron -1200 Smelt with carbon Hematite Fe2O3
Arsenic 1250 Heat the sulfide Orpiment As2S3
Zinc 1300 Smelt with wool Calamine ZnCO3 (smithsonite) & Zn4Si2O7(OH)2·H2O (hemimorphite)
Antimony 1540 Smelt with iron Stibnite Sb2S3
Phosphorus 1669 Heat NaPO3 Excrement
Cobalt 1735 Smelt with carbon Cobaltite CoAsS
Platinum 1735 Naturally occuring
Nickel 1751 Smelt with carbon Nickeline NiAs
Bismuth 1753 Isolated from lead
Hydrogen 1766 Hot iron + steam Water
Oxygen 1771 Heat HgO
Nitrogen 1772 Isolated from air
Manganese 1774 Smelt with carbon Pyrolusite MnO2
Molybdenum 1781 Smelt with carbon Molybdenite MoS2
Tungsten 1783 Smelt with carbon Wolframite (Fe,Mn)WO4
Chromium 1797 Smelt with carbon Crocoite PbCrO4
Palladium 1802 Isolated from Pt
Osmium 1803 Isolated from Pt
Iridium 1803 Isolated from Pt
Rhodium 1804 Isolated from Pt
Sodium 1807 Electrolysis
Potassium 1807 Electrolysis
Magnesium 1808 Electrolysis Magnesia MgCO3
Cadmium 1817 Isolated from zinc
Lithium 1821 Electrolysis of LiO2 Petalite LiAlSi4O10
Zirconium 1824 Smelt with potassium Zircon ZrSiO4
Aluminum 1827 Smelt with potassium
Silicon 1823 Smelt with potassium
Beryllium 1828 Smelt with potassium Beryl Be3Al2Si6O18
Thorium 1929 Smelt with potassium Gadolinite (Ce,La,Nd,Y)2FeBe2Si2O10
Vanadium 1831 Smelt VCl2 with H2 Vanadinite Pb5(VO4)3Cl
Uranium 1841 Smelt with potassium Uranite UO2
Ruthenium 1844 Isolated from Pt
Tantalum 1864 Smelt with hydrogen Tantalite [(Fe,Mn)Ta2O6]
Niobium 1864 Smelt with hydrogen Tantalite [(Fe,Mn)Ta2O6]
Fluorine 1886 Electrolysis
Helium 1895 From uranium ore
Titanium 1910 Smelt with sodium Ilmenite FeTiO3
Hafnium 1924 Isolated from zirconium
Rhenium 1928 Isolated from Pt
Scandium 1937 Electrolysis Gadolinite FeTiO3
-384 -322 Aristotle. Wrote "Meteorology"
-370 -285 Theophrastus. Wrote "De Mineralibus"
77 Pliny the Elder publishes "Natural History"
973 1050 Al Biruni. Published "Gems"
1546 Georgius Agricola publishes "On the Nature of Rocks"
1556 Georgius Agricola publishes "On Metals"
1609 de Boodt publishes a catalog of minerals
1669 Brand: Discovery of phosphorus
1714 John Woodward publishes "Naturalis historia telluris illustrata & aucta", a mineral catalog
1735 Brandt: Discovery of cobalt
1777 Lavoisier: Discovery of sulfur
1778 Lavoisier: Discovery of oxygen and prediction of silicon
1783 Lavoisier: Discovery of hydrogen
1784 T. Olof Bergman publishes "Manuel du mineralogiste, ou sciagraphie du regne mineral",
and founds analytical chemistry
1778 Lavoisier: Discovery of oxygen
1801 Rene Just Huay publishes "Traite de Mineralogie", founding crystallography
1811 Avogadro publishes "Avogadro's law"
1860 The Karlsruhe Congress publishes a table of atomic weights
1869 Mendeleev publishes the periodic table
Shear modulus = S = 82 GJoules/meter3
Density = D = 7900 kg/meter3
Sword worthiness = Q = S/D = 10.4 MJoules/kg
-600 Wootz steel developed in India and is renowned as the finest steel in the world.
1700 The technique for making Wootz steel is lost.
1790 Wootz steel begins to be studied by the British Royal Society.
1838 Anosov replicates Wootz steel.
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon),
and cementite (iron carbide, Fe, 6.7% carbon).
Cu2O + C → 2 Cu + CO
At low temperature copper stays in the form of Cu2O and at high
temperature it gives the oxygen to carbon and becomes pure copper.
3 Fe2O3 + C → 2 Fe3O4 + CO
Fe3O4 + C → 3 FeO + CO
FeO + C → Fe + CO
Oxidation state = Number of electrons each iron atom gives to oxygen
Oxidation state
CuO 2
Cu2O 1
Cu 0
Fe2O3 3
Fe3O4 8/3
FeO 2
Fe 0
Smelt Method Year Abundance
(C) (ppm)
Gold <0 * Ancient .0031
Silver <0 * Ancient .08
Platinum <0 * 1735 .0037
Mercury <0 heat -2000 .067
Palladium <0 chem 1802 .0063
Copper 80 C -5000 68
Sulfur 200 * Ancient 420
Lead 350 C -6500 10
Nickel 500 C 1751 90
Cadmium 500 C 1817 .15
Cobalt 525 ? 1735 30
Tin 725 C -3200 2.2
Iron 750 C -1000 63000
Phosphorus 750 heat 1669 10000
Tungsten 850 C 1783 1100
Potassium 850 e- 1807 15000
Zinc 975 C 1746 79
Sodium 1000 e- 1807 23000
Chromium 1250 C 1797 140
Niobium 1300 H 1864 17
Manganese 1450 C 1774 1120
Vanadium 1550 ? 1831 190
Silicon 1575 K 1823 270000
Titanium 1650 Na 1910 66000
Magnesium 1875 e- 1808 29000
Lithium 1900 e- 1821 17
Aluminum 2000 K 1827 82000
Uranium 2000 K 1841 1.8
Beryllium 2350 K 1828 1.9
Smelt: Temperature required to smelt with carbon
Method: Method used to purify the metal when it was first discovered
*: The element occurs in its pure form naturally
C: Smelt with carbon
K: Smelt with potassium
Na: Smelt with sodium
H: Smelt with hydrogen
e-: Electrolysis
heat: Heat causes the oxide to decompose into pure metal. No carbon required.
chem: Chemical separation
Discovery: Year the element was first obtained in pure form
Abundance: Abundance in the Earth's crust in parts per million
Elements with a low carbon smelting temperature were discovered in ancient
times unless the element was rare. Cobalt was discovered in 1735, the first new
metal since antiquity, and this inspired scientists to smelt every known
mineral in the hope that it would yield a new metal. By 1800 all the rare
elements that were carbon smeltable were discovered.
Fe2O3 + 2 Al → 2 Fe + Al2O3
Oxidation state Oxidation state
at left at right
2 M2O ↔ 4 M + O2 1 0
4 MO ↔ 2 M2O + O2 2 1
2 M3O4 ↔ 6 MO + O2 8/3 2
6 M2O3 ↔ 4 M3O4 + O2 3 8/3
2 M2O3 ↔ 4 MO + O2 3 2
2 MO ↔ 2 M + O2 2 0
2/3 M2O3 ↔ 4/3 M + O2 3 0
1 MO2 ↔ 1 M + O2 4 0
2 MO2 ↔ 2 MO + O2 4 2
Color Colorant carat ($)
Painite 55000 CaZrAl9O15(BO3)
Diamond Clear 1400 C
Ruby Red Chromium 15000 Al2O3
Sapphire Blue Iron 650 Al2O3
Sapphire yellow Titanium Al2O3
Sapphire Orange Copper Al2O3
Sapphire Green Magnesium Al2O3
Emerald Green Chromium Be3Al2(SiO3)6
Beryl Aqua Iron Be3Al2(SiO3)6 AKA "aquamarine"
Morganite Orange Manganese 300 Be3Al2(SiO3)6
Topaz Topaz Al2SiO4(F,OH)2
Spinel Red Red MgAl2O4
Quartz Clear SiO2
Amethyst Purple Iron SiO2
Citrine Yellow SiO2
Zircon Red ZrSiO4
Garnet Orange [Mg,Fe,Mn]3Al2(SiO4)3 & Ca3[Cr,Al,Fe]2(SiO4)3
Garnet Blue 1500 [Mg,Fe,Mn]3Al2(SiO4)3 & Ca3[Cr,Al,Fe]2(SiO4)3
Opal SiO2·nH2O
Opal Black 11000 SiO2·nH2O
Jet Black Lignite
Peridot Green (Mg,Fe)2SiO4
Pearl White CaCO3
Jade Green NaAlSi2O6
Amber Orange Resin
White: High conductivity
Red: Low conductivity
Electric Thermal Density Electric C/Ct Heat Heat Melt $/kg Young Tensile Poisson Brinell
conduct conduct conduct/ cap cap number hardness
(e7 A/V/m) (W/K/m) (g/cm^3) Density (AK/VW) (J/g/K) (J/cm^3K) (K) (GPa) (GPa) (GPa)
Silver 6.30 429 10.49 .60 147 .235 2.47 1235 590 83 .17 .37 .024
Copper 5.96 401 8.96 .67 147 .385 3.21 1358 6 130 .21 .34 .87
Gold 4.52 318 19.30 .234 142 .129 2.49 1337 24000 78 .124 .44 .24
Aluminum 3.50 237 2.70 1.30 148 .897 2.42 933 2 70 .05 .35 .245
Beryllium 2.5 200 1.85 1.35 125 1.825 3.38 1560 850 287 .448 .032 .6
Magnesium 2.3 156 1.74 1.32 147 1.023 1.78 923 3 45 .22 .29 .26
Iridium 2.12 147 22.56 .094 144 .131 2.96 2917 13000 528 1.32 .26 1.67
Rhodium 2.0 150 12.41 .161 133 .243 3.02 2237 13000 275 .95 .26 1.1
Tungsten 1.89 173 19.25 .098 137 .132 2.54 3695 50 441 1.51 .28 2.57
Molybdenum 1.87 138 10.28 .182 136 .251 2896 24 330 .55 .31 1.5
Cobalt 1.7 100 8.90 .170 .421 1768 30 209 .76 .31 .7
Zinc 1.69 116 7.14 .388 693 2 108 .2 .25 .41
Nickel 1.4 90.9 8.91 .444 1728 15
Ruthenium 1.25 117 12.45 2607 5600
Cadmium 1.25 96.6 8.65 594 2 50 .078 .30 .20
Osmium 1.23 87.6 22.59 .130 3306 12000
Indium 1.19 81.8 7.31 430 750 11 .004 .45 .009
Iron 1.0 80.4 7.87 .449 1811 211 .35 .29 .49
Palladium .95 71.8 1828
Tin .83 66.8 505 22 47 .20 .36 .005
Chromium .79 93.9 .449 2180
Platinum .95 .133 2041
Tantalum .76 .140 3290
Gallium .74 303
Thorium .68
Niobium .55 53.7 2750
Rhenium .52 .137 3459
Vanadium .5 30.7 2183
Uranium .35
Titanium .25 21.9 .523 1941
Scandium .18 15.8 1814
Neodymium .156 1297
Mercury .10 8.30 .140 234
Manganese .062 7.81 1519
Germanium .00019 1211
Diamondiso 10 3320
Diamond e-16 2200 .509
Nanotube 10 3500 Carbon nanotube. Electric conductivity = e-16 laterally
Tube bulk 200 Carbon nanotubes in bulk
Graphene 10 5000
Graphite 2 400 .709 Natural graphite
Al Nitride e-11 180
Brass 1.5 120
Steel 45 Carbon steel
Bronze .65 40
Steel Cr .15 20 Stainless steel (usually 10% chromium)
Quartz (C) 12 Crystalline quartz. Thermal conductivity is anisotropic
Quartz (F) e-16 2 Fused quartz
Granite 2.5
Marble 2.2
Ice 2
Concrete 1.5
Limestone 1.3
Soil 1
Glass e-12 .85
Water e-4 .6
Seawater 1 .6
Brick .5
Plastic .5
Wood .2
Wood (dry) .1
Plexiglass e-14 .18
Rubber e-13 .16
Snow .15
Paper .05
Plastic foam .03
Air 5e-15 .025
Nitrogen .025 1.04
Oxygen .025 .92
Silica aerogel .01
Siemens: Amperes^2 Seconds^3 / kg / meters^2 = 1 Ohm^-1
For most metals,
Electric conductivity / Thermal conductivity ~ 140 J/g/K
Teslas
Field generated by brain 10-12
Wire carrying 1 Amp .00002 1 cm from the wire
Earth magnetic field .0000305 at the equator
Neodymium magnet 1.4
Magnetic resonance imaging machine 8
Large Hadron Collider magnets 8.3
Field for frog levitation 16
Strongest electromagnet 32.2 without using superconductors
Strongest electromagnet 45 using superconductors
Neutron star 1010
Magnetar neutron star 1014
MVolt/meter
Air 3
Glass 12
Polystyrene 20
Rubber 20
Distilled water 68
Vacuum 30 Depends on electrode shape
Diamond 2000
Relative permittivity
Vacuum 1 (Exact)
Air 1.00059
Polyethylene 2.5
Sapphire 10
Concrete 4.5
Glass ~ 6
Rubber 7
Diamond ~ 8
Graphite ~12
Silicon 11.7
Water (0 C) 88
Water (20 C) 80
Water (100 C) 55
TiO2 ~ 150
SrTiO3 310
BaSrTiO3 500
Ba TiO3 ~ 5000
CaCuTiO3 250000
Relative Magnetic Maximum Critical
permeability moment frequency temperature
(kHz) (K)
Metglas 2714A 1000000 100 Rapidly-cooled metal
Iron 200000 2.2 1043
Iron + nickel 100000 Mu-metal or permalloy
Cobalt + iron 18000
Nickel 600 .606 627
Cobalt 250 1.72 1388
Carbon steel 100
Neodymium magnet 1.05
Manganese 1.001
Air 1.000
Superconductor 0
Dysprosium 10.2 88
Gadolinium 7.63 292
EuO 6.8 69
Y3Fe5O12 5.0 560
MnBi 3.52 630
MnAs 3.4 318
NiO + Fe 2.4 858
CrO2 2.03 386
293 K 300 K 500 K
Beryllium 35.6 37.6 99
Magnesium 43.9 45.1 78.6
Aluminum 26.5 27.33 49.9
Copper 16.78 17.25 30.9
Silver 15.87 16.29 28.7
Electric quantities | Thermal quantities
|
Q = Charge Coulomb | Etherm= Thermal energy Joule
I = Current Amperes | Itherm= Thermal current Watts
E = Electric field Volts/meter | Etherm= Thermal field Kelvins/meter
C = Electric conductivity Amperes/Volt/meter | Ctherm= Thermal conductivity Watts/meter/Kelvin
A = Area meter^2 | A = Area meter^2
Z = Distance meter | Z = Distance meter^2
J = Current flux Amperes/meter^2 | Jtherm= Thermal flux Watts/meter^2
= I / A | = Ittherm / A
= C * E | = Ctherm * Etherm
V = Voltage Volts | Temp = Temperature difference Kelvin
= E Z | = Etherm Z
= I R | = Itherm Rtherm
R = Resistance Volts/Ampere = Ohms | Rtherm= Thermal resistance Kelvins/Watt
= Z / (A C) | = Z / (A Ct)
H = Current heating Watts/meter^3 |
= E J |
P = Current heating power Watts |
= E J Z A |
= V I |
Continuum quantity Macroscopic quantity
E <-> V
C <-> R = L / (A C)
J = C E <-> I = V / R
H = E J <-> P = V I
Critical Critical Type
temperature field
(Kelvin) (Teslas)
Magnesium-Boron2 39 55 2 MRI machines
Niobium3-Germanium 23.2 37 2 Field for thin films. Not widely used
Magnesium-Boron2-C 34 36 Doped with 5% carbon
Niobium3-Tin 18.3 30 2 High-performance magnets. Brittle
Vanadium3-Gallium 14.2 19 2
Niobium-Titanium 10 15 2 Cheaper than Niobium3-Tin. Ductile
Niobium3-Aluminum
Technetium 11.2 2
Niobium 9.26 .82 2
Vanadium 5.03 1 2
Tantalum 4.48 .09 1
Lead 7.19 .08 1
Lanthanum 6.3 1
Mercury 4.15 .04 1
Tungsten 4 1 Not BCS
Tin 3.72 .03 1
Indium 3.4 .028
Rhenium 2.4 .03 1
Thallium 2.4 .018
Thallium 2.39 .02 1
Aluminum 1.2 .01 1
Gallium 1.1
Gadolinium 1.1
Protactinium 1.4
Thorium 1.4
Thallium 2.4
Molybdenum .92
Zinc .85 .0054
Osmium .7
Zirconium .55
Cadmium .52 .0028
Ruthenium .5
Titanium .4 .0056
Iridium .1
Lutetium .1
Hafnium .1
Uranium .2
Beryllium .026
Tungsten .015
HgBa2Ca2Cu3O8 134 2
HgBa2Ca Cu2O6 128 2
YBa2Cu3O7 92 2
C60Cs2Rb 33 2
C60Rb 28 2 2
C60K3 19.8 .013 2
C6Ca 11.5 .95 2 Not BCS
Diamond:B 11.4 4 2 Diamond doped with boron
In2O3 3.3 3 2
The critical fields for Niobium-Titanium, Niobium3-Tin, and Vanadium3-Gallium
are for 4.2 Kelvin.
Boiling point (Kelvin)
Water 273
Ammonia 248
Freon R12 243
Freon R22 231
Propane 230
Acetylene 189
Ethane 185
Xenon 165.1
Krypton 119.7
Oxygen 90.2
Argon 87.3
Nitrogen 77.4 Threshold for cheap superconductivity
Neon 27.1
Hydrogen 20.3 Cheap MRI machines
Helium-4 4.23 High-performance magnets
Helium-3 3.19
The record for Niobium3-Tin is 2643 Amps/mm^2 at 12 T and 4.2 K.
Pressure = P (Pascals or Newtons/meter2 or Joules/meter3)
Temperature = T (Kelvin)
Volume = Vol (meters3)
Total gas kinetic energy = E (Joules)
Kinetic energy per volume = e = E/Vol (Joules/meter3)
Number of gas molecules = N
Mass of a gas molecule = M
Gas molecules per volume = n = N / Vol
Gas density = D = N M / Vol
Avogadro number = Avo= 6.022⋅1023 moles-1
Moles of gas molecules = Mol= N / Avo
Boltzmann constant = k = 1.38⋅10-23 Joules/Kelvin
Gas constant = R = k Avo = 8.31 Joules/Kelvin/mole
Gas molecule thermal speed = Vth
Mean kinetic energy / gas molecule= ε = E / n = ½ M Vth2 (Definition of the mean thermal speed)
Gas pressure arises from the kinetic energy of gas molecules and has units of
energy/volume.
The ideal gas law can be written in the following forms:
P = 2⁄3 e Form used in physics
= R Mol T / Vol Form used in chemistry
= k N T / Vol
= 1⁄3 N M Vth2/ Vol
= 1⁄3 D Vth2
= k T D / M
Gas simulation at phet.colorado.edu
Derivation of the ideal gas law
1660 Boyle law P Vol = Constant at fixed T
1802 Charles law T Vol = Constant at fixed P
1802 Gay-Lussac law T P = Constant at fixed Vol
1811 Avogadro law Vol / N = Constant at fixed T and P
1834 Clapeyron law P Vol / T = Constant combined ideal gas law
Molecule mass = M
Thermal speed = Vth
Boltzmann constant = k = 1.38⋅10-23 Joules/Kelvin
Molecule mean kinetic energy = ε
A gas molecule moving in N dimensions has N degrees
of freedom. In 3D the mean energy of a gas molecule is
ε = 3⁄2 k T = ½ M V2th
Adiabatic constant = γ
= 5/3 for monatomic molecules such as helium, neon, krypton, argon, and xenon
= 7/5 for diatomic molecules such as H2, O2, and N2
= 7/5 for air, which is 21% O2, 78% N2, and 1% Ar
≈ 1.31 for a triatomic gas such as CO2
Pressure = P
Density = D
Sound speed = Vsound
Mean thermal speed = Vth
K.E. per molecule = ε = ½ M Vth2
V2sound = γ P / D = 1⁄3 γ V2th
The sound speed depends on temperature and not on density or pressure.
Vsound = .68 Vth
These laws are derived in the appendix.
M in atomic mass units
Helium atom 4
Neon atom 20
Nitrogen molecule 28
Oxygen molecule 32
Argon atom 40
Krypton atom 84
Xenon atom 131
A helium atom has a smaller mass than a nitrogen molecule and hence has a
higher sound speed. This is why the pitch of your voice increases if you
inhale helium. Inhaling xenon makes you sound like Darth Vader. Then you pass
out because Xenon is an anaesthetic.
1635 Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660 Viviani and Borelli produce the first accurate measurement of the speed of
sound, giving a value of 350 m/s.
1660 Hooke's law published. The force on a spring is proportional to the change
in length.
1662 Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
1687 Newton publishes the Principia Mathematica, which contains the first analytic
calculation of the speed of sound. The calculated value was 290 m/s.
Newton's calculation was correct if one assumes that a gas behaves like Boyle's
law and Hooke's law.
Melt Boil Solid Liquid Gas Mass Sound speed
(K) (K) density density density (AMU) at 20 C
g/cm3 g/cm3 g/cm3 (m/s)
He .95 4.2 .125 .000179 4.00 1007
Ne 24.6 27.1 1.21 .000900 20.18
Ar 83.8 87.3 1.40 .00178 39.95 319
Kr 115.8 119.9 2.41 .00375 83.80 221
Xe 161.4 165.1 2.94 .00589 131.29 178
H2 14 20 .070 .000090 2.02 1270
N2 63 77 .81 .00125 28.01 349
O2 54 90 1.14 .00143 32.00 326
Air .0013 29.2 344 79% N2, 21% O2, 1% Ar
H2O 273 373 .917 1.00 .00080 18.02
CO2 n/a 195 1.56 n/a .00198 44.00 267
CH4 91 112 .42 .00070 16.04 446
CH5OH 159 352 .79 .00152 34.07 Alcohol
Gas density is for 0 Celsius and 1 Bar. Liquid density is for the boiling point,
except for water, which is for 4 Celsius.
M = Mass of a gas molecule
V = Thermal speed
E = Mean energy of a gas molecule
= 1/2 M V^2
H = Characteristic height of an atmosphere
g = Gravitational acceleration
Suppose a molecule at the surface of the Earth is moving upward with speed V and suppose
it doesn't collide with other air molecules. It will reach a height of
M H g = 1/2 M V^2
This height H is the characteristic height of an atmosphere.
Pressure of air at sea level = 1 Bar
Pressure of air in Denver = .85 Bar One mile high
Pressure of air at Mount Everest = 1/4 Bar 10 km high
The density of the atmosphere scales as
Density ~ (Density At Sea Level) * exp(-E/E0)
where E is the gravitational potential energy of a gas molecule and E0 is the
characteristic thermal energy given by
E0 = M H g = 1/2 M V^2
Expressed in terms of altitude h,
Density ~ Density At Sea Level * exp(-h/H)
For oxygen,
E0 = 3/2 * Boltzmann_Constant * Temperature
E0 is the same for all molecules regardless of mass, and H depends on the
molecule's mass. H scales as
H ~ Mass^-1
S = Escape speed
T = Temperature
B = Boltzmann constant
= 1.38e-23 Joules/Kelvin
g = Planet gravity at the surface
M = Mass of heavy molecule m = Mass of light molecule
V = Thermal speed of heavy molecule v = Thermal speed of light molecule
E = Mean energy of heavy molecule e = Mean energy of light molecule
H = Characteristic height of heavy molecule h = Characteristic height of light molecule
= E / (M g) = e / (m g)
Z = Energy of heavy molecule / escape energy z = Energy of light molecule / escape energy
= .5 M V^2 / .5 M S^2 = .5 m v^2 / .5 m S^2
= V^2 / S^2 = v^2 / S^2
For an ideal gas, all molecules have the same mean kinetic energy.
E = e = 1.5 B T
.5 M V^2 = .5 m v^2 = 1.5 B T
The light molecules tend to move faster than the heavy ones. This is why
your voice increases in pitch when you breathe helium. Breathing a heavy gas such
as Xenon makes you sound like Darth Vader.
V^2 << S^2 <-> Z << 1
Escape Atmos Temp H2 N2 Z Z
speed density (K) km/s km/s (H2) (N2)
km/s (kg/m^3)
Jupiter 59.5 112 1.18 .45 .00039 .000056
Saturn 35.5 84 1.02 .39 .00083 .00012
Neptune 23.5 55 .83 .31 .0012 .00018
Uranus 21.3 53 .81 .31 .0014 .00021
Earth 11.2 1.2 287 1.89 .71 .028 .0041
Venus 10.4 67 735 3.02 1.14 .084 .012
Mars 5.03 .020 210 1.61 .61 .103 .015
Titan 2.64 5.3 94 1.08 .41 .167 .024
Europa 2.02 0 102 1.12 .42 .31 .044
Moon 2.38 0 390 2.20 .83 .85 .12
Ceres .51 0 168 1.44 .55 8.0 1.14
Even if an object has enough gravity to capture an atmosphere, it can still lose it
to the solar wind. Also, the upper atmosphere tends to be hotter than at the
surface, increasing the loss rate.
Thermal Speed < 1/5 Escape speed
Thermal speed of molecules ~ Escape speed
In the gas simulation at phet.colorado.edu, you can move the wall and watch the
gas change temperature.
3 * Boltzmann_Constant * Temperature ~ MassOfMolecules * Escape_Speed^2
For the sun, what is the temperature of a proton moving at the escape speed?
This sets the scale of the temperature of the core of the sun. The minimum temperature
for hydrogen fusion is 4 million Kelvin.
Escape speed (km/s) Core composition
Sun 618. Protons, electrons, helium
Earth 11.2 Iron
Mars 5.03 Iron
Moon 2.38 Iron
Ceres .51 Iron
M = Mass of molecule
V = Speed of the molecule
L = Space between the walls
With each collision, the momentum change = 2 M V
Force = Change in momentum / Time between collisions = M V^2 / L
Suppose a gas molecule is in a cube of volume L^3 and a molecule bounces back
and forth between two opposite walls (never touching the other four walls).
The pressure on these walls is
Pressure = Force / Area
= M V^2 / L^3
= M V^2 / Volume
Pressure * Volume = M V^2
This is the ideal gas law in one dimension. For a molecule moving in 3D,
Velocity^2 = (Velocity in X direction)^2
+ (Velocity in Y direction)^2
+ (Velocity in Z direction)^2
Characteristic thermal speed in 3D = 3 * Characteristic thermal speed in 1D.
To produce the 3D ideal gas law, replace V^2 with 1/3 V^2 in the 1D equation.
Pressure * Volume = 1/3 M V^2 Where V is the characteristic thermal speed of the gas
This is the pressure for a gas with one molecule. If there are n molecules,
Pressure Volume = n 1/3 M V^2 Ideal gas law in 3D
If a gas consists of molecules with a mix of speeds, the thermal speed is defined as
Kinetic dnergy density of gas molecules = E = (n / Volume) 1/2 M V^2
Using this, the ideal gas law can be written as
Pressure = 2/3 E
= 1/3 Density V^2
= 8.3 Moles Temperature / Volume
The last form comes from the law of thermodynamics:
M V^2 = 3 B T
Total gravitational energy = -2 * Total kinetic energy
just like for a single satellite on a circular orbit.
Gravitational energy of the sun = -2 * Kinetic energy of protons in the sun
Because of Hooke's law, springs oscillate with a constant frequency.
X = Displacement of a spring
V = Velocity of the spring
A = Acceleration of the spring
F = Force on the spring
M = Spring mass
Q = Spring constant
q = (K/M)^(1/2)
t = time
T = Spring oscillation period
Hooke's law and Newton's law:
F = - Q X = M A
A = - (Q/M) X = - q^2 X
This equation is solved with
X = sin(q t)
V = q cos(q t)
A = -q^2 sin(q t) = - q^2 X
The oscillation period of the spring is
T = 2 Pi / q
= 2 Pi (M/Q)^(1/2)
According to Boyle's law, a gas functions like a spring and hence a gas oscillates
like a spring. An oscillation in a gas is a sound wave.
P = Pressure
dP = Change in pressure
Vol = Volume
dVol= Change in volume
If you change the volume of a gas according to Boyle's law,
P Vol = Constant
P dVol + Vol dP = 0
dP = - (P/Vol) dVol
The change in pressure is proportional to the change in volume.
This is equivalent to Hooke's law, where pressure takes the role of force
and the change in volume takes the role of displacement of the spring.
This is the mechanism behind sound waves.
In Boyle's law, the change in volume is assumed to be slow so the gas
has time to equilibrate temperature with its surroundings. In this case
the temperature is constant as the volume changes and the change is
"isothermal".
P Vol = Constant
If the change in volume is fast then the walls do work on the molecules,
changing their temperature. If there isn't enough time to equilibrate
temperature with the surroundings then the change is "adiabatic". You can see
this in action with the "Gas" simulation at phet.colorado.edu.
Moving the wall changes the thermal speed of molecules and hence the temperature.
If a gas consists of pointlike particles then
Vol = Volume of the gas
Ek = Total kinetic energy of gas molecules within the volume
E = Total energy of gas molecules within the volume
= Kinetic energy plus the energy from molecular rotation and vibration
dE = Change in energy as the volume changes
P = Pressure
dP = Change in pressure as the volume changes
D = Density
C = Speed of sound in the gas
d = Number of degrees of freedom of a gas molecule
= 3 for a monotomic gas such as Helium
= 5 for a diatomic gas such as nitrogen
G = Adiabatic constant
= 1 + 2/d
= 5/3 for a monatomic gas
= 7/5 for a diatomic gas
k = Boltzmann constant
T = Temperature
The ideal gas law is
P Vol = (2/3) Ek (Derived in www.jaymaron.com/gas/gas.html)
This law is equivalent to the formula that appears in chemistry.
P Vol = Moles R T
For a gas in thermal equilibrium each degree of freedom has a mean energy of
.5 k T. For a gas of pointlike particles (monotomic) there are three degrees of
freedom, one each for motion in the X, Y, and Z direction. In this case d=3.
The mean kinetic energy of each gas molecule is 3 * (.5 k T).
The total mean energy of each gas molecule is also 3 * (.5 k T).
Ek = 3 * (.5 k T)
E = d * (.5 k T)
Ek = (3/d) E
If you change the volume of a gas adiabatically, the walls change the kinetic and
rotational energy of the gas molecules.
dE = -P dVol
The ideal gas law in terms of E instead of Ek is
P Vol = (2/d) E
dP = (2/d) (dE/Vol - E dVol/Vol^2)
= (2/d) [-P dVol/Vol - (d/2) P dVol/Vol]
= -(1+2/d) P dVol/Vol
= - G P dVol/Vol
This equation determines the speed of sound in a gas.
C^2 = G P / D
For air,
P = 1.01e5 Newtons/meter^2
D = 1.2 kg/meter^3
Newton assumed G=1 from Boyle's law, yielding a sound speed of
C = 290 m/s
The correct value for air is G=7/5, which gives a sound speed of
C = 343 m/s
which is in accord with the measurement.
For a gas, G can be measured by measuring the sound speed. The results are
Helium 5/3 Monatomic molecule
Argon 5/3 Monatonic molecule
Air 7/5 4/5 Nitrogen and 1/5 Oxygen
Oxygen 7/5 Diatomic molecule
Nitrogen 7/5 Diatomic molecule
The fact that G is not equal to 1 was the first solid evidence for the
existence of atoms and it also contained a clue for quantum mechanics. If a
gas is a continuum (like Hooke's law) it has G=1 and if it consists of
pointlike particles (monatonic) it has G=5/3. This explains helium and argon
but not nitrogen and oxygen. Nitrogen and oxygen are diatomic molecules and
their rotational degrees of freedom change Gamma.
Kinetic degrees Rotational degrees Gamma
of freedom of freedom
Monatonic gas 3 0 5/3
Diatomic gas T < 1000 K 3 2 7/5
Diatomic gas, T > 1000 K 3 3 4/3
Quantum mechanics freezes out one of the rotation modes at low temperature.
Without quantum mechanics, diatomic molecules would have Gamma=4/3 at room
temperature.
E = Energy
dE = Change in energy
e = Energy density
Vol= Volume
P = Pressure
The volume expands as the universe expands.
dE = - P dVol
For dark energy, the energy density "e" is constant in space and so
dE = e dVol
Hence,
P = - e
Dark energy has a negative pressure, which means that it behaves differently
from a continuum and from particles.
Yield Density Strength/Density
strength (g/cm3) (GJoule/kg)
(GPascal)
Beryllium .34 1.85 .186
Aluminum + Be .41 2.27 .181
LiMgAlScTi 1.97 2.67 .738
Titanium .22 4.51 .050
Titanium + AlVCrMo 1.20 4.6 .261
Vanadium .53 6.0 .076
AlCrFeCoNiTi 2.26 6.5 .377
AlCrFeCoNiMo 2.76 7.1 .394
Steel .25 7.9 .032 Iron plus carbon
Copper .12 9.0 .013
"Yield strength" is the maximum pressure a material can sustain before
deforming. "Strength/Density" is the strength-to-weight ratio.
Steel is stronger and lighter than copper.
Name Owner
Sword Longclaw Jon Snow
Sword Heartsbane Samwell Tarly
Dagger Arya
Sword Ice Eddard Stark Reforged into Oathkeeper and Widow's Wail
Sword Oathkeeper Brienne of Tarth
Sword Widow's Wail The Crown
Sword Lady Forlorn Ser Lyn Corbray
Sword Nightfall Ser Harras Harlow
Sword Red Rain Lord Dunstan Drumm
Arakh Caggo
Armor Euron Greyjoy
Horn Dragonbinder The Citadel of The Maesters
Some Maesters carry links of Valyrian steel, a symbol of mastery of the highest arts.
Reflectivity
Black paint .025
Super black .004 Nickel-phosphorus alloy
Vantablack .00035 Carbon nanotubes
Quantity Electricity Thermal Viscosity
Stuff Coulomb Joule Momentum
Stuff/volume Coulomb/m^3 Joule/m^3 Momentum/m^3
Flow = Stuff/time Coulomb/second Joule/s Momentum/s
Potential Volts Kelvin Momentum/m^3
Field Volts/meter Kelvins/meter Momentum/m^3/m
Flow density = Flow/m^2 Amperes/meter^2 Watts/meter^2 Momentum/s/m^2
Conductivity Amperes/Volt/meter Watts/meter/Kelvin m^2/s
Resistance Volts/Ampere Kelvins/Watt s/m^3
Flow density = Conductivity * Field
Flow = Potential / Resistance
Field = -Gradient(Potential)
Fluid density = ρ (kg/meter3)
Fluid velocity = V
Fluid momentum density = U = D V
Kinematic viscosity = νk (meters2 / second)
Dynamic viscosity = νd = ρ νk (Pascal seconds)
Lagrangian time deriv. = Dt
Dt U = ∇⋅(νd∇U)
Dt V = ∇⋅(νk∇V)
Dynamic Kinematic Density
viscosity viscosity (kg/m3)
(Pa s) (m2/s)
Hydrogen .00000876
Nitrogen .0000178
Air .0000183 .0000150 1.22
Helium .000019
Oxygen .0000202
Xenon .0000212
Acetone .00031
Benzine .00061
Water at 2 C .00167
Water at 10 C .00131 .0000010 1000
Water at 20 C .00100 1000
Water at 30 C .000798 1000
Water at 100 C .000282 1000
Mercury .00153 .00000012
Blood .0035
Motor oil .065
Olive oil .081
Honey 6
Peanut butter 250
Asthenosphere 7e19 Weak layer between the curst and mantle
Upper mantle .8e21
Lower mantle 1.5e21
1 Stokes = 1 cm2/s = 10-4 m2/s
Schmidt number = Momentum diffusivity / Mass diffusivity
Prandtl number = Momentum diffusivity / Thermal diffusivity
Magnetic Prandtl number = Momentum diffusivity / Magnetic diffusivity
Prandtl Schmidt
Air .7 .7
Water 7
Liquid metals << 1
Oils >> 1
n = Electron density
M = Electron mass
V = Electron thermal velocity
Q = Proton charge
k = Boltzmann constant
Temp = Temperature
Xdebye = Debye length (k*Temp/n/Q^2/(4 Pi Ke))^.5
Xgyro = Electron gyro radius M V / Q B
Fgyro = Electron gyrofrequency
Electron Temp Debye Magnetic
density (K) (m) field (T)
(m^-3)
Solar core e32 e7 e-11 -
ITER 1.0e20 e8 e-4 5.3
Laser fusion 6.0e32 e8 - National Ignition Facility. density=1000 g/cm^3
Gas discharge e16 e4 e-4 -
Ionosphere e12 e3 e-3 e-5
Magnetosphere e7 e7 e2 e-8
Solar wind e6 e5 e1 e-9
Interstellar e5 e4 e1 e-10
Intergalactic e0 e6 e5 -
ITER ion temperature = 8.0 keV
ITER electron temperature = 8.8 keV
ITER confinement time = 400 seconds
Compression Heating Fusion Heating Density Year
laser (MJ) laser (MJ) energy time (kg/m^3)
(MJ) (s)
NOVA .3 1984. LLNL
National Ignition Facility (NIF) 330 - 20 .9 2010
HiPER .2 .07 30 e-11 .3 Future
String Height of Height of String String
length Tension (Newtons) top string bottom string length length
mm E A D G C mm mm inch violin=1
Violin 320 80 50 45 45 3.2 5.2 12.6 1
Viola 388 65 55 55 55 4.8 6.2 15.3 1.21
Cello 690 160 130 130 130 5.2 8.2 27.2 2.2
Bass 1060 160 160 160 160 41.3 3.3
Guitar 650 120 120 120 120 25.6 2.0
Bass guitar 860 160 160 160 160 33.6 2.7
Values for a violin A-string
L = Length of a string = .32 meters
F = Vibration frequency of the string = 440 Hertz
V = Speed of a wave on the string = 281.6 meters/second
= 2 F L
For a given instrument and string frequency, the wavespeed is fixed.
WaveSpeed^2 = Tension / (Density * Pi * Radius^2)
The variables you can vary for a string are {Tension, Density, Radius}.
Once you have chosen the frequency and length of the string then these variables
are related by
Tension = Constant * Density * Radius^2
SoundSpeed^2 = (7/5) Pressure / Density
Force = Force on the string
A = Area of the string
S = Stress on the string
= Force / A
Smax = Tensile strength
= Maximum string stress before breaking
Z = Strength to weight ratio
Z = Smax / Density
Tensile Density Z/10^6 Young's
strength modulus
(GPa) (g/cm^3) (J/kg) (GPa)
Carbon nanotube 7 .116 60.3 Technology not yet developed
Nylon .045 1.15 .04 5
Kevlar 3.6 1.44 2.5
Zylon 5.8 1.5 3.9
Gut .2 1.5 .13 6
Magnesium alloy .4 1.8 .22
Aluminum .05 2.7
Titanium alloy .94 4.5 .21
Nickel .20 8.9
Chromium .28 7.2
Steel alloy 2.0 7.9 .25 220
Brass .55 8.7
Silver .17 10.5
Tungsten .55 19.2 .029
Gold .13 19.3
Osmium 1.0 22.6
Iridium
F = String frequency
R = String radius
A = String cross-sectional area
= Pi R^2
D = String density
L = String length
Force= String tension force (Newtons)
S = Tensile stress (Pascals)
= Force / A
Smax = Maximum string tensile stress before breaking
= Tensile strength
V = Speed of a wave on the string
= SquareRoot(P/D)
Z = String strength-to-weight ratio
= S/D
Fmax = Maximum frequency of a string
The maximum frequency of a string happens when S=Smax.
Fmax = V / (2L)
= SquareRoot(Smax/D) / (2L)
= SquareRoot(Z) / (2L)
The maximum frequency of a string depends on the strength-to-weight ratio Z.
Values for Z for various string materials are given in the table above.
Steel alloy is often used for the highest-frequency strings on a violin or
piano.
Gut Steel Zylon Carbon Tungsten
nanotube
Violin 563 781 2960 12100 266
Viola 465 644 2440 3160 220
Cello 261 362 1370 5620 123
Bass 170 236 895 3660 80
Guitar 277 385 1519 5973 131
Bass guitar 209 291 1148 4514 99
Frequencies are in Hertz.
Frequency = Constant * SquareRoot(Smax/D) / R
String frequency is inversely proportional to radius. A string can be made an
octave lower by doubling the radius.
-
Freq Length Diameter
(Hz) (mm) (mm)
Violin G 196 320 .46
Viola C 130 388 .62
Cello C 65 690 1.07
Bass E 41 1060 1.18
Guitar E 82 650 .90
Bass guitar E 41 860 1.7
Density Price
(g/cm^3) ($/g)
Zylon 1.5 Cheap
Tungsten 19.2 .05
Gold 19.3 40
Rhenium 21.0 10
Platinum 21.4 80
Iridium 22.4 20
Osmium 22.6 20
R = String radius
L = String length
D = String density
Y = Young's modulus for the string
Force= Tension force on the string
N = An integer greater than or equal to 1
Fn = Frequency of overtone N
= N F (1 + C N^2)
C = Constant of inharmonicity
= Pi^3 R^4 Y / (8 L^2 Force)
If C=0 then there is no inharmonicity and the overtones are exact integer multiples
of the fundamental mode. If the string has finite thickness then the frequencies
of the overtones shift.
C = Pi Force Y / (128 D^2 F^4 L^6)
Increasing the density decreases the inharmonicity.
String Tension Frequency Density Radius Young's C
length (Newtons) (Hertz) (g/cm^3) (mm) modulus
(mm) (GPa)
Violin E gut 320 80 660 1.5 .31 6 .000026
Violin E steel 320 80 660 7.9 .13 220 .000033
Violin G steel 320 45 196 7.9 .34 220 .00012
Viola C steel 388 55 130 7.9 .47 220 .00019
Cello C steel 690 130 65 7.9 .81 220 .000098
Bass E steel 1060 160 41 7.9 .92 220 .000047
Guitar E steel 650 140 82 7.9 .70 220 .000058
Bass guitar E 860 220 41 7.9 1.34 220 .00017
If we set the frequency shift from inharmonicity equal to the frequency resolution
for human hearing,
N^2 C = 1/170
If C=.0001 then N=7.7 (The inharmonicity appears at the 8th overtone)
L = Length of the string
R = Outer radius of the string
r = Radius of the inner core
= K R where K is a dimensionless constant
Y = Young's modulus of the core material
D = Density of the outer winding
Force= Force on the string
= k L where k is a constant
Y = Young's modulus of the core
S = Stress on the inner core
= Force / (Pi r^2)
s = Strain on the inner core
= S/Y
C = Constant of inharmonicity
= Pi^3 R^4 Y / (8 L^2 Force)
= Pi Force Y / (128 D^2 F^4 L^6)
The strain should be as large as possible to minimize the Young's modulus, but
if it is too large then the string loses functionality. We assume that the
strain is a constant value.
Force / (Pi r^2) = Y s
The larger the value of "r" the lower the value of "Y" and the lower the inharmonicity.
Force = Pi R^2 4 D F^2 L^2
= Pi r^2 Y s
We have
4 D F^2 L^2 = K^2 Y s
The inharmonicity is
C = Pi Force Y / (128 D^2 F^4 L^6)
= Pi Force 4 D F^2 L^2 / (128 K^2 s D^2 F^4 L^6)
= Pi Force / (32 K^2 D F^2 s L^4)
= Constant * Force / (F^2 L^4)
If we assume that
Force = Constant * L
then
C = Constant / (F^2 L^3)
The lowest practical frequency of an instrument scales as L^(-3/2).
Relative inharmonicity = 1/(Freq^2 Length^3)
The relative inharmonicity of the lowest string for various instruments is
given by the following table. The value is similar for all instruments.
Freq Length Relative inharmonicity
(Hz) (mm) = 1/(Freq^2 Length^3)
Violin G 196 320 .00079
Viola C 130 388 .00101
Cello C 65 690 .00072
Bass E 41 1060 .00050
Guitar E 82 650 .00054
Bass guitar E 41 860 .00094
Note Freq Tension Core Core Outer Core Core
(Hertz) stress radius radius Young strain
(N) (GPa) (mm) (GPa)
Viola C 130.4 50 .2 .28 .70 70 .0155
Viola C 65.2 50 .2 .28 1.30 70 .0155
Viola C 65.2 50 1.0 .126 1.25 70 .0155
© Jason Maron, all rights reserved.
Data from Wikipedia unless otherwise specified.
Hydrogen White
Carbon Black
Nitrogen Blue
Oxygen Red
Sulfur Yellow
Scoville scale (relative capsaicin content)
Ghost pepper 1000000
Trinidad 1000000 Trinidad moruga scorpion
Naga Morich 1000000
Habanero 250000
Cayenne pepper 40000
Malagueta pepper 40000
Tabasco 40000
Jalapeno 5000
Guajillo pepper 5000
Cubanelle 500
Banana pepper 500
Bell pepper 50
Pimento 50
Molecule Relative hotness
Rresiniferatoxin 16000
Tinyatoxin 5300
Capsaicin 16 Chili pepper
Nonivamide 9.2 Chili pepper
Shogaol .16 Ginger
Piperine .1 Black pepper
Gingerol .06 Ginger
Capsiate .016 Chili pepper
© Jason Maron, all rights reserved.
Data from Wikipedia unless otherwise specified.
Particle Charge Mass (kg) Mass / Proton mass
Proton +1 1.673⋅10-27 1
Neutron 0 1.675⋅10-27 1.0012
Electron -1 9.109⋅10-31 .000544
.png)
|
|---|