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For other uses, see Isotope (disambiguation).
Isotopes are any of the several different forms of an element each having different atomic mass (mass number). Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of neutrons. Therefore, isotopes have different mass numbers, which give the total number of nucleons—the number of protons plus neutrons.
A nuclide is any particular atomic nucleus with a specific atomic number Z and mass number A; it is equivalently an atomic nucleus with a specific number of protons and neutrons. Collectively, all the isotopes of all the elements form the set of nuclides. The distinction between the terms isotope and nuclide has somewhat blurred, and they are often used interchangeably. Isotope is best used when referring to several different nuclides of the same element; nuclide is more generic and is used when referencing only one nucleus or several nuclei of different elements. For example, it is more correct to say that an element such as fluorine consists of one stable nuclide rather than that it has one stable isotope.
In IUPAC nomenclature, isotopes and nuclides are specified by the name of the particular element, implicitly giving the atomic number, followed by a hyphen and the mass number (e.g. helium-3, carbon-12, carbon-13, iodine-131 and uranium-238). In symbolic form, the number of nucleons is denoted as a superscripted prefix to the chemical symbol (e.g. 3He, 12C, 13C, 131I and 238U).
The term isotope was coined in 1913 by Margaret Todd, a Scottish doctor, during a conversation with Frederick Soddy (to whom she was distantly related by marriage). Soddy, a chemist at Glasgow University, explained that it appeared from his investigations as if several elements occupied each position in the periodic table. Hence Todd suggested the Greek for "at the same place" as a suitable name. Soddy adopted the term and went on to win the Nobel Prize for Chemistry in 1921 for his work on radioactive substances.
In the bottom right corner of JJ Thomson's photographic plate are markings for the two isotopes of neon: neon-20 and neon-22.In 1913, as part of his exploration into the composition of canal rays, JJ Thomson channeled a stream of ionized neon through a magnetic and an electric field and measured its deflection by placing a photographic plate in its path. Thomson observed two patches of light on the photographic plate (see image on right), which suggested two different parabolas of deflection. Thomson concluded that some of the atoms in the gas were of higher mass than the rest.
Contents [hide]
1 Variation in properties between isotopes
2 Occurrence in nature
3 Molecular mass of isotopes
4 Applications of isotopes
4.1 Use of chemical properties
4.2 Use of nuclear properties
5 See also
6 External links
[edit] Variation in properties between isotopes
A neutral atom has the same number of electrons as protons. Thus, different isotopes of a given element all have the same number of protons and electrons and the same electronic structure; because the chemical behavior of an atom is largely determined by its electronic structure, isotopes exhibit nearly identical chemical behavior. The main exception to this is the kinetic isotope effect: due to their larger masses, heavier isotopes tend to react somewhat more slowly than lighter isotopes of the same element.
This "mass effect" is most pronounced for protium (1H) vis-à-vis deuterium (2H), because deuterium has twice the mass of protium. For heavier elements the relative mass difference between isotopes is much less, and the mass effect is usually negligible.
Similarly, two molecules which differ only in the isotopic nature of their atoms (isotopologues) will have identical electronic structure and therefore almost indistinguishable physical and chemical properties (again with deuterium providing the primary exception to this rule). The vibrational modes of a molecule are determined by its shape and by the masses of its constituent atoms. Consequently, isotopologues will have different sets of vibrational modes. Since vibrational modes allow a molecule to absorb photons of corresponding energies, isotopologues have different optical properties in the infrared range.
Although isotopes exhibit nearly identical electronic and chemical behavior, their nuclear behavior varies dramatically. Atomic nuclei consist of protons and neutrons bound together by the strong nuclear force. Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, allow some separation between the positively charged protons, reducing the electrostatic repulsion. Neutrons also stabilize the nucleus because at short ranges they attract each other and protons equally by the strong nuclear force, and this also offsets the electrical repulsion between protons. For this reason, one or more neutrons are necessary for two or more protons to be bound into a nucleus. As the number of protons increases, additional neutrons are needed to form a stable nucleus; for example, although the neutron to proton ratio of 3He is 1:2, the neutron/proton ratio of 238U is greater than 3:2. If too many or too few neutrons are present, the nucleus is unstable and subject to nuclear decay.
[edit] Occurrence in nature
Most elements have several different isotopes that can be found in nature. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear decay; short-lived nuclides quickly decay away, while their long-lived counterparts endure. However, this does not mean that short-lived species disappear entirely; many are continually produced through the decay of longer-lived nuclides. Also, short-lived isotopes such as those of promethium have been detected in the spectra of stars, where they presumably are being continuously made by stellar nucleosynthesis. The tabulated atomic masses of elements are averages that account for the presence of multiple isotopes with different masses.
According to generally accepted cosmology, virtually all nuclides other than isotopes of hydrogen and helium (and traces of some isotopes of lithium, beryllium and boron-- see big bang nucleosynthesis) were built in stars and supernovae. Their respective abundances here result from the quantities formed by these processes, their spread through the galaxy, and their rates of decay. After the initial coalescence of the solar system, isotopes were redistributed according to mass. The isotopic composition of elements is different on different planets, making it possible to determine the origin of meteorites.
Tuesday, August 14, 2007
Isotopes of oxygen
Isotopes of oxygen
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Oxygen (O)
Standard atomic mass: 15.9994(3) u
The isotopes of oxygen include 3 stable nuclei and 14 unstable nuclei.
Contents [hide]
1 Table
1.1 Notes
2 References
3 See also
[edit] Table
nuclide
symbol Z(p) N(n)
isotopic mass (u)
half-life nuclear
spin representative
isotopic
composition
(mole fraction) range of natural
variation
(mole fraction)
excitation energy
12O 8 4 12.034405(20) 580(30)E-24 s [0.40(25) MeV] 0+
13O 8 5 13.024812(10) 8.58(5) ms (3/2-)
14O 8 6 14.00859625(12) 70.598(18) s 0+
15O 8 7 15.0030656(5) 122.24(16) s 1/2-
16O 8 8 15.99491461956(16) STABLE 0+ 0.99757(16) 0.99738-0.99776
17O 8 9 16.99913170(12) STABLE 5/2+ 0.00038(1) 0.00037-0.00040
18O 8 10 17.9991610(7) STABLE 0+ 0.00205(14) 0.00188-0.00222
19O 8 11 19.003580(3) 26.464(9) s 5/2+
20O 8 12 20.0040767(12) 13.51(5) s 0+
21O 8 13 21.008656(13) 3.42(10) s (1/2,3/2,5/2)+
22O 8 14 22.00997(6) 2.25(15) s 0+
23O 8 15 23.01569(13) 82(37) ms 1/2+#
24O 8 16 24.02047(25) 65(5) ms 0+
25O 8 17 25.02946(28)# <50 ns (3/2+)#
26O 8 18 26.03834(28)# <40 ns 0+
27O 8 19 27.04826(54)# <260 ns 3/2+#
28O 8 20 28.05781(64)# <100 ns 0+
[edit] Notes
The precision of the isotope abundances and atomic mass is limited through variations. The given ranges should be applicable to any normal terrestrial material.
Values marked # are not purely derived from experimental data, but at least partly from systematic trends. Spins with weak assignment arguments are enclosed in parentheses.
Uncertainties are given in concise form in parentheses after the corresponding last digits. Uncertainty values denote one standard deviation, except isotopic composition and standard atomic mass from IUPAC which use expanded uncertainties.
[edit] References
Isotope masses from Ame2003 Atomic Mass Evaluation by G. Audi, A.H. Wapstra, C. Thibault, J. Blachot and O. Bersillon in Nuclear Physics A729 (2003).
Isotopic compositions and standard atomic masses from Atomic weights of the elements. Review 2000 (IUPAC Technical Report). Pure Appl. Chem. Vol. 75, No. 6, pp. 683-800, (2003) and Atomic Weights Revised (2005).
Half-life, spin, and isomer data selected from these sources. Editing notes on this article's talk page.
Audi, Bersillon, Blachot, Wapstra. The Nubase2003 evaluation of nuclear and decay properties, Nuc. Phys. A 729, pp. 3-128 (2003).
National Nuclear Data Center, Brookhaven National Laboratory. Information extracted from the NuDat 2.1 database (retrieved Sept. 2005).
David R. Lide (ed.), Norman E. Holden in CRC Handbook of Chemistry and Physics, 85th Edition, online version. CRC Press. Boca Raton, Florida (2005). Section 11, Table of the Isotopes.
[edit] See also
Oxygen isotope ratio cycle
Oxygen
Isotopes of nitrogen Isotopes of oxygen Isotopes of fluorine
Index to isotope pages
Retrieved from "http://en.wikipedia.org/wiki/Isotopes_of_oxygen"
Categories: Oxygen | Isotopes
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From Wikipedia, the free encyclopedia
Jump to: navigation, search
Oxygen (O)
Standard atomic mass: 15.9994(3) u
The isotopes of oxygen include 3 stable nuclei and 14 unstable nuclei.
Contents [hide]
1 Table
1.1 Notes
2 References
3 See also
[edit] Table
nuclide
symbol Z(p) N(n)
isotopic mass (u)
half-life nuclear
spin representative
isotopic
composition
(mole fraction) range of natural
variation
(mole fraction)
excitation energy
12O 8 4 12.034405(20) 580(30)E-24 s [0.40(25) MeV] 0+
13O 8 5 13.024812(10) 8.58(5) ms (3/2-)
14O 8 6 14.00859625(12) 70.598(18) s 0+
15O 8 7 15.0030656(5) 122.24(16) s 1/2-
16O 8 8 15.99491461956(16) STABLE 0+ 0.99757(16) 0.99738-0.99776
17O 8 9 16.99913170(12) STABLE 5/2+ 0.00038(1) 0.00037-0.00040
18O 8 10 17.9991610(7) STABLE 0+ 0.00205(14) 0.00188-0.00222
19O 8 11 19.003580(3) 26.464(9) s 5/2+
20O 8 12 20.0040767(12) 13.51(5) s 0+
21O 8 13 21.008656(13) 3.42(10) s (1/2,3/2,5/2)+
22O 8 14 22.00997(6) 2.25(15) s 0+
23O 8 15 23.01569(13) 82(37) ms 1/2+#
24O 8 16 24.02047(25) 65(5) ms 0+
25O 8 17 25.02946(28)# <50 ns (3/2+)#
26O 8 18 26.03834(28)# <40 ns 0+
27O 8 19 27.04826(54)# <260 ns 3/2+#
28O 8 20 28.05781(64)# <100 ns 0+
[edit] Notes
The precision of the isotope abundances and atomic mass is limited through variations. The given ranges should be applicable to any normal terrestrial material.
Values marked # are not purely derived from experimental data, but at least partly from systematic trends. Spins with weak assignment arguments are enclosed in parentheses.
Uncertainties are given in concise form in parentheses after the corresponding last digits. Uncertainty values denote one standard deviation, except isotopic composition and standard atomic mass from IUPAC which use expanded uncertainties.
[edit] References
Isotope masses from Ame2003 Atomic Mass Evaluation by G. Audi, A.H. Wapstra, C. Thibault, J. Blachot and O. Bersillon in Nuclear Physics A729 (2003).
Isotopic compositions and standard atomic masses from Atomic weights of the elements. Review 2000 (IUPAC Technical Report). Pure Appl. Chem. Vol. 75, No. 6, pp. 683-800, (2003) and Atomic Weights Revised (2005).
Half-life, spin, and isomer data selected from these sources. Editing notes on this article's talk page.
Audi, Bersillon, Blachot, Wapstra. The Nubase2003 evaluation of nuclear and decay properties, Nuc. Phys. A 729, pp. 3-128 (2003).
National Nuclear Data Center, Brookhaven National Laboratory. Information extracted from the NuDat 2.1 database (retrieved Sept. 2005).
David R. Lide (ed.), Norman E. Holden in CRC Handbook of Chemistry and Physics, 85th Edition, online version. CRC Press. Boca Raton, Florida (2005). Section 11, Table of the Isotopes.
[edit] See also
Oxygen isotope ratio cycle
Oxygen
Isotopes of nitrogen Isotopes of oxygen Isotopes of fluorine
Index to isotope pages
Retrieved from "http://en.wikipedia.org/wiki/Isotopes_of_oxygen"
Categories: Oxygen | Isotopes
ViewsArticle Discussion Edit this page History Personal toolsSign in / create account Navigation
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Contents
Featured content
Current events
Random article
interaction
About Wikipedia
Community portal
Recent changes
Contact Wikipedia
Make a donation
Help
Search
Toolbox
What links here
Related changes
Upload file
Special pages
Printable version
Permanent link
Cite this article
This page was last modified 07:27, 27 June 2007. All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.)
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a US-registered 501(c)(3) tax-deductible nonprofit charity.
Privacy policy About Wikipedia Disclaimers
CAS registry number
CAS registry number
From Wikipedia, the free encyclopedia
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CAS registry numbers are unique numerical identifiers for chemical compounds, polymers, biological sequences, mixtures and alloys. They are also referred to as CAS numbers, CAS RNs or CAS #s.
Chemical Abstracts Service (CAS), a division of the American Chemical Society, assigns these identifiers to every chemical that has been described in the literature. The intention is to make database searches more convenient, as chemicals often have many names. Almost all molecule databases today allow searching by CAS number.
As of June 2007, there were 31,745,275 organic and inorganic substances and 59,039,087 sequences in the CAS registry.[1] Around 50,000 new numbers are added each week.
CAS also maintains and sells a database of these chemicals, known as the CAS registry.
Contents [hide]
1 Format
2 Isomers, enzymes, and mixtures
3 Searches
4 Notes
5 See also
6 External links
[edit] Format
A CAS registry number is separated by hyphens into three parts, the first consisting of up to 6 digits, the second consisting of two digits, and the third consisting of a single digit serving as a check digit. The numbers are assigned in increasing order and do not have any inherent meaning. The checksum is calculated by taking the last digit times 1, the next digit times 2, the next digit times 3 etc., adding all these up and computing the sum modulo 10. For example, the CAS number of water is 7732-18-5: the checksum is calculated as (8×1 + 1×2 + 2×3 + 3×4 + 7×5 + 7×6) = 105; 105 mod 10 = 5.
[edit] Isomers, enzymes, and mixtures
Different stereoisomers of a molecule receive different CAS numbers: D-glucose has 50-99-7, L-glucose has 921-60-8, α-D-glucose has 26655-34-5, etc. Occasionally, whole classes of molecules receive a single CAS number: the group of alcohol dehydrogenases has 9031-72-5. An example of a mixture with a CAS number is mustard oil (8007-40-7).
[edit] Searches
When using CAS numbers for database searches, it is useful to include the numbers of closely related compounds. For instance, to search for information about cocaine (CAS 50-36-2), one should consider including cocaine hydrochloride (CAS 53-21-4), since that is the most common form of cocaine when used as a drug.
[edit] Notes
^ CAS Registry Number and Substance Counts
[edit] See also
EC number (Enzyme Commission)
EC# (EINECS and ELINCS)
International Chemical Identifier (InChI)
PubChem
SMILES
UN number
Chemical database
[edit] External links
CAS registry description, by the Chemical Abstracts Service
To find the CAS number of a compound given its name, formula or structure, the following free resources can be used:
PubChem
R&D Chemicals
NIH ChemIDplus
NIST Chemistry WebBook
NCI Database Browser
Chemfinder
European chemical Substances Information System (ESIS) - useful for finding EC#
Retrieved from "http://en.wikipedia.org/wiki/CAS_registry_number"
Categories: Chemical numbering schemes | American Chemical Society
From Wikipedia, the free encyclopedia
Jump to: navigation, search
CAS registry numbers are unique numerical identifiers for chemical compounds, polymers, biological sequences, mixtures and alloys. They are also referred to as CAS numbers, CAS RNs or CAS #s.
Chemical Abstracts Service (CAS), a division of the American Chemical Society, assigns these identifiers to every chemical that has been described in the literature. The intention is to make database searches more convenient, as chemicals often have many names. Almost all molecule databases today allow searching by CAS number.
As of June 2007, there were 31,745,275 organic and inorganic substances and 59,039,087 sequences in the CAS registry.[1] Around 50,000 new numbers are added each week.
CAS also maintains and sells a database of these chemicals, known as the CAS registry.
Contents [hide]
1 Format
2 Isomers, enzymes, and mixtures
3 Searches
4 Notes
5 See also
6 External links
[edit] Format
A CAS registry number is separated by hyphens into three parts, the first consisting of up to 6 digits, the second consisting of two digits, and the third consisting of a single digit serving as a check digit. The numbers are assigned in increasing order and do not have any inherent meaning. The checksum is calculated by taking the last digit times 1, the next digit times 2, the next digit times 3 etc., adding all these up and computing the sum modulo 10. For example, the CAS number of water is 7732-18-5: the checksum is calculated as (8×1 + 1×2 + 2×3 + 3×4 + 7×5 + 7×6) = 105; 105 mod 10 = 5.
[edit] Isomers, enzymes, and mixtures
Different stereoisomers of a molecule receive different CAS numbers: D-glucose has 50-99-7, L-glucose has 921-60-8, α-D-glucose has 26655-34-5, etc. Occasionally, whole classes of molecules receive a single CAS number: the group of alcohol dehydrogenases has 9031-72-5. An example of a mixture with a CAS number is mustard oil (8007-40-7).
[edit] Searches
When using CAS numbers for database searches, it is useful to include the numbers of closely related compounds. For instance, to search for information about cocaine (CAS 50-36-2), one should consider including cocaine hydrochloride (CAS 53-21-4), since that is the most common form of cocaine when used as a drug.
[edit] Notes
^ CAS Registry Number and Substance Counts
[edit] See also
EC number (Enzyme Commission)
EC# (EINECS and ELINCS)
International Chemical Identifier (InChI)
PubChem
SMILES
UN number
Chemical database
[edit] External links
CAS registry description, by the Chemical Abstracts Service
To find the CAS number of a compound given its name, formula or structure, the following free resources can be used:
PubChem
R&D Chemicals
NIH ChemIDplus
NIST Chemistry WebBook
NCI Database Browser
Chemfinder
European chemical Substances Information System (ESIS) - useful for finding EC#
Retrieved from "http://en.wikipedia.org/wiki/CAS_registry_number"
Categories: Chemical numbering schemes | American Chemical Society
Speed of Sound
Speed of sound
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This page is about the physical speed of sound waves in a medium. For other uses of the term and related terms, see Speed of sound (disambiguation).
Sound measurements
Sound pressure p
Sound pressure level (SPL)
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c
Sound is a vibration that travels through an elastic medium as a wave. The speed of sound describes how much distance such a wave travels in a given amount of time. The speed varies with the medium employed (for example, sound waves move faster through water than through air), as well as with the properties of the medium, especially temperature. The term is commonly used to refer specifically to the speed of sound in air. At sea level, at a temperature of 21 °C (70 °F) and under normal atmospheric conditions, the speed of sound is 344 m/s (1238 km/h, or 769 mph, or 1128 ft/s or 661.5 kt).
The speed of sound is sometimes used in describing the nature of substances (see the article on sodium).
In conventional use and in scientific literature sound velocity, v, and sound speed, c, are used synonymously and should not be confused with sound particle velocity (also symbolized as v), which is the velocity of the individual particles.
In the Earth's atmosphere, the speed varies with atmospheric conditions; the most important factor is the temperature. Air pressure has almost no effect on sound speed. It has no effect at all in an ideal gas approximation, because pressure and density both contribute to sound velocity equally, and in an ideal gas the two effects cancel out, leaving only the effect of temperature. Sound usually travels more slowly with greater altitude, due to reduced temperature, creating a negative sound speed gradient. In the stratosphere, the speed of sound increases with height due to heating within the ozone layer, producing a positive sound speed gradient.
Humidity has a small, but measurable effect on sound speed. Sound travels slightly (0.1%-0.6%) faster in humid air. The approximate speed of sound in 0% humidity (dry) air, in metres per second (m·s-1), at temperatures near 0 °C, can be calculated from:
where is the temperature in degrees Celsius (°C).
This equation is derived from the first two terms of the Taylor expansion of the following equation:
The value of 331.3 m/s, which represents the 0 °C speed, is probably the most defensible based on theoretical (and some measured) values of the specific heat ratio, γ. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas γ is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.
This equation is correct to a wider temperature range, but still depends on the approximation of heat capacity being independent of temperature, and will fail particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's stratosphere. A derivation of these equations will be given in a later section.
Contents [hide]
1 Basic concept
2 Details
2.1 Speed in solids
2.2 Speed in fluids
2.3 Speed in ideal gases and in air
2.3.1 Temperatures in Celsius
2.4 Tables
3 Effect of frequency and gas composition
4 Mach number
5 Experimental methods
5.1 Single-shot timing methods
5.2 Other methods
6 Gradients
7 References
8 See also
9 External links
[edit] Basic concept
The transmission of sound can be explained using a toy model consisting of an array of balls interconnected by springs. For a real material the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to their springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly). Effects like dispersion and reflection can also be understood using this model.
In a real material, the stiffness of the springs is called the elastic modulus, and the mass corresponds to the density. All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones. For instance, sound will travel faster in iron than uranium, and faster in hydrogen than nitrogen, due to the lower density of the first material of each set. At the same time, sound will travel faster in iron than hydrogen, because the internal bonds in a solid like iron are much stronger than the gaseous bonds between hydrogen molecules. In general, solids will have a higher speed of sound than liquids, and liquids will have a higher speed of sound than gases.
Some textbooks mistakenly state that the speed of sound increases with increasing density. This is usually illustrated by presenting data for three materials, such as air, water and steel. With only these three examples it indeed appears that speed is correlated to density, yet including only a few more examples would show this assumption to be incorrect.
[edit] Details
In general, the speed of sound c is given by
where
C is a coefficient of stiffness
ρ is the density
Thus the speed of sound increases with the stiffness of the material, and decreases with the density. For general equations of state, if classical mechanics is used, the speed of sound c is given by
where differentiation is taken with respect to adiabatic change.
If relativistic effects are important, the speed of sound may be calculated from the relativistic Euler equations.
In a non-dispersive medium sound speed is independent of sound frequency, so the speeds of energy transport and sound propagation are the same. For audible sounds air is a non-dispersive medium. But air does contain a small amount of CO2 which is a dispersive medium, and it introduces dispersion to air at ultrasonic frequencies (> 28 kHz).[citation needed]
In a dispersive medium sound speed is a function of sound frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its own phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves -- see optical dispersion for a description.
[edit] Speed in solids
In a solid, there is a non-zero stiffness both for volumetric and shear deformations. Hence, in a solid it is possible to generate sound waves with different velocities dependent on the deformation mode.
In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:
where
E is Young's modulus
ρ (rho) is density
Thus in steel the speed of sound is approximately 5100 m·s-1.
In a solid with lateral dimensions much larger than the wavelength, the sound velocity is higher. It is found by replacing Young's modulus with the plane wave modulus, which can be expressed in terms of the Young's modulus and Poisson's ratio as:
[edit] Speed in fluids
In a fluid the only non-zero stiffness is to volumetric deformation (a fluid does not sustain shear forces).
Hence the speed of sound in a fluid is given by
where
K is the bulk modulus of the fluid
The speed of sound in water is of interest to anyone using underwater sound as a tool, whether in a laboratory, a lake or the ocean. Examples are sonar, acoustic communication and acoustical oceanography. See Discovery of Sound in the Sea for other examples of the uses of sound in the ocean (by both man and other animals). In fresh water, sound travels at about 1497 m/s at 25 °C. See Technical Guides - Speed of Sound in Pure Water for an online calculator.
Sound speed as a function of depth at a position north of Hawaii in the Pacific Ocean derived from the 2005 World Ocean Atlas. The SOFAR channel is centered on the minimum in sound speed at ca. 750-m depth.In salt water that is free of air bubbles or suspended sediment, sound travels at about 1500 m/s. The speed of sound in seawater depends on pressure (hence depth), temperature (a change of 1 °C ~ 4 m/s), and salinity (a change of 1‰ ~ 1 m/s), and empirical equations have been derived to accurately calculate sound speed from these variables. Other factors affecting sound speed are minor. For more information see Dushaw et al. (1993).
A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie (1981)
c(T, S, z) = a1 + a2T + a3T2 + a4T3 + a5(S - 35) + a6z + a7z2 + a8T(S - 35) + a9Tz3
where T, S, and z are temperature in degrees Celsius, salinity in parts per thousand and depth in metres, respectively. The constants a1, a2, ..., a9 are:
a1 = 1448.96, a2 = 4.591, a3 = -5.304×10-2, a4 = 2.374×10-4, a5 = 1.340, a6 = 1.630×10-2, a7 = 1.675×10-7, a8 = -1.025×10-2, a9 = -7.139×10-13
with check value 1550.744 m/s for T=25 °C, S=35‰, z=1000 m. This equation is accurate to O(0.2 m/s). See Technical Guides - Speed of Sound in Sea-Water for an online calculator.
Other equations for sound speed in sea water have slightly greater accuracy, but are far more complicated, e.g., that by V. A. Del Grosso (1974) and the Chen-Millero-Li Equation (1994).[1] [2]
[edit] Speed in ideal gases and in air
For a gas, K (the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids) is approximately given by
thus
Where:
γ is the adiabatic index also known as the isentropic expansion factor. It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume(Cp / Cv), and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression.
p is the pressure.
ρ is the density
Using the ideal gas law to replace p with NRT/V, and replacing ρ with NM/V, the equation for an ideal gas becomes:
where
cideal is the speed of sound in an ideal gas.
R (approximately 8.3145 J·mol-1·K-1) is the molar gas constant.[1]
k is the Boltzmann constant
γ (gamma) is the adiabatic index (sometimes assumed 7/5 = 1.400 for diatomic molecules from kinetic theory, assuming from quantum theory a temperature range at which thermal energy is fully partitioned into rotation (rotations are fully excited), but none into vibrational modes. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at 0 degrees Celsius, for air. Gamma is assumed from kinetic theory to be exactly 5/3 = 1.6667 for monoatomic molecules such as noble gases).
T is the absolute temperature in kelvins.
M is the molar mass in kilograms per mole. The mean molar mass for dry air is about .0289645 kg/mole.
m is the mass of a single molecule in kilograms.
This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for cair have been found to vary slightly from experimentally determined values.:[3]
Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic. His result was missing the factor of γ but was otherwise correct.
Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of requires that the gas exist in a temperature range high enough that rotational heat capacity is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insigificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode, have energies too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See the section on gases in heat capacity for a more complete discussion of this phenomenon.
[edit] Temperatures in Celsius
If temperatures in degrees Celsius(°C) are to be used to calculate air speed in the region near 273 kelvins, then Celsius temperature may be used.
For dry air, where (theta) is the temperature in degrees Celsius(°C).
Making the following numerical substitutions: , where is the molar gas constant, , and using the ideal diatomic gas value of
Then:
Using the first two terms of the Taylor expansion:
The derivation includes the two approximate equations which were given in the introduction. For Celsius temperatures which are negative, the second term of the equation right hand side, is negative.
[edit] Tables
In the standard atmosphere:
T0 is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m·s-1 (= 1086.9 ft/s = 1193 km·h-1 = 741.1 mph = 644.0 knots). Values ranging from 331.3-331.6 may be found in reference literature, however.
T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m·s-1 (= 1126.0 ft/s = 1236 km·h-1 = 767.8 mph = 667.2 knots).
T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m·s-1 (= 1135.6 ft/s = 1246 km·h-1 = 774.3 mph = 672.8 knots).
In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere - actual conditions may vary.
Effect of temperature
in °C c in m·s-1 ρ in kg·m-3 Z in N·s·m-3
−10 325.2 1.342 436.1
−5 328.3 1.317 432.0
0 331.3 1.292 428.4
+5 334.3 1.269 424.3
+10 337.3 1.247 420.6
+15 340.3 1.225 416.8
+20 343.2 1.204 413.2
+25 346.1 1.184 409.8
+30 349.0 1.165 406.3
is the temperature in °C
c is the speed of sound in m·s-1
ρ is the density in kg·m-3
Z is the characteristic acoustic impedance in N·s·m-3 (Z=ρ·c)
Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:
Altitude Temperature m·s-1 km·h-1 mph knots
Sea level 15 °C (59 °F) 340 1225 761 661
11 000 m−20 000 m
(Cruising altitude of commercial jets,
and first supersonic flight) -57 °C (-70 °F) 295 1062 660 573
29 000 m (Flight of X-43A) -48 °C (-53 °F) 301 1083 673 585
[edit] Effect of frequency and gas composition
The medium in which a sound wave is travelling does not always respond adiabatically, and as a result the speed of sound can vary with frequency.[4]
The limitations of the concept of speed of sound due to extreme attenuation are also of concern. The attenuation which exists at sea level for high frequencies applies to successively lower frequencies as atmospheric pressure decreases, or as the mean free path increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes.:[3]
The molecular composition of the gas contributes both as the mass (M) of the molecules, and their heat capacities, and so both have an influence on speed of sound. In general, at the same molecular mass, monatomic gases have slightly higher sound speeds (over 9% higher) due to the fact that they have a higher γ (5/3 = 1.67) than diatomics do (7/5 = 1.4). Thus, at the same molecular mass, the sound speed of a monatomic gas goes up by a factor of
= 1.09
This gives the 9 % difference, and would be a typical ratio for sound speeds at room temperature in helium vs. deuterium, each with a molecular weight of 4. Sound travels faster in helium than deuterium because adiabatic compression heats helium more, since the helium molecules can store heat energy from compression only in translation, but not rotation. Thus helium molecules (monatomic molecules) travel faster in a sound wave and transmit sound faster. (Sound generally travels at about 70% of the mean molecular velocity in gases).
Note that in this example we have assumed that temperature is low enough that heat capacities are not influenced by molecular vibration (see heat capacity). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas gives the gas additional ways to store heat which do not affect temperature, and thus do not affect molecular velocity and sound velocity. Thus, the effect of higher temperatures and vibrational heat capacity acts to increase the difference between sound speed in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.
[edit] Mach number
Main article: Mach number.
Mach number, a useful quantity in aerodynamics, is the ratio of an object's speed to the speed of sound in the medium through which it is passing (again, usually air). At altitude, for reasons explained, Mach number is a function of temperature.
Aircraft flight instruments, however, operate using pressure differential to compute Mach number; not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the impact pressure sensed by a Pitot tube is dependent on altitude as well as speed.
Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from the Bernoulli equation for M<1:[5]
where
M is Mach number
qc is impact pressure and
P is static pressure.
The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:
where
M is Mach number
qc is impact pressure measured behind a normal shock
P is static pressure.
As can be seen, M appears on both sides of the equation. The easiest method to solve the supersonic M calculation is to enter both the subsonic and supersonic equations into a computer spread sheet such as Microsoft Excel, OpenOffice.org Calc, or some equivalent program. First determine if M is indeed greater than 1.0 by calculating M from the subsonic equation. If M is greater than 1.0 at that point, then use the value of M from the subsonic equation as the initial condition in the supersonic equation. Then perform a simple iteration of the supersonic equation, each time using the last computed value of M, until M converges to a value--usually in just a few iterations.[5]
[edit] Experimental methods
A range of different methods exist for the measurement of sound in air.
[edit] Single-shot timing methods
The simplest concept is the measurement made using two microphones and a fast recording device such as a digital storage scope. This method uses the following idea.
If a sound source and two microphones are arranged in a straight line, with the sound source at one end, then the following can be measured:
1. The distance between the microphones (x), called microphone basis. 2. The time of arrival between the signals (delay) reaching the different microphones (t)
Then v = x / t
An older method is to create a sound at one end of a field with an object that can be seen to move when it creates the sound. When the observer sees the sound-creating device act they start a stopwatch and when the observer hears the sound they stop their stopwatch. Again using v = x / t you can calculate the speed of sound. A separation of at least 200 m between the two experimental parties is required for good results with this method.
[edit] Other methods
In these methods the time measurement has been replaced by a measurement of the inverse of time (frequency).
Kundt's tube is an example of an experiment which can be used to measure the speed of sound in a small volume. It has the advantage of being able to measure the speed of sound in any gas. This method uses a powder to make the nodes and antinodes visible to the human eye. This is an example of a compact experimental setup.
A tuning fork can be held near the mouth of a long pipe which is dipping into a barrel of water. In this system it is the case that the pipe can be brought to resonance if the length of the air column in the pipe is equal to ({1+2n}λ/4) where n is an integer. As the antinodal point for the pipe at the open end is slightly outside the mouth of the pipe it is best to find two or more points of resonance and then measure half a wavelength between these.
Here it is the case that v = fλ
[edit] Gradients
Normally sound waves spread out in an inverse square law, and rapidly dissipate.
However, in the ocean (the 'deep sound channel' or SOFAR channel), variations in the speed of sound create a layer where the speed of sound is at a minimum and any sound waves generated spread out in a substantially flat layer- refraction keeps the sound constrained to spread out in an inverse law, which carries the sound very much further.
A similar effect occurs in the atmosphere and Project_Mogul was an attempt to detect the sound of nuclear weapons using this principle, and was successfully able to detect a nuclear explosion at a considerable distance.
[edit] References
^ Article Abstract
^ dushaw-jasa-93
^ a b U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.
^ A B Wood, A Textbook of Sound (Bell, London, 1946)
^ a b Olson, Wayne M. (2002). "AFFTC-TIH-99-02, Aircraft Performance Flight Testing." (PDF). Air Force Flight Test Center, Edwards AFB, CA, United States Air Force.
Del Grosso, V. A., 1974. New equation for the speed of sound in natural waters (with comparisons to other equations). J. Acoust. Soc. Am., 56, pp. 1084-1091.
Dushaw, B. D., P. F. Worcester, B. D. Cornuelle, and B. M. Howe, 1993. On equations for the speed of sound in seawater. J. Acoust. Soc. Am., 93, pp. 255-275.
Mackenzie, K. V., 1981. Discussion of sea water sound-speed determinations. J. Acoust. Soc. Am., 70, pp. 801-806.
Applied Physics Laboratory - University of Washington, 1994. APL-UW High-Frequency Ocean Environmental Acoustic Models Handbook. APL-UW TR 9407, pp. I1-I2.
[edit] See also
Sound barrier
SOFAR channel
Underwater acoustics
[edit] External links
Calculation: Speed of sound in air and the temperature
Speed of sound - temperature matters, not air pressure
Properties Of The U.S. Standard Atmosphere 1976
How to measure the speed of sound in a laboratory
Speed of sound in water and water steam as function of pressure & temperature
Teaching resource for 14-16yrs on sound including speed of sound
Technical Guides - Speed of Sound in Pure Water
Technical Guides - Speed of Sound in Sea-Water
Retrieved from "http://en.wikipedia.org/wiki/Speed_of_sound"
Categories: Sound measurements | All articles with unsourced statements | Articles with unsourced statements since February 2007 | Chemical properties | Fluid dynamics | Units of velocity
From Wikipedia, the free encyclopedia
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This page is about the physical speed of sound waves in a medium. For other uses of the term and related terms, see Speed of sound (disambiguation).
Sound measurements
Sound pressure p
Sound pressure level (SPL)
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c
Sound is a vibration that travels through an elastic medium as a wave. The speed of sound describes how much distance such a wave travels in a given amount of time. The speed varies with the medium employed (for example, sound waves move faster through water than through air), as well as with the properties of the medium, especially temperature. The term is commonly used to refer specifically to the speed of sound in air. At sea level, at a temperature of 21 °C (70 °F) and under normal atmospheric conditions, the speed of sound is 344 m/s (1238 km/h, or 769 mph, or 1128 ft/s or 661.5 kt).
The speed of sound is sometimes used in describing the nature of substances (see the article on sodium).
In conventional use and in scientific literature sound velocity, v, and sound speed, c, are used synonymously and should not be confused with sound particle velocity (also symbolized as v), which is the velocity of the individual particles.
In the Earth's atmosphere, the speed varies with atmospheric conditions; the most important factor is the temperature. Air pressure has almost no effect on sound speed. It has no effect at all in an ideal gas approximation, because pressure and density both contribute to sound velocity equally, and in an ideal gas the two effects cancel out, leaving only the effect of temperature. Sound usually travels more slowly with greater altitude, due to reduced temperature, creating a negative sound speed gradient. In the stratosphere, the speed of sound increases with height due to heating within the ozone layer, producing a positive sound speed gradient.
Humidity has a small, but measurable effect on sound speed. Sound travels slightly (0.1%-0.6%) faster in humid air. The approximate speed of sound in 0% humidity (dry) air, in metres per second (m·s-1), at temperatures near 0 °C, can be calculated from:
where is the temperature in degrees Celsius (°C).
This equation is derived from the first two terms of the Taylor expansion of the following equation:
The value of 331.3 m/s, which represents the 0 °C speed, is probably the most defensible based on theoretical (and some measured) values of the specific heat ratio, γ. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas γ is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.
This equation is correct to a wider temperature range, but still depends on the approximation of heat capacity being independent of temperature, and will fail particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's stratosphere. A derivation of these equations will be given in a later section.
Contents [hide]
1 Basic concept
2 Details
2.1 Speed in solids
2.2 Speed in fluids
2.3 Speed in ideal gases and in air
2.3.1 Temperatures in Celsius
2.4 Tables
3 Effect of frequency and gas composition
4 Mach number
5 Experimental methods
5.1 Single-shot timing methods
5.2 Other methods
6 Gradients
7 References
8 See also
9 External links
[edit] Basic concept
The transmission of sound can be explained using a toy model consisting of an array of balls interconnected by springs. For a real material the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to their springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly). Effects like dispersion and reflection can also be understood using this model.
In a real material, the stiffness of the springs is called the elastic modulus, and the mass corresponds to the density. All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones. For instance, sound will travel faster in iron than uranium, and faster in hydrogen than nitrogen, due to the lower density of the first material of each set. At the same time, sound will travel faster in iron than hydrogen, because the internal bonds in a solid like iron are much stronger than the gaseous bonds between hydrogen molecules. In general, solids will have a higher speed of sound than liquids, and liquids will have a higher speed of sound than gases.
Some textbooks mistakenly state that the speed of sound increases with increasing density. This is usually illustrated by presenting data for three materials, such as air, water and steel. With only these three examples it indeed appears that speed is correlated to density, yet including only a few more examples would show this assumption to be incorrect.
[edit] Details
In general, the speed of sound c is given by
where
C is a coefficient of stiffness
ρ is the density
Thus the speed of sound increases with the stiffness of the material, and decreases with the density. For general equations of state, if classical mechanics is used, the speed of sound c is given by
where differentiation is taken with respect to adiabatic change.
If relativistic effects are important, the speed of sound may be calculated from the relativistic Euler equations.
In a non-dispersive medium sound speed is independent of sound frequency, so the speeds of energy transport and sound propagation are the same. For audible sounds air is a non-dispersive medium. But air does contain a small amount of CO2 which is a dispersive medium, and it introduces dispersion to air at ultrasonic frequencies (> 28 kHz).[citation needed]
In a dispersive medium sound speed is a function of sound frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its own phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves -- see optical dispersion for a description.
[edit] Speed in solids
In a solid, there is a non-zero stiffness both for volumetric and shear deformations. Hence, in a solid it is possible to generate sound waves with different velocities dependent on the deformation mode.
In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:
where
E is Young's modulus
ρ (rho) is density
Thus in steel the speed of sound is approximately 5100 m·s-1.
In a solid with lateral dimensions much larger than the wavelength, the sound velocity is higher. It is found by replacing Young's modulus with the plane wave modulus, which can be expressed in terms of the Young's modulus and Poisson's ratio as:
[edit] Speed in fluids
In a fluid the only non-zero stiffness is to volumetric deformation (a fluid does not sustain shear forces).
Hence the speed of sound in a fluid is given by
where
K is the bulk modulus of the fluid
The speed of sound in water is of interest to anyone using underwater sound as a tool, whether in a laboratory, a lake or the ocean. Examples are sonar, acoustic communication and acoustical oceanography. See Discovery of Sound in the Sea for other examples of the uses of sound in the ocean (by both man and other animals). In fresh water, sound travels at about 1497 m/s at 25 °C. See Technical Guides - Speed of Sound in Pure Water for an online calculator.
Sound speed as a function of depth at a position north of Hawaii in the Pacific Ocean derived from the 2005 World Ocean Atlas. The SOFAR channel is centered on the minimum in sound speed at ca. 750-m depth.In salt water that is free of air bubbles or suspended sediment, sound travels at about 1500 m/s. The speed of sound in seawater depends on pressure (hence depth), temperature (a change of 1 °C ~ 4 m/s), and salinity (a change of 1‰ ~ 1 m/s), and empirical equations have been derived to accurately calculate sound speed from these variables. Other factors affecting sound speed are minor. For more information see Dushaw et al. (1993).
A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie (1981)
c(T, S, z) = a1 + a2T + a3T2 + a4T3 + a5(S - 35) + a6z + a7z2 + a8T(S - 35) + a9Tz3
where T, S, and z are temperature in degrees Celsius, salinity in parts per thousand and depth in metres, respectively. The constants a1, a2, ..., a9 are:
a1 = 1448.96, a2 = 4.591, a3 = -5.304×10-2, a4 = 2.374×10-4, a5 = 1.340, a6 = 1.630×10-2, a7 = 1.675×10-7, a8 = -1.025×10-2, a9 = -7.139×10-13
with check value 1550.744 m/s for T=25 °C, S=35‰, z=1000 m. This equation is accurate to O(0.2 m/s). See Technical Guides - Speed of Sound in Sea-Water for an online calculator.
Other equations for sound speed in sea water have slightly greater accuracy, but are far more complicated, e.g., that by V. A. Del Grosso (1974) and the Chen-Millero-Li Equation (1994).[1] [2]
[edit] Speed in ideal gases and in air
For a gas, K (the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids) is approximately given by
thus
Where:
γ is the adiabatic index also known as the isentropic expansion factor. It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume(Cp / Cv), and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression.
p is the pressure.
ρ is the density
Using the ideal gas law to replace p with NRT/V, and replacing ρ with NM/V, the equation for an ideal gas becomes:
where
cideal is the speed of sound in an ideal gas.
R (approximately 8.3145 J·mol-1·K-1) is the molar gas constant.[1]
k is the Boltzmann constant
γ (gamma) is the adiabatic index (sometimes assumed 7/5 = 1.400 for diatomic molecules from kinetic theory, assuming from quantum theory a temperature range at which thermal energy is fully partitioned into rotation (rotations are fully excited), but none into vibrational modes. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at 0 degrees Celsius, for air. Gamma is assumed from kinetic theory to be exactly 5/3 = 1.6667 for monoatomic molecules such as noble gases).
T is the absolute temperature in kelvins.
M is the molar mass in kilograms per mole. The mean molar mass for dry air is about .0289645 kg/mole.
m is the mass of a single molecule in kilograms.
This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for cair have been found to vary slightly from experimentally determined values.:[3]
Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic. His result was missing the factor of γ but was otherwise correct.
Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of requires that the gas exist in a temperature range high enough that rotational heat capacity is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insigificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode, have energies too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See the section on gases in heat capacity for a more complete discussion of this phenomenon.
[edit] Temperatures in Celsius
If temperatures in degrees Celsius(°C) are to be used to calculate air speed in the region near 273 kelvins, then Celsius temperature may be used.
For dry air, where (theta) is the temperature in degrees Celsius(°C).
Making the following numerical substitutions: , where is the molar gas constant, , and using the ideal diatomic gas value of
Then:
Using the first two terms of the Taylor expansion:
The derivation includes the two approximate equations which were given in the introduction. For Celsius temperatures which are negative, the second term of the equation right hand side, is negative.
[edit] Tables
In the standard atmosphere:
T0 is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m·s-1 (= 1086.9 ft/s = 1193 km·h-1 = 741.1 mph = 644.0 knots). Values ranging from 331.3-331.6 may be found in reference literature, however.
T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m·s-1 (= 1126.0 ft/s = 1236 km·h-1 = 767.8 mph = 667.2 knots).
T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m·s-1 (= 1135.6 ft/s = 1246 km·h-1 = 774.3 mph = 672.8 knots).
In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere - actual conditions may vary.
Effect of temperature
in °C c in m·s-1 ρ in kg·m-3 Z in N·s·m-3
−10 325.2 1.342 436.1
−5 328.3 1.317 432.0
0 331.3 1.292 428.4
+5 334.3 1.269 424.3
+10 337.3 1.247 420.6
+15 340.3 1.225 416.8
+20 343.2 1.204 413.2
+25 346.1 1.184 409.8
+30 349.0 1.165 406.3
is the temperature in °C
c is the speed of sound in m·s-1
ρ is the density in kg·m-3
Z is the characteristic acoustic impedance in N·s·m-3 (Z=ρ·c)
Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:
Altitude Temperature m·s-1 km·h-1 mph knots
Sea level 15 °C (59 °F) 340 1225 761 661
11 000 m−20 000 m
(Cruising altitude of commercial jets,
and first supersonic flight) -57 °C (-70 °F) 295 1062 660 573
29 000 m (Flight of X-43A) -48 °C (-53 °F) 301 1083 673 585
[edit] Effect of frequency and gas composition
The medium in which a sound wave is travelling does not always respond adiabatically, and as a result the speed of sound can vary with frequency.[4]
The limitations of the concept of speed of sound due to extreme attenuation are also of concern. The attenuation which exists at sea level for high frequencies applies to successively lower frequencies as atmospheric pressure decreases, or as the mean free path increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes.:[3]
The molecular composition of the gas contributes both as the mass (M) of the molecules, and their heat capacities, and so both have an influence on speed of sound. In general, at the same molecular mass, monatomic gases have slightly higher sound speeds (over 9% higher) due to the fact that they have a higher γ (5/3 = 1.67) than diatomics do (7/5 = 1.4). Thus, at the same molecular mass, the sound speed of a monatomic gas goes up by a factor of
= 1.09
This gives the 9 % difference, and would be a typical ratio for sound speeds at room temperature in helium vs. deuterium, each with a molecular weight of 4. Sound travels faster in helium than deuterium because adiabatic compression heats helium more, since the helium molecules can store heat energy from compression only in translation, but not rotation. Thus helium molecules (monatomic molecules) travel faster in a sound wave and transmit sound faster. (Sound generally travels at about 70% of the mean molecular velocity in gases).
Note that in this example we have assumed that temperature is low enough that heat capacities are not influenced by molecular vibration (see heat capacity). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas gives the gas additional ways to store heat which do not affect temperature, and thus do not affect molecular velocity and sound velocity. Thus, the effect of higher temperatures and vibrational heat capacity acts to increase the difference between sound speed in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.
[edit] Mach number
Main article: Mach number.
Mach number, a useful quantity in aerodynamics, is the ratio of an object's speed to the speed of sound in the medium through which it is passing (again, usually air). At altitude, for reasons explained, Mach number is a function of temperature.
Aircraft flight instruments, however, operate using pressure differential to compute Mach number; not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the impact pressure sensed by a Pitot tube is dependent on altitude as well as speed.
Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from the Bernoulli equation for M<1:[5]
where
M is Mach number
qc is impact pressure and
P is static pressure.
The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:
where
M is Mach number
qc is impact pressure measured behind a normal shock
P is static pressure.
As can be seen, M appears on both sides of the equation. The easiest method to solve the supersonic M calculation is to enter both the subsonic and supersonic equations into a computer spread sheet such as Microsoft Excel, OpenOffice.org Calc, or some equivalent program. First determine if M is indeed greater than 1.0 by calculating M from the subsonic equation. If M is greater than 1.0 at that point, then use the value of M from the subsonic equation as the initial condition in the supersonic equation. Then perform a simple iteration of the supersonic equation, each time using the last computed value of M, until M converges to a value--usually in just a few iterations.[5]
[edit] Experimental methods
A range of different methods exist for the measurement of sound in air.
[edit] Single-shot timing methods
The simplest concept is the measurement made using two microphones and a fast recording device such as a digital storage scope. This method uses the following idea.
If a sound source and two microphones are arranged in a straight line, with the sound source at one end, then the following can be measured:
1. The distance between the microphones (x), called microphone basis. 2. The time of arrival between the signals (delay) reaching the different microphones (t)
Then v = x / t
An older method is to create a sound at one end of a field with an object that can be seen to move when it creates the sound. When the observer sees the sound-creating device act they start a stopwatch and when the observer hears the sound they stop their stopwatch. Again using v = x / t you can calculate the speed of sound. A separation of at least 200 m between the two experimental parties is required for good results with this method.
[edit] Other methods
In these methods the time measurement has been replaced by a measurement of the inverse of time (frequency).
Kundt's tube is an example of an experiment which can be used to measure the speed of sound in a small volume. It has the advantage of being able to measure the speed of sound in any gas. This method uses a powder to make the nodes and antinodes visible to the human eye. This is an example of a compact experimental setup.
A tuning fork can be held near the mouth of a long pipe which is dipping into a barrel of water. In this system it is the case that the pipe can be brought to resonance if the length of the air column in the pipe is equal to ({1+2n}λ/4) where n is an integer. As the antinodal point for the pipe at the open end is slightly outside the mouth of the pipe it is best to find two or more points of resonance and then measure half a wavelength between these.
Here it is the case that v = fλ
[edit] Gradients
Normally sound waves spread out in an inverse square law, and rapidly dissipate.
However, in the ocean (the 'deep sound channel' or SOFAR channel), variations in the speed of sound create a layer where the speed of sound is at a minimum and any sound waves generated spread out in a substantially flat layer- refraction keeps the sound constrained to spread out in an inverse law, which carries the sound very much further.
A similar effect occurs in the atmosphere and Project_Mogul was an attempt to detect the sound of nuclear weapons using this principle, and was successfully able to detect a nuclear explosion at a considerable distance.
[edit] References
^ Article Abstract
^ dushaw-jasa-93
^ a b U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.
^ A B Wood, A Textbook of Sound (Bell, London, 1946)
^ a b Olson, Wayne M. (2002). "AFFTC-TIH-99-02, Aircraft Performance Flight Testing." (PDF). Air Force Flight Test Center, Edwards AFB, CA, United States Air Force.
Del Grosso, V. A., 1974. New equation for the speed of sound in natural waters (with comparisons to other equations). J. Acoust. Soc. Am., 56, pp. 1084-1091.
Dushaw, B. D., P. F. Worcester, B. D. Cornuelle, and B. M. Howe, 1993. On equations for the speed of sound in seawater. J. Acoust. Soc. Am., 93, pp. 255-275.
Mackenzie, K. V., 1981. Discussion of sea water sound-speed determinations. J. Acoust. Soc. Am., 70, pp. 801-806.
Applied Physics Laboratory - University of Washington, 1994. APL-UW High-Frequency Ocean Environmental Acoustic Models Handbook. APL-UW TR 9407, pp. I1-I2.
[edit] See also
Sound barrier
SOFAR channel
Underwater acoustics
[edit] External links
Calculation: Speed of sound in air and the temperature
Speed of sound - temperature matters, not air pressure
Properties Of The U.S. Standard Atmosphere 1976
How to measure the speed of sound in a laboratory
Speed of sound in water and water steam as function of pressure & temperature
Teaching resource for 14-16yrs on sound including speed of sound
Technical Guides - Speed of Sound in Pure Water
Technical Guides - Speed of Sound in Sea-Water
Retrieved from "http://en.wikipedia.org/wiki/Speed_of_sound"
Categories: Sound measurements | All articles with unsourced statements | Articles with unsourced statements since February 2007 | Chemical properties | Fluid dynamics | Units of velocity
Paramagnetism
Paramagnetism
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Simple Illustration of a paramagnetic probe made up from miniature magnets.Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility). However, unlike ferromagnets which are also attracted to magnetic fields, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field.
Contents [hide]
1 Introduction
2 Curie's law
3 Paramagnetic materials
3.1 Elements
3.2 Compounds
4 See also
5 References
6 External links
[edit] Introduction
Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments (dipoles), even in the absence of an applied field. This generally occurs due to the presence of unpaired electrons in the atomic/molecular electron orbitals. In pure paramagnetism, the dipoles do not interact with one another and are randomly oriented in the absence of an external field due to thermal agitation, resulting in zero net magnetic moment. When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field. In the classical description, this alignment can be understood to occur due to a torque being provided on the magnetic moments by an applied field, which tries to align the dipoles parallel to the applied field. However, the truer origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum.
If there is sufficient energy exchange between neighbouring dipoles they will interact, and may spontaneously align or anti-align and form magnetic domains, resulting in ferromagnetism (permanent magnets) or antiferromagnetism, respectively. Paramagnetic behaviour can also be observed in ferromagnetic materials that are above their Curie temperature, and in antiferromagnets above their Néel temperature.
In general paramagnetic effects are quite small: the magnetic susceptibility is of the order of 10−3 to 10−5 for most paramagnets, but may be as high as 10-1 for synthetic paramagnets such as ferrofluids.
[edit] Curie's law
For low levels of magnetisation, the magnetisation of paramagnets is approximated by Curie's law:
where
M is the resulting magnetization
B is the magnetic flux density of the applied field, measured in teslas
T is absolute temperature, measured in kelvins
C is a material-specific Curie constant
This law indicates that the susceptibiliy of paramagnetic materials is inversely proportional to their temperature. However, Curie's law is only valid under conditions of low magnetisation, since it does not consider the saturation of magnetisation that occurs when the atomic dipoles are all aligned in parallel (after everything is aligned, increasing the external field will not increase the total magnetisation since there can be no further alignment).
[edit] Paramagnetic materials
[edit] Elements
Elements can be paramagnetic if they have unpaired electrons.
The following are some examples of paramagnetic elements:
Aluminium Al [13] (metal) — Al is the preferred paramagnetic material in theoretical designs of lunar mass driver applications using regolith as an ore.
Barium Ba [56] (metal)
Calcium Ca [20] (metal) [Ar]4s2 — diamagnetic
Oxygen. O [8] (non-metal)
Platinum Pt [78] (metal)
Sodium Na [11] (metal)
Strontium Sr [38] (metal)
Uranium U [92] (metal)
Magnesium Mg [12] (metal) 1s2 2s2 2p6 3s2 — diamagnetic
Technetium Tc [43] (artificial)
Dysprosium Dy [66] (metal) — ferromagnetic
[edit] Compounds
Many salts of the d and f transitional metal group show paramagnetic behaviour.
Examples are:
Copper sulphate
Dysprosium oxide
Ferric chloride
Ferric oxide
Holmium oxide
Manganese chloride
Some simple molecules contain unpaired electrons and are thus paramagnetic. The most common is the diatomic oxygen molecule.
[edit] See also
Pierre Curie
Ferromagnetism
Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass
[edit] References
Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).
Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
John David Jackson, Classical Electrodynamics (Wiley: New York, 1999).
[edit] External links
Classification of Magnetic Materials by Applied Alloy Chemistry Group at University of Birmingham.
Retrieved from "http://en.wikipedia.org/wiki/Paramagnetism"
Categories: Electric and magnetic fields in matter | Magnetism | Fundamental physics concepts
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Simple Illustration of a paramagnetic probe made up from miniature magnets.Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility). However, unlike ferromagnets which are also attracted to magnetic fields, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field.
Contents [hide]
1 Introduction
2 Curie's law
3 Paramagnetic materials
3.1 Elements
3.2 Compounds
4 See also
5 References
6 External links
[edit] Introduction
Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments (dipoles), even in the absence of an applied field. This generally occurs due to the presence of unpaired electrons in the atomic/molecular electron orbitals. In pure paramagnetism, the dipoles do not interact with one another and are randomly oriented in the absence of an external field due to thermal agitation, resulting in zero net magnetic moment. When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field. In the classical description, this alignment can be understood to occur due to a torque being provided on the magnetic moments by an applied field, which tries to align the dipoles parallel to the applied field. However, the truer origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum.
If there is sufficient energy exchange between neighbouring dipoles they will interact, and may spontaneously align or anti-align and form magnetic domains, resulting in ferromagnetism (permanent magnets) or antiferromagnetism, respectively. Paramagnetic behaviour can also be observed in ferromagnetic materials that are above their Curie temperature, and in antiferromagnets above their Néel temperature.
In general paramagnetic effects are quite small: the magnetic susceptibility is of the order of 10−3 to 10−5 for most paramagnets, but may be as high as 10-1 for synthetic paramagnets such as ferrofluids.
[edit] Curie's law
For low levels of magnetisation, the magnetisation of paramagnets is approximated by Curie's law:
where
M is the resulting magnetization
B is the magnetic flux density of the applied field, measured in teslas
T is absolute temperature, measured in kelvins
C is a material-specific Curie constant
This law indicates that the susceptibiliy of paramagnetic materials is inversely proportional to their temperature. However, Curie's law is only valid under conditions of low magnetisation, since it does not consider the saturation of magnetisation that occurs when the atomic dipoles are all aligned in parallel (after everything is aligned, increasing the external field will not increase the total magnetisation since there can be no further alignment).
[edit] Paramagnetic materials
[edit] Elements
Elements can be paramagnetic if they have unpaired electrons.
The following are some examples of paramagnetic elements:
Aluminium Al [13] (metal) — Al is the preferred paramagnetic material in theoretical designs of lunar mass driver applications using regolith as an ore.
Barium Ba [56] (metal)
Calcium Ca [20] (metal) [Ar]4s2 — diamagnetic
Oxygen. O [8] (non-metal)
Platinum Pt [78] (metal)
Sodium Na [11] (metal)
Strontium Sr [38] (metal)
Uranium U [92] (metal)
Magnesium Mg [12] (metal) 1s2 2s2 2p6 3s2 — diamagnetic
Technetium Tc [43] (artificial)
Dysprosium Dy [66] (metal) — ferromagnetic
[edit] Compounds
Many salts of the d and f transitional metal group show paramagnetic behaviour.
Examples are:
Copper sulphate
Dysprosium oxide
Ferric chloride
Ferric oxide
Holmium oxide
Manganese chloride
Some simple molecules contain unpaired electrons and are thus paramagnetic. The most common is the diatomic oxygen molecule.
[edit] See also
Pierre Curie
Ferromagnetism
Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass
[edit] References
Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).
Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
John David Jackson, Classical Electrodynamics (Wiley: New York, 1999).
[edit] External links
Classification of Magnetic Materials by Applied Alloy Chemistry Group at University of Birmingham.
Retrieved from "http://en.wikipedia.org/wiki/Paramagnetism"
Categories: Electric and magnetic fields in matter | Magnetism | Fundamental physics concepts
Magnetism
Magnetism
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other senses of this word, see magnetism (disambiguation) or Electromagnetic induction.
Magnetic lines of force of a bar magnet shown by iron filings on paperIn physics, magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties are nickel, iron and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field.
Contents [hide]
1 History
2 Physics of magnetism
2.1 Magnetism, electricity, and special relativity
2.2 Magnetic fields and forces
2.3 Magnetic dipoles
2.4 Magnetic monopoles
2.5 Atomic magnetic dipoles
3 Types of magnets
3.1 Electromagnets
3.2 Permanent and temporary magnets
3.2.1 Magnetic metallic elements
3.2.2 Composites
3.2.2.1 Ceramic or ferrite
3.2.2.2 Alnico
3.2.2.3 Injection molded
3.2.2.4 Flexible
3.2.3 Rare earth magnets
3.2.3.1 Samarium-cobalt
3.2.3.2 Neodymium-iron-boron (NIB)
3.2.4 Single-molecule magnets (SMMs) and single-chain magnets (SCMs)
3.2.5 Nano-structured magnets
4 Units of electromagnetism
4.1 SI units related to magnetism
4.2 Other units
5 See also
6 References
7 External links
[edit] History
Aristotle attributes the first scientific theory on magnetism to Thales, who lived from about 625 BC to about 545 BC. [1] In China, the earliest literary reference to magnetism lies in a 4th century BC book called Book of the Devil Valley Master (鬼谷子): "The lodestone makes iron come or it attracts it."[1] The earliest mention of the attraction of a needle appears in a work composed between 20 and 100 AD (Louen-heng): "A lodestone attracts a needle."[2] The ancient Chinese scientist Shen Kuo (1031-1095) was the first person to write of the magnetic needle compass and improved the accuracy of navigation by employing the astronomical concept of true north (Dream Pool Essays, 1088 AD), and by the 12th century the Chinese were known to use the lodestone compass for navigation. Alexander Neckham, by 1187, was the first in Europe to describe the compass and its use for navigation.
An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Oersted, a professor at the University of Copenhagen, discovered more or less by accident that an electric current could influence a compass needle. This landmark experiment is known as Oersted's Experiment. Several other experiments followed, with André-Marie Ampère, Carl Friedrich Gauss, Michael Faraday, and others finding further links between magnetism and electricity. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism. In 1905, Einstein used these laws in motivating his theory of special relativity[3], in the process showing that electricity and magnetism are fundamentally interlinked and inseparable.
Electromagnetism has continued to develop into the twentieth century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model.
[edit] Physics of magnetism
[edit] Magnetism, electricity, and special relativity
As a consequence of Einstein's theory of special relativity, electricity and magnetism are understood to be fundamentally interlinked. Both magnetism without electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account the resulting theory (electromagnetism) is fully consistent with special relativity[4][5]. In particular, a phenomenon that appears purely electric to one observer may be purely magnetic to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism (analogously to how special relativity "mixes" space and time into spacetime).
[edit] Magnetic fields and forces
Main article: magnetic field
The phenomenon of magnetism is "mediated" by the magnetic field -- i.e., an electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.
To an excellent approximation (but ignoring some quantum effects---see quantum electrodynamics), Maxwell's equations (which simplify to the Biot-Savart law in the case of steady currents) describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically charged particles are in motion---for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum effects, i.e. from quantum-mechanical spin.
The same situations which create magnetic fields (charge moving in a current or in an atom, and intrinsic magnetic dipoles) are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.
When a charged particle moves through a magnetic field B, it feels a force F given by the cross product:
where is the electric charge of the particle, is the velocity vector of the particle, and is the magnetic field. Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is
where is the angle between the and vectors.
One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration (with the middle finger crossing under the index finger), the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right hand rule.
[edit] Magnetic dipoles
Main article: magnetic dipole
A very common type of magnetic field seen in nature is a dipoles, having a "South pole" and a "North pole"; terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the 'north' magnetic pole of the earth must be magnetically 'south'.
A magnetic field contains energy, and physical systems stabilize into the configuration with the lowest energy. Therefore, when placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby canceling the net field strength as much as possible and lowering the energy stored in that field to a minimum. For instance, two identical bar magnets placed side-to-side normally line up North to South, resulting in a much smaller net magnetic field, and resist any attempts to reorient them to point in the same direction. The energy required to reorient them in that configuration is then stored in the resulting magnetic field, which is double the strength of the field of each individual magnet. (This is, of course, why a magnet used as a compass interacts with the Earth's magnetic field to indicate North and South).
An alternative, equivalent formulation, which is often easier to apply but perhaps offers less insight, is that a magnetic dipole in a magnetic field experiences a torque and a force which can be expressed in terms of the field and the strength of the dipole (i.e., its magnetic dipole moment). For these equations, see magnetic dipole.
[edit] Magnetic monopoles
Main article: Magnetic monopole
Regular bar magnets have two "poles": north and south. Like poles will repel each other, and unlike poles will attract. These poles cannot be separated: when a bar magnet is cut in half across the axis joining those poles, each of the resulting pieces are normal (albeit smaller) bar magnets, each with its own north pole and south pole.
A monopole (if they exist) would be an isolated north pole, not attached to a south pole, or vice versa. It would have "magnetic charge" analogous to electric charge. A bar magnet cannot be broken into monopoles because its magnetism (see ferromagnetism is ultimately due to circulating current (electrons orbiting nuclei) and intrinsic spin dipoles, both of which are at root dipolar in nature. Indeed, despite systematic searches since 1931, as of 2006, magnetic monopoles have never been observed, and could very well not exist.[6]
Nevertheless, some theoretical physics models predict the existence of magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge---that is, why the observed elementary particles carry charges that are multiples of the charge of the electron. (Since then, other explanations of the quantization of electric charge, not involving monopoles, have been formulated; see spontaneous symmetry breaking and electroweak theory.)
Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). Using these models to estimate the number of monopoles created in the big bang, the initial results that contradicted cosmological observations---the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.[7]
[edit] Atomic magnetic dipoles
The physical cause of the magnetism of objects, as distinct from electrical currents, is the atomic magnetic dipole. Magnetic dipoles, or magnetic moments, result on the atomic scale from the two kinds of movement of electrons. The first is the orbital motion of the electron around the nucleus; this motion can be considered as a current loop, resulting in an orbital dipole magnetic moment. The second, much stronger, source of electronic magnetic moment is due to a quantum mechanical property called the spin dipole magnetic moment (although current quantum mechanical theory states that electrons neither physically spin, nor orbit the nucleus).
Dipole moment of a bar magnet.The overall magnetic moment of the atom is the net sum of all of the magnetic moments of the individual electrons. Because of the tendency of magnetic dipoles to oppose each other to reduce the net energy, in an atom the opposing magnetic moments of some pairs of electrons cancel each other, both in orbital motion and in spin magnetic moments. Thus, in the case of an atom with a completely filled electron shell or subshell, the magnetic moments normally completely cancel each other out and only atoms with partially-filled electron shells have a magnetic moment, whose strength depends on the number of unpaired electrons.
The differences in configuration of the electrons in various elements thus determine the nature and magnitude of the atomic magnetic moments, which in turn determine the differing magnetic properties of various materials. Several forms of magnetic behavior have been observed in different materials, including:
Diamagnetism
Paramagnetism
Molecular magnet
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
Metamagnetism
Spin glass
Superparamagnetism
Magnetars, stars with extremely powerful magnetic fields, are also known to exist.
[edit] Types of magnets
[edit] Electromagnets
Since all magnetism is caused by moving charges, all magnets are in fact electromagnets. However, we usually refer to magnets made from electrical wire wound around a magnetic material, such as iron as electromagnets. This form of magnet is useful in cases where a magnet must be switched on or off; for instance, large cranes to lift junked automobiles.
For the case of electric current moving through a wire, the resulting field is directed according to the "right hand rule." If the right hand is used as a model, and the thumb of the right hand points along the wire from positive towards the negative side ("conventional current", the reverse of the direction of actual movement of electrons), then the magnetic field will wrap around the wire in the direction indicated by the fingers of the right hand. As can be seen geometrically, if a loop or helix of wire is formed such that the current is traveling in a circle, then all of the field lines in the center of the loop are directed in the same direction, resulting in a magnetic dipole whose strength depends on the current around the loop, or the current in the helix multiplied by the number of turns of wire. In the case of such a loop, if the fingers of the right hand are directed in the direction of conventional current flow (i.e., positive to negative, the opposite direction to the actual flow of electrons), the thumb will point in the direction corresponding to the North pole of the dipole.
[edit] Permanent and temporary magnets
A permanent magnet retains its magnetism without an external magnetic field whereas a temporary magnet is only magnetic while within another magnetic field. Inducing magnetism in steel results in a permanent magnet but iron loses its magnetism when the inducing field is withdrawn. A temporary magnet such as iron is thus a good material for electromagnets. Magnets are made by stroking with another magnet, tapping while fixed in a magnetic field or placing inside a solenoid coil supplied with a direct current. A permanent magnet may be de-magnetised by subjecting it to heating or sharp blows or placing it inside a solenoid supplied with a reducing alternating current.
[edit] Magnetic metallic elements
Many materials have unpaired electron spins, and the majority of these materials are paramagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as "magnetic"). Due to the way their regular crystalline atomic structure causes their spins to interact, some metals are (ferro)magnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring (ferro)magnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various manmade products, all based, however, on naturally magnetic elements.
[edit] Composites
[edit] Ceramic or ferrite
Ceramic, or ferrite, magnets are made of a sintered composite of powdered iron oxide and barium/strontium carbonate ceramic. Due to the low cost of the materials and manufacturing methods, inexpensive magnets (or nonmagnetized ferromagnetic cores, for use in electronic component such as radio antennas, for example) of various shapes can be easily mass produced. The resulting magnets are noncorroding, but brittle and must be treated like other ceramics.
[edit] Alnico
Alnico magnets are made by casting or sintering a combination of aluminium, nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as a metal.
[edit] Injection molded
Injection molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties.
[edit] Flexible
Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.
[edit] Rare earth magnets
Main article: Rare-earth magnet
'Rare earth' (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons.) The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore these elements are used in compact high-strength magnets where their higher price is not a concern.
[edit] Samarium-cobalt
Samarium-cobalt magnets are highly resistant to oxidation, with higher magnetic strength and temperature resistance than alnico or ceramic materials. Sintered samarium-cobalt magnets are brittle and prone to chipping and cracking and may fracture when subjected to thermal shock.
[edit] Neodymium-iron-boron (NIB)
Neodymium magnets, more formally referred to as neodymium-iron-boron (NdFeB) magnets, have the highest magnetic field strength, but are inferior to samarium cobalt in resistance to oxidation and temperature. This type of magnet has traditionally been expensive, due to both the cost of raw materials and licensing of the patents involved. This high cost limited their use to applications where such high strengths from a compact magnet are critical. Use of protective surface treatments such as gold, nickel, zinc and tin plating and epoxy resin coating can provide corrosion protection where required. Beginning in the 1980s, NIB magnets have increasingly become less expensive and more popular in other applications such as controversial children's magnetic building toys. Even tiny neodymium magnets are very powerful and have important safety considerations.[8]
[edit] Single-molecule magnets (SMMs) and single-chain magnets (SCMs)
In the 1990s it was discovered that certain molecules containing paramagnetic metal ions are capable of storing a magnetic moment at very low temperatures. These are very different from conventional magnets that store information at a "domain" level and theoretically could provide a far denser storage medium than conventional magnets. In this direction research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:
a large ground state spin value (S), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres.
a negative value of the anisotropy of the zero field splitting (D)
Most SMM's contain manganese, but can also be found with vanadium, iron, nickel and cobalt clusters. More recently it has been found that some chain systems can also display a magnetization which persists for long times at relatively higher temperatures. These systems have been called single-chain magnets.
[edit] Nano-structured magnets
Some nano-structured materials exhibit energy waves called magnons that coalesce into a common ground state in the manner of a Bose-Einstein condensate.
See results from NIST published April 2005,[9] or[10]
[edit] Units of electromagnetism
[edit] SI units related to magnetism
editSI electromagnetism units
Symbol [citation needed] Name of Quantity Derived Units Unit Base Units
I Magnitude of current ampere (SI base unit) A A = W/V = C/s
q Electric charge, Quantity of electricity coulomb C A·s
V Potential difference or Electromotive force volt V J/C = kg·m2·s−3·A−1
R, Z, X Resistance, Impedance, Reactance ohm Ω V/A = kg·m2·s−3·A−2
ρ Resistivity ohm metre Ω·m kg·m3·s−3·A−2
P Power, Electrical watt W V·A = kg·m2·s−3
C Capacitance farad F C/V = kg−1·m−2·A2·s4
Elastance reciprocal farad F−1 V/C = kg·m2·A−2·s−4
ε Permittivity farad per metre F/m kg−1·m−3·A2·s4
χe Electric susceptibility (dimensionless) - -
G, Y, B Conductance, Admittance, Susceptance siemens S Ω−1 = kg−1·m−2·s3·A2
σ Conductivity siemens per metre S/m kg−1·m−3·s3·A2
B Magnetic flux density, Magnetic induction tesla T Wb/m2 = kg·s−2·A−1 = N·A−1·m−1
Φm Magnetic flux weber Wb V·s = kg·m2·s−2·A−1
H Magnetic field strength,Magnetic field intensity ampere per metre A/m A·m−1
Reluctance ampere-turn per weber A/Wb kg−1·m−2·s2·A2
L Inductance henry H Wb/A = V·s/A = kg·m2·s−2·A−2
μ Permeability henry per metre H/m kg·m·s−2·A−2
χm Magnetic susceptibility (dimensionless)
Π and Π * Electric and Magnetic hertzian vector potentials n/a n/a
[edit] Other units
gauss-The gauss, abbreviated as G, is the cgs unit of magnetic flux density or magnetic induction (B).
oersted-The oersted is the CGS unit of magnetic field strength.
maxwell-is the CGS unit for the magnetic flux.
μo -common symbol for the permeability of free space (4πx10-7 N/(ampere-turn)2).
[edit] See also
Wikibooks has more about this subject:
School science how-toElectrostatics
Magnetostatics
Electromagnetism
Plastic magnet
Magnet
Magnetic field
Magnetic bearing
Magnet therapy
Magnetic circuit
Michael Faraday
Micromagnetism
James Clerk Maxwell
Coercivity
Spin wave
Spontaneous magnetization
Sensor
Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass
[edit] References
Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press. ISBN 0-12-269951-3.
^ Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” Isis, Vol. 45, No. 2. (Jul., 1954), p.175
^ Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” Isis, Vol. 45, No. 2. (Jul., 1954), p.176
^ A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905. http://www.fourmilab.ch/etexts/einstein/specrel/www/.
^ A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905. http://www.fourmilab.ch/etexts/einstein/specrel/www/.
^ Griffiths, David J. (1998). Introduction to Electrodynamics, 3rd ed., Prentice Hall. ISBN 0-13-805326-X. , chapter 12
^ Milton mentions some inconclusive events (p.60) and still concludes that "no evidence at all of magnetic monopoles has survived" (p.3). Milton, Kimball A. (June 2006). "Theoretical and experimental status of magnetic monopoles". Reports on Progress in Physics 69 (6): 1637-1711. DOI:10.1088/0034-4885/69/6/R02. .
^ Guth, Alan (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus. ISBN 0-201-32840-2. .
^ Magnet Man, Magnet Basics - Safety Considerations accessed 6 October 2006.
^ Nanomagnets Bend The Rules. Retrieved on November 14, 2005.
^ Nanomagnets bend the rules. Retrieved on November 14, 2005.
[edit] External links
Look up Magnetism in
Wiktionary, the free dictionary.Electromagnetism - a chapter from an online textbook
Magnetic Force and Field on Project PHYSNET
On the Magnet, 1600 First scientific book on magnetism by the father of electrical engineering. Full English text, full text search.
Electromagnetism
Electricity · Magnetism
Electrostatics
Electric charge
Coulomb's law
Electric field
Gauss's law
Electric potential
Electric dipole moment
Magnetostatics
Ampère's Circuital law
Magnetic field
Magnetic flux
Biot-Savart law
Magnetic dipole moment
Electrodynamics
Electrical current
Lorentz force law
Electromotive force
(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
(EMF) Electromagnetic field
(EM) Electromagnetic radiation
Electrical Network
Electrical conduction
Electrical resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
Tensors in Relativity
Electromagnetic tensor
Electromagnetic stress-energy tensor
This box: view • talk • edit
Retrieved from "http://en.wikipedia.org/wiki/Magnetism"
Categories: All articles with unsourced statements | Articles with unsourced statements since February 2007 | Electric and magnetic fields in matter | Magnetism
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other senses of this word, see magnetism (disambiguation) or Electromagnetic induction.
Magnetic lines of force of a bar magnet shown by iron filings on paperIn physics, magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties are nickel, iron and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field.
Contents [hide]
1 History
2 Physics of magnetism
2.1 Magnetism, electricity, and special relativity
2.2 Magnetic fields and forces
2.3 Magnetic dipoles
2.4 Magnetic monopoles
2.5 Atomic magnetic dipoles
3 Types of magnets
3.1 Electromagnets
3.2 Permanent and temporary magnets
3.2.1 Magnetic metallic elements
3.2.2 Composites
3.2.2.1 Ceramic or ferrite
3.2.2.2 Alnico
3.2.2.3 Injection molded
3.2.2.4 Flexible
3.2.3 Rare earth magnets
3.2.3.1 Samarium-cobalt
3.2.3.2 Neodymium-iron-boron (NIB)
3.2.4 Single-molecule magnets (SMMs) and single-chain magnets (SCMs)
3.2.5 Nano-structured magnets
4 Units of electromagnetism
4.1 SI units related to magnetism
4.2 Other units
5 See also
6 References
7 External links
[edit] History
Aristotle attributes the first scientific theory on magnetism to Thales, who lived from about 625 BC to about 545 BC. [1] In China, the earliest literary reference to magnetism lies in a 4th century BC book called Book of the Devil Valley Master (鬼谷子): "The lodestone makes iron come or it attracts it."[1] The earliest mention of the attraction of a needle appears in a work composed between 20 and 100 AD (Louen-heng): "A lodestone attracts a needle."[2] The ancient Chinese scientist Shen Kuo (1031-1095) was the first person to write of the magnetic needle compass and improved the accuracy of navigation by employing the astronomical concept of true north (Dream Pool Essays, 1088 AD), and by the 12th century the Chinese were known to use the lodestone compass for navigation. Alexander Neckham, by 1187, was the first in Europe to describe the compass and its use for navigation.
An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Oersted, a professor at the University of Copenhagen, discovered more or less by accident that an electric current could influence a compass needle. This landmark experiment is known as Oersted's Experiment. Several other experiments followed, with André-Marie Ampère, Carl Friedrich Gauss, Michael Faraday, and others finding further links between magnetism and electricity. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism. In 1905, Einstein used these laws in motivating his theory of special relativity[3], in the process showing that electricity and magnetism are fundamentally interlinked and inseparable.
Electromagnetism has continued to develop into the twentieth century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model.
[edit] Physics of magnetism
[edit] Magnetism, electricity, and special relativity
As a consequence of Einstein's theory of special relativity, electricity and magnetism are understood to be fundamentally interlinked. Both magnetism without electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account the resulting theory (electromagnetism) is fully consistent with special relativity[4][5]. In particular, a phenomenon that appears purely electric to one observer may be purely magnetic to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism (analogously to how special relativity "mixes" space and time into spacetime).
[edit] Magnetic fields and forces
Main article: magnetic field
The phenomenon of magnetism is "mediated" by the magnetic field -- i.e., an electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.
To an excellent approximation (but ignoring some quantum effects---see quantum electrodynamics), Maxwell's equations (which simplify to the Biot-Savart law in the case of steady currents) describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically charged particles are in motion---for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum effects, i.e. from quantum-mechanical spin.
The same situations which create magnetic fields (charge moving in a current or in an atom, and intrinsic magnetic dipoles) are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.
When a charged particle moves through a magnetic field B, it feels a force F given by the cross product:
where is the electric charge of the particle, is the velocity vector of the particle, and is the magnetic field. Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is
where is the angle between the and vectors.
One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration (with the middle finger crossing under the index finger), the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right hand rule.
[edit] Magnetic dipoles
Main article: magnetic dipole
A very common type of magnetic field seen in nature is a dipoles, having a "South pole" and a "North pole"; terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the 'north' magnetic pole of the earth must be magnetically 'south'.
A magnetic field contains energy, and physical systems stabilize into the configuration with the lowest energy. Therefore, when placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby canceling the net field strength as much as possible and lowering the energy stored in that field to a minimum. For instance, two identical bar magnets placed side-to-side normally line up North to South, resulting in a much smaller net magnetic field, and resist any attempts to reorient them to point in the same direction. The energy required to reorient them in that configuration is then stored in the resulting magnetic field, which is double the strength of the field of each individual magnet. (This is, of course, why a magnet used as a compass interacts with the Earth's magnetic field to indicate North and South).
An alternative, equivalent formulation, which is often easier to apply but perhaps offers less insight, is that a magnetic dipole in a magnetic field experiences a torque and a force which can be expressed in terms of the field and the strength of the dipole (i.e., its magnetic dipole moment). For these equations, see magnetic dipole.
[edit] Magnetic monopoles
Main article: Magnetic monopole
Regular bar magnets have two "poles": north and south. Like poles will repel each other, and unlike poles will attract. These poles cannot be separated: when a bar magnet is cut in half across the axis joining those poles, each of the resulting pieces are normal (albeit smaller) bar magnets, each with its own north pole and south pole.
A monopole (if they exist) would be an isolated north pole, not attached to a south pole, or vice versa. It would have "magnetic charge" analogous to electric charge. A bar magnet cannot be broken into monopoles because its magnetism (see ferromagnetism is ultimately due to circulating current (electrons orbiting nuclei) and intrinsic spin dipoles, both of which are at root dipolar in nature. Indeed, despite systematic searches since 1931, as of 2006, magnetic monopoles have never been observed, and could very well not exist.[6]
Nevertheless, some theoretical physics models predict the existence of magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge---that is, why the observed elementary particles carry charges that are multiples of the charge of the electron. (Since then, other explanations of the quantization of electric charge, not involving monopoles, have been formulated; see spontaneous symmetry breaking and electroweak theory.)
Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). Using these models to estimate the number of monopoles created in the big bang, the initial results that contradicted cosmological observations---the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.[7]
[edit] Atomic magnetic dipoles
The physical cause of the magnetism of objects, as distinct from electrical currents, is the atomic magnetic dipole. Magnetic dipoles, or magnetic moments, result on the atomic scale from the two kinds of movement of electrons. The first is the orbital motion of the electron around the nucleus; this motion can be considered as a current loop, resulting in an orbital dipole magnetic moment. The second, much stronger, source of electronic magnetic moment is due to a quantum mechanical property called the spin dipole magnetic moment (although current quantum mechanical theory states that electrons neither physically spin, nor orbit the nucleus).
Dipole moment of a bar magnet.The overall magnetic moment of the atom is the net sum of all of the magnetic moments of the individual electrons. Because of the tendency of magnetic dipoles to oppose each other to reduce the net energy, in an atom the opposing magnetic moments of some pairs of electrons cancel each other, both in orbital motion and in spin magnetic moments. Thus, in the case of an atom with a completely filled electron shell or subshell, the magnetic moments normally completely cancel each other out and only atoms with partially-filled electron shells have a magnetic moment, whose strength depends on the number of unpaired electrons.
The differences in configuration of the electrons in various elements thus determine the nature and magnitude of the atomic magnetic moments, which in turn determine the differing magnetic properties of various materials. Several forms of magnetic behavior have been observed in different materials, including:
Diamagnetism
Paramagnetism
Molecular magnet
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
Metamagnetism
Spin glass
Superparamagnetism
Magnetars, stars with extremely powerful magnetic fields, are also known to exist.
[edit] Types of magnets
[edit] Electromagnets
Since all magnetism is caused by moving charges, all magnets are in fact electromagnets. However, we usually refer to magnets made from electrical wire wound around a magnetic material, such as iron as electromagnets. This form of magnet is useful in cases where a magnet must be switched on or off; for instance, large cranes to lift junked automobiles.
For the case of electric current moving through a wire, the resulting field is directed according to the "right hand rule." If the right hand is used as a model, and the thumb of the right hand points along the wire from positive towards the negative side ("conventional current", the reverse of the direction of actual movement of electrons), then the magnetic field will wrap around the wire in the direction indicated by the fingers of the right hand. As can be seen geometrically, if a loop or helix of wire is formed such that the current is traveling in a circle, then all of the field lines in the center of the loop are directed in the same direction, resulting in a magnetic dipole whose strength depends on the current around the loop, or the current in the helix multiplied by the number of turns of wire. In the case of such a loop, if the fingers of the right hand are directed in the direction of conventional current flow (i.e., positive to negative, the opposite direction to the actual flow of electrons), the thumb will point in the direction corresponding to the North pole of the dipole.
[edit] Permanent and temporary magnets
A permanent magnet retains its magnetism without an external magnetic field whereas a temporary magnet is only magnetic while within another magnetic field. Inducing magnetism in steel results in a permanent magnet but iron loses its magnetism when the inducing field is withdrawn. A temporary magnet such as iron is thus a good material for electromagnets. Magnets are made by stroking with another magnet, tapping while fixed in a magnetic field or placing inside a solenoid coil supplied with a direct current. A permanent magnet may be de-magnetised by subjecting it to heating or sharp blows or placing it inside a solenoid supplied with a reducing alternating current.
[edit] Magnetic metallic elements
Many materials have unpaired electron spins, and the majority of these materials are paramagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as "magnetic"). Due to the way their regular crystalline atomic structure causes their spins to interact, some metals are (ferro)magnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring (ferro)magnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various manmade products, all based, however, on naturally magnetic elements.
[edit] Composites
[edit] Ceramic or ferrite
Ceramic, or ferrite, magnets are made of a sintered composite of powdered iron oxide and barium/strontium carbonate ceramic. Due to the low cost of the materials and manufacturing methods, inexpensive magnets (or nonmagnetized ferromagnetic cores, for use in electronic component such as radio antennas, for example) of various shapes can be easily mass produced. The resulting magnets are noncorroding, but brittle and must be treated like other ceramics.
[edit] Alnico
Alnico magnets are made by casting or sintering a combination of aluminium, nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as a metal.
[edit] Injection molded
Injection molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties.
[edit] Flexible
Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.
[edit] Rare earth magnets
Main article: Rare-earth magnet
'Rare earth' (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons.) The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore these elements are used in compact high-strength magnets where their higher price is not a concern.
[edit] Samarium-cobalt
Samarium-cobalt magnets are highly resistant to oxidation, with higher magnetic strength and temperature resistance than alnico or ceramic materials. Sintered samarium-cobalt magnets are brittle and prone to chipping and cracking and may fracture when subjected to thermal shock.
[edit] Neodymium-iron-boron (NIB)
Neodymium magnets, more formally referred to as neodymium-iron-boron (NdFeB) magnets, have the highest magnetic field strength, but are inferior to samarium cobalt in resistance to oxidation and temperature. This type of magnet has traditionally been expensive, due to both the cost of raw materials and licensing of the patents involved. This high cost limited their use to applications where such high strengths from a compact magnet are critical. Use of protective surface treatments such as gold, nickel, zinc and tin plating and epoxy resin coating can provide corrosion protection where required. Beginning in the 1980s, NIB magnets have increasingly become less expensive and more popular in other applications such as controversial children's magnetic building toys. Even tiny neodymium magnets are very powerful and have important safety considerations.[8]
[edit] Single-molecule magnets (SMMs) and single-chain magnets (SCMs)
In the 1990s it was discovered that certain molecules containing paramagnetic metal ions are capable of storing a magnetic moment at very low temperatures. These are very different from conventional magnets that store information at a "domain" level and theoretically could provide a far denser storage medium than conventional magnets. In this direction research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:
a large ground state spin value (S), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres.
a negative value of the anisotropy of the zero field splitting (D)
Most SMM's contain manganese, but can also be found with vanadium, iron, nickel and cobalt clusters. More recently it has been found that some chain systems can also display a magnetization which persists for long times at relatively higher temperatures. These systems have been called single-chain magnets.
[edit] Nano-structured magnets
Some nano-structured materials exhibit energy waves called magnons that coalesce into a common ground state in the manner of a Bose-Einstein condensate.
See results from NIST published April 2005,[9] or[10]
[edit] Units of electromagnetism
[edit] SI units related to magnetism
editSI electromagnetism units
Symbol [citation needed] Name of Quantity Derived Units Unit Base Units
I Magnitude of current ampere (SI base unit) A A = W/V = C/s
q Electric charge, Quantity of electricity coulomb C A·s
V Potential difference or Electromotive force volt V J/C = kg·m2·s−3·A−1
R, Z, X Resistance, Impedance, Reactance ohm Ω V/A = kg·m2·s−3·A−2
ρ Resistivity ohm metre Ω·m kg·m3·s−3·A−2
P Power, Electrical watt W V·A = kg·m2·s−3
C Capacitance farad F C/V = kg−1·m−2·A2·s4
Elastance reciprocal farad F−1 V/C = kg·m2·A−2·s−4
ε Permittivity farad per metre F/m kg−1·m−3·A2·s4
χe Electric susceptibility (dimensionless) - -
G, Y, B Conductance, Admittance, Susceptance siemens S Ω−1 = kg−1·m−2·s3·A2
σ Conductivity siemens per metre S/m kg−1·m−3·s3·A2
B Magnetic flux density, Magnetic induction tesla T Wb/m2 = kg·s−2·A−1 = N·A−1·m−1
Φm Magnetic flux weber Wb V·s = kg·m2·s−2·A−1
H Magnetic field strength,Magnetic field intensity ampere per metre A/m A·m−1
Reluctance ampere-turn per weber A/Wb kg−1·m−2·s2·A2
L Inductance henry H Wb/A = V·s/A = kg·m2·s−2·A−2
μ Permeability henry per metre H/m kg·m·s−2·A−2
χm Magnetic susceptibility (dimensionless)
Π and Π * Electric and Magnetic hertzian vector potentials n/a n/a
[edit] Other units
gauss-The gauss, abbreviated as G, is the cgs unit of magnetic flux density or magnetic induction (B).
oersted-The oersted is the CGS unit of magnetic field strength.
maxwell-is the CGS unit for the magnetic flux.
μo -common symbol for the permeability of free space (4πx10-7 N/(ampere-turn)2).
[edit] See also
Wikibooks has more about this subject:
School science how-toElectrostatics
Magnetostatics
Electromagnetism
Plastic magnet
Magnet
Magnetic field
Magnetic bearing
Magnet therapy
Magnetic circuit
Michael Faraday
Micromagnetism
James Clerk Maxwell
Coercivity
Spin wave
Spontaneous magnetization
Sensor
Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass
[edit] References
Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press. ISBN 0-12-269951-3.
^ Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” Isis, Vol. 45, No. 2. (Jul., 1954), p.175
^ Li Shu-hua, “Origine de la Boussole 11. Aimant et Boussole,” Isis, Vol. 45, No. 2. (Jul., 1954), p.176
^ A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905. http://www.fourmilab.ch/etexts/einstein/specrel/www/.
^ A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905. http://www.fourmilab.ch/etexts/einstein/specrel/www/.
^ Griffiths, David J. (1998). Introduction to Electrodynamics, 3rd ed., Prentice Hall. ISBN 0-13-805326-X. , chapter 12
^ Milton mentions some inconclusive events (p.60) and still concludes that "no evidence at all of magnetic monopoles has survived" (p.3). Milton, Kimball A. (June 2006). "Theoretical and experimental status of magnetic monopoles". Reports on Progress in Physics 69 (6): 1637-1711. DOI:10.1088/0034-4885/69/6/R02. .
^ Guth, Alan (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus. ISBN 0-201-32840-2. .
^ Magnet Man, Magnet Basics - Safety Considerations accessed 6 October 2006.
^ Nanomagnets Bend The Rules. Retrieved on November 14, 2005.
^ Nanomagnets bend the rules. Retrieved on November 14, 2005.
[edit] External links
Look up Magnetism in
Wiktionary, the free dictionary.Electromagnetism - a chapter from an online textbook
Magnetic Force and Field on Project PHYSNET
On the Magnet, 1600 First scientific book on magnetism by the father of electrical engineering. Full English text, full text search.
Electromagnetism
Electricity · Magnetism
Electrostatics
Electric charge
Coulomb's law
Electric field
Gauss's law
Electric potential
Electric dipole moment
Magnetostatics
Ampère's Circuital law
Magnetic field
Magnetic flux
Biot-Savart law
Magnetic dipole moment
Electrodynamics
Electrical current
Lorentz force law
Electromotive force
(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
(EMF) Electromagnetic field
(EM) Electromagnetic radiation
Electrical Network
Electrical conduction
Electrical resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
Tensors in Relativity
Electromagnetic tensor
Electromagnetic stress-energy tensor
This box: view • talk • edit
Retrieved from "http://en.wikipedia.org/wiki/Magnetism"
Categories: All articles with unsourced statements | Articles with unsourced statements since February 2007 | Electric and magnetic fields in matter | Magnetism
Van der Waals radius
Van der Waals radius
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Element radius (Å)
Hydrogen 1.20
Carbon 1.7
Nitrogen 1.55
Oxygen 1.52
Fluorine 1.35
Phosphorus 1.9
Sulfur 1.85
Chlorine 1.8
The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. Van der Waals radii are determined from measurements of atomic spacing between pairs of unbonded atoms in crystals.
The van der Waals radius is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics.
Real gases do not behave exactly as predicted. In some cases the deviation can be extremely large. For example, ideal gases could never become liquids or solids, no matter how much they were cooled or compressed. Modifications of the ideal gas law, , were therefore proposed. Particularly useful and well known is the van der Waals equation of state: , where a and b are adjustable parameters determined from experimental measurements carried out on actual gases. Their values vary from gas to gas.
The van der Waals equation also has a microscopic interpretation. Molecules interact with one another. The interaction is strongly repulsive at very short distance, becomes mildly attractive at intermediate range, and vanishes at long distance. The ideal gas law must be corrected when attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding neighbours from a certain amount of territory around each molecule. Thus, a fraction of the total space becomes unavailable to each molecule as it executes random motion. In the equation of state, this volume of exclusion (nb) should be subtracted from the volume of the container (V), thus: (V - nb). The other term that is introduced in the van der Waals equation, , describes a weak attractive force among molecules, which increases when n increases or V decreases and molecules become more crowded together.
Contents [hide]
1 Van der Waals volume
2 See also
3 References
4 External links
[edit] Van der Waals volume
The van der Waals volume of an atom is the volume of a sphere with the Van der Waals radius of the atom.
Two atoms which are not chemically bonded have a minimum distance between their centers, which is equal to the sum of their Van der Waals radii. However, if the atoms are bonded by a covalent bond, the distance between their centers is smaller.
Therefore, the van der Waals volume of a molecule with covalent bonds is smaller than the sum of the van der Waals volumes of the atoms.
The van der Waals volume of a system of molecules is the sum of their van der Waals volumes.
[edit] See also
van der Waals constant
van der Waals equation
van der Waals force
van der Waals potential
[edit] References
L. Pauling, The Nature of the Chemical Bond, Cornell University Press, USA, 1945.
[edit] External links
van der Waals radii at Webelements
Structural Biology Glossary: van der Waals radii
Retrieved from "http://en.wikipedia.org/wiki/Van_der_Waals_radius"
Category: Chemical properties
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Element radius (Å)
Hydrogen 1.20
Carbon 1.7
Nitrogen 1.55
Oxygen 1.52
Fluorine 1.35
Phosphorus 1.9
Sulfur 1.85
Chlorine 1.8
The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. Van der Waals radii are determined from measurements of atomic spacing between pairs of unbonded atoms in crystals.
The van der Waals radius is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics.
Real gases do not behave exactly as predicted. In some cases the deviation can be extremely large. For example, ideal gases could never become liquids or solids, no matter how much they were cooled or compressed. Modifications of the ideal gas law, , were therefore proposed. Particularly useful and well known is the van der Waals equation of state: , where a and b are adjustable parameters determined from experimental measurements carried out on actual gases. Their values vary from gas to gas.
The van der Waals equation also has a microscopic interpretation. Molecules interact with one another. The interaction is strongly repulsive at very short distance, becomes mildly attractive at intermediate range, and vanishes at long distance. The ideal gas law must be corrected when attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding neighbours from a certain amount of territory around each molecule. Thus, a fraction of the total space becomes unavailable to each molecule as it executes random motion. In the equation of state, this volume of exclusion (nb) should be subtracted from the volume of the container (V), thus: (V - nb). The other term that is introduced in the van der Waals equation, , describes a weak attractive force among molecules, which increases when n increases or V decreases and molecules become more crowded together.
Contents [hide]
1 Van der Waals volume
2 See also
3 References
4 External links
[edit] Van der Waals volume
The van der Waals volume of an atom is the volume of a sphere with the Van der Waals radius of the atom.
Two atoms which are not chemically bonded have a minimum distance between their centers, which is equal to the sum of their Van der Waals radii. However, if the atoms are bonded by a covalent bond, the distance between their centers is smaller.
Therefore, the van der Waals volume of a molecule with covalent bonds is smaller than the sum of the van der Waals volumes of the atoms.
The van der Waals volume of a system of molecules is the sum of their van der Waals volumes.
[edit] See also
van der Waals constant
van der Waals equation
van der Waals force
van der Waals potential
[edit] References
L. Pauling, The Nature of the Chemical Bond, Cornell University Press, USA, 1945.
[edit] External links
van der Waals radii at Webelements
Structural Biology Glossary: van der Waals radii
Retrieved from "http://en.wikipedia.org/wiki/Van_der_Waals_radius"
Category: Chemical properties
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