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Manometer

Manometer

A manometer is a pressure measuring instrument, often also called pressure gauge.

Description

The oldest type is the liquid-column manometer. A very simple version is a U-shaped tube half-full of liquid where the measured pressure is applied to one side of the tube whilst the reference pressure (which might be that of the atmosphere) is applied to the other. The difference in liquid level represents the applied pressure. It is quite easy to make a homemade manometer. A single-limb liquid-column manometer has a larger reservoir instead of one side of the U-tube and has a scale beside the narrower column. The column may be inclined to further amplify the liquid movement. Liquid-column manometers can be used to measure small differences between great pressures. homemade A second type uses the deflection of a flexible membrane that seals a fixed pressure reference volume to determine the pressure. The amount of deflection is repeatable for known pressures so the pressure can be determined using a lookup table. A third variant (Bourdon gauge) uses a coiled tube which as it expands due to pressure increase causes a rotation of an arm connected to the tube. One use of manometers is to measure vacuum pressures, especially in the range from 0.001 atmospheres to 1 atm. They are helpful because the deflection of the manometer is not dependent upon the type of gas being measured, unlike other types of vacuum gauges in this pressure range. The deflection of the piston is often one half of a capacitor, so that when the piston moves, the capacitance of the device changes. This is a common way (with proper calibrations) to get a very precise, electronic reading from a manometer, and this configuration is called a capacitive manometer vacuum gauge.

European (CEN) Standard

- EN 472 : Pessure gauge - Vocabulary.
- EN 837-1 : Pressure gauges. Bourdon tube pressure gauges. Dimensions, metrology, requirements and testing.
- EN 837-2 : Pressure gauges. Selection and installation recommendations for pressure gauges.
- EN 837-3 : Pressure gauges. Diaphragm and capsule pressure gauges. Dimensions, metrology, requirements and testing..

Patents

: W. R. Valcourt : "Overflow valve for a manometer "

External links

- [http://www.komar.org/faq/manometer/ Home-Made manometer] Category:Measuring instruments

Pressure

:For the psychological or political context, see Peer pressure. Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. Mathematically: :

p = F/A\,

where p is the pressure, F is the normal force, and A is the area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume. A closely related quantity is the stress tensor σ which relates the vector force F to the vector area A via :

\mathbf=\mathbf

This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure. shear

Example

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The gradient of pressure is force density. In the human body, baroreceptors monitor blood pressure.

Relative or gauge pressure

For gases, pressure is sometimes measured, not as an absolute pressure, but relative to atmospheric pressure; such measurements are sometimes called gauge pressure. An example of this is the air pressure in a car tire, which might be said to be "220 kPa," but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa." Where space is limited, such as on gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)," is permitted. In non-SI technical work, a gauge pressure is sometimes written as "32 psig," though the other methods explained above that avoid attaching characters to the unit of pressure are preferred [http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 ¹].

Scalar nature of pressure

In static gas, the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Hydrostatic pressure

Hydrostatic pressure is the pressure due to the weight of a fluid. :p = ρgh where ρ (rho) is density of the fluid, g is acceleration due to gravity, and h is height of the fluid above the point being measured. See also Pascal's law.

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation. The pressure of a moving fluid can be measured using a Pitot probe, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressure.

Units

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m^-2 or kg·m^-1·s^-2). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m². Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar. The cgs unit of pressure is the barye (ba). It is equal to 1 dyn·cm^-2. Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI; the unit of force in SI is the newton (N). The technical atmosphere (symbol: at) is 1 kgf/cm². Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa. The obsolete unit inch of mercury (inHg) is still sometimes used in the United States. Blood pressure is still measured in millimetres of mercury in most of the world, and lung pressures in centimeters of water are still common. These obsolete manometric units of pressure are based on the pressure exerted by the weight of some "standard" fluid under some "standard" gravity. They are effectively attempts to define a unit for expressing the readings of a manometer. When millimetres or inches of mercury are used today, they have precise definitions that can be expressed in terms of SI units. The water-based units depend on the density of water, a measured, rather than defined, quantity. The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows. :standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa. A rule of thumb commonly used by scuba divers is that one atmosphere is approximately equal to the pressure exerted by ten metres of water. Non-SI units presently or formerly in use include the following.
- atmosphere.
- manometric units:
- centimetre, inch, and millimetre of mercury (Torr).
- millimetre, centimetre, metre, inch, and foot of water.
- imperial units:
- kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch.
- pound-force, ton-force (short), and ton-force (long) per square foot.
- non-SI metric units:
- bar, millibar.
- kilogram-force, or kilopond, per square centimetre (technical atmosphere).
- gram-force and tonne-force (metric ton-force) per square centimetre.
- barye (dyne per square centimetre).
- kilogram-force and tonne-force per square metre.
- sthene per square metre (pieze).

External links

- [http://calc.skyrocket.de/en/ Online unit converter] - conversion of many different units.
- [http://avc.comm.nsdlib.org/cgi-bin/wiki_grade_interface.pl?An_Exercise_In_Air_Pressure An exercise in air pressure]
- [http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html Pressure being a scalar quantity] Category:Diving Category:Meteorology Category:Physical quantity Category:Thermodynamics ko:압력 ms:Tekanan ja:圧力

Measuring instrument

]] In physics and engineering, measurement is the activity of comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the measurement results in a given number for the relationship between the item under study and the referenced unit of measurement. Measuring instruments are the means by which this translation is made. All measuring instruments are subject to varying degrees of instrument error. Physicists use a vast range of instruments to perform their measurements. These range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators.
- Mass
- balance
- weighing scales
- mass spectrometer
- katharometer :History of Weights and Measures
- Time
- calendar
- chronometer
- clock
- atomic clock
- radiometric dating :Timeline of time measurement technology
- Length (i.e., distance)
- altimeter (measures height)
- architect's scale
- engineer's scale
- interferometer
- micrometer
- odometer
- opisometer
- ruler
- tape measure
- laser rangefinder
- ultrasound distance measure
- GPS
- Electronic distance meter
- Area
- planimeter
- Angles
- sextant
- theodolite
- protractor
- Temperature
- thermometer
- thermocouples
- thermistors
- pyrometers
- electromagnetic spectroscopy
- Humidity
- hygrometer
- Pressure
- barometer
- manometer
- Pitot tube (used to determine speed)
- anemometer (used to determine wind speed)
- tire-pressure gauge
- Flow
- pH
- Level
- spirit level
- laser line level
- Dumpy level
- Radiation
- geiger counter
- Nichols radiometer
- Sound
- Light
- Photometer
- Spectrometer
- Speed
- speedometer
- airspeed indicator
- Electrical properties
- electrometer (measures charge)
- ammeter (measures electrical current)
- galvanometer (measures current)
- ohmmeter (measures resistance)
- voltmeter (measures voltage)
- Wheatstone bridge
- multimeter (measures all of the above)
- oscilloscope
- watt meter (measures power)
- electric energy meter (measures energy)
- Hardness
- durometer
- Uncategorized
- colorimeter (measures absorbance, and thus concentration)
- radiometry
- sicroscope
- spectroscopy is an important tool used by physicists.

Reference

In general, a reference is something that refers or points to something else, or acts as a connection or a link between two things. The objects it links may be concrete, such as books or locations, or abstract, such as data, thoughts, or memories. The object which is named by a reference, or to which the reference points, is the referent. The term reference is used with different specialized meanings in a variety of fields, as follows:

Semantics

In semantics, reference is generally construed as the relation between nouns or pronouns and objects that are named by them. Hence the word "John" refers to John; the word "it" refers to some previously specified object. The objects referred to are called the "referents" of the word. Sometimes the word-object relation is called "denotation". Reference is not in general the same as meaning, as words can often be meaningful without having a referent. Fictional and mythological names such as "Bo-Peep" and "Hercules" show that this is possible. As Frege discovered, reference cannot be treated as identical with meaning: "Hesperos" (an ancient Greek name for the evening star) and "Phosphorus" (an ancient Greek name for the morning star) both refer to Venus, but the astronomical fact that '"Hesperos" is "Phosphorus"' can still be informative, even if the 'meanings' of both "Hesperos" and "Phosphorus" are already known. This problem led Frege to distinguish between the sense of a word and its reference.

Art

In Art, a reference is an item from which a work is based. This may include an existing artwork, a reproduced (i.e. photo) or directly observed (i.e. person) object, or the artist's memory.

Computer science

In computer science, references are datatypes which refer to an object elsewhere in memory, and are used to construct a wide variety of data structures such as linked lists. Most programming languages support some form of reference. See reference (computer science). The C++ programming language has a specific type of reference also referred to as a reference; see reference (C Plus Plus).

Geometry

A reference point is a location used to describe another one, by giving the relative position. Similarly we have the concept of frame of reference (both in physics and figuratively), etc.

Libraries

In a library, the word reference may refer to a dictionary, encyclopedia, or other reference work that contains many brief articles that cover a broad scope of knowledge in one book, or a set of books. However, the word reference is also used to mean a book that cannot be taken from the room, or from the building. Many of the books in the reference department of a library are reference works, but some are books that are simply too large or valuable to loan out. Conversely, selected reference works may be shelved with other circulating books, and may be loaned out.

Scholarship

A reference may also be a text (not necessarily a reference text) that has been used in the creation of a piece of work such as an essay, report, or oration. Its primary purpose is to allow people who receive such work to examine the author's sources, either for validity, or simply to learn more about the subject. Such items are often listed at the end of an article or book in a reference list.Copying of copyrighted material without required permisions amounts to 'plagiarism'.

Personal references

In the labour market, a reference is a letter to a prospective employer regarding a job applicant's characteristics. Usually the person providing the reference - the referee - is a previous boss, or someone of some distinction in government, the clergy, or education, who can personally vouch for the applicant's employability.

Canadian law

A Reference is a procedure through which the government of Canada can submit legal questions to the Supreme Court of Canada. The Court will consider the question and publish an opinion which is treated as binding in law.

Earth's atmosphere

Earth's atmosphere is a layer of gases surrounding the planet Earth and retained by the Earth's gravity. It contains roughly 78% nitrogen and 21% oxygen, with trace amounts of other gases. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation and reducing temperature extremes between day and night. The atmosphere has no abrupt cut-off. It slowly becomes thinner and fades away into space. There is no definite boundary between the atmosphere and outer space. Three-quarters of the atmosphere's mass is within 11 km of the planetary surface. In the United States, persons who travel above an altitude of 50.0 miles (80.5 km) are designated as astronauts. An altitude of 120 km (75 mi or 400,000 ft) marks the boundary where atmospheric effects become noticeable during re-entry. The Karman line, at 100 km (62 mi), is also frequently used as the boundary between atmosphere and space.

Temperature and the atmospheric layers

The temperature of the Earth's atmosphere varies with altitude; the mathematical relationship between temperature and altitude varies between the different atmospheric layers:
- troposphere: From the Greek word tropos meaning to turn or mix. The troposphere is the lowest layer of the atmosphere starting at the surface going up to between 7 km at the poles and 17 km at the equator with some variation due to weather factors. The troposphere has a great deal of vertical mixing due to solar heating at the surface. This heating warms air masses, which then rise to release latent heat as sensible heat that further buoys the air mass. This process continues until all water vapor is removed. In the troposphere, on average, temperature decreases with height due to expansive cooling.
- stratosphere: from that 7–17 km range to about 50 km, temperature increasing with height.
- mesosphere: from about 50 km to the range of 80 km to 85 km, temperature decreasing with height.
- thermosphere: from 80–85 km to 640+ km, temperature increasing with height. The boundaries between these regions are named the tropopause, stratopause, and mesopause. The average temperature of the atmosphere at the surface of earth is 14 °C.

Various atmospheric regions

Atmospheric regions are also named in other ways:
- ionosphere — the region containing ions: approximately the mesosphere and thermosphere up to 550 km.
- exosphere — above the ionosphere, where the atmosphere thins out into space.
- magnetosphere — the region where the Earth's magnetic field interacts with the solar wind from the Sun. It extends for tens of thousands of kilometers, with a long tail away from the Sun.
- ozone layer — or ozonosphere, approximately 10 - 50 km, where stratospheric ozone is found. Note that even within this region, ozone is a minor constituent by volume.
- upper atmosphere — the region of the atmosphere above the mesopause.
- Van Allen radiation belts — regions where particles from the Sun become concentrated.

Pressure

:Barometric Formula: (used for airplane flight) barometric formula :Main article: Atmospheric pressure :Nasa mathematical model: NRLMSISE-00 Atmospheric pressure is a direct result of the weight of the air. This means that air pressure varies with location and time because the amount (and weight) of air above the earth varies with location and time. Atmospheric pressure drops by ~50% at an altitude of about 5 km (equivalently, about 50% of the total atmospheric mass is within the lowest 5 km). The average atmospheric pressure, at sea level, is about 101.3 kilopascals (about 14.7 pounds per square inch).

Thickness of the atmosphere

The atmosphere is present to heights of 1000 km. or more. But at this height it is so thin and at such low pressure that it's almost like it isn't there.
- 57.8% of the atmosphere is below the summit of Mount Everest.
- 72% of the atmosphere is below the common flight height of airplanes, (about 10000 m or 32800 ft).
- 99.99999% of the atmosphere is below the highest X-15 plane flight on August 22, 1963 which reached an altitude of 354,300 ft or 108 km. Therefore, most of the atmosphere is below 100 km (99.9999%) although in the rarified region above this there are auroras, and other atmospheric effects.

Composition

aurora
Source for figures above: [http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html NASA]
Carbon dioxide and methane updated (to 1998) by IPCC TAR table 6.1 [http://www.grida.no/climate/ipcc_tar/wg1/221.htm]

Minor components of air not listed above include:
- The mean molecular mass of air is 28.97 g/mol.

Heterosphere

Below an altitude of about 100 km, the Earth's atmosphere has a more-or-less uniform composition (apart from water vapor) as described above. However, above about 100 km, the Earth's atmosphere begins to have a composition which varies with altitude. This is essentially because, in the absence of mixing, the density of a gas falls off exponentially with increasing altitude, but at a rate which depends on the molecular mass. Thus higher mass constituents, such as oxygen and nitrogen, fall off more quickly than lighter constituents such as helium, molecular hydrogen, and atomic hydrogen. Thus there is a layer, called the heterosphere, in which the earth's atmosphere has varying composition. As the altitude increases, the atmosphere is dominated successively by helium, molecular hydrogen, and atomic hydrogen. The precise altitude of the heterosphere and the layers it contains varies significantly with temperature.[http://www.oma.be/BIRA-IASB/Public/Research/Thermo/Thermotxt.en.html]

Density and mass

The density of air at sea level is about 1.2 kg/m³. Natural variations of the barometric pressure occur at any one altitude as a consequence of weather. This variation is relatively small for inhabited altitudes but much more pronounced in the outer atmosphere and space due to variable solar radiation The atmospheric density decreases as the altitude increases. This variation can be approximately modeled using the barometric formula. More sophisticated models are used by meteorologists and space agencies to predict weather and orbital decay of satellites. The total mass of the atmosphere is about 5.1 × 10¹⁸ kg, or about 0.9 ppm of the Earth's total mass. The above composition percentages are done by volume. Assuming that the gases act like ideal gases, we can add the percentages p multiplied by their molar masses m, to get a total t = sum (p·m). Any element's percent by mass is then p·m/t. When we do this to the above percentages, we get that, by mass, the composition of the atmosphere is 75.523% N₂, 23.133% O₂, 1.288% Ar, 0.053% CO₂, 0.001267% Ne, 0.00029% CH₄, 0.00033% Kr, 0.000724% He, and 0.0000038 % H₂. ppm This graph is from the NRLMSISE-00 atmosphere model, which has as inputs: latitude, longitude, date, time of day, altitude, solar flux, and the earth's magnetic field daily index.

The evolution of the Earth's atmosphere

model The history of the Earth's atmosphere prior to one billion years ago is poorly understood, but the following presents a plausible sequence of events. This remains an active area of research. The modern atmosphere is sometimes referred to as Earth's "third atmosphere", in order to distinguish the current chemical composition from two notably different previous compositions. The original atmosphere was primarily helium and hydrogen. Heat (from the still-molten crust, and the sun) dissipated this atmosphere. About 3.5 billion years ago, the surface had cooled enough to form a crust, still heavily populated with volcanoes which released steam, carbon dioxide, and ammonia. This led to the "second atmosphere", which was primarily carbon dioxide and water vapor, with some nitrogen but virtually no oxygen (though very recent simulations run at the University of Waterloo and University of Colorado in 2005 suggested that it may have had up to 40% hydrogen [http://newsrelease.uwaterloo.ca/news.php?id=4348]). This second atmosphere had approximately 100 times as much gas as the current atmosphere. It is generally believed that the greenhouse effect, caused by high levels of carbon dioxide, kept the Earth from freezing. During the next few billion years, water vapor condensed to form rain and oceans, which began to dissolve carbon dioxide. Approximately 50% of the carbon dioxide would be absorbed into the oceans. One of the earliest types of bacteria were the cyanobacteria. Fossil evidence indicates that these bacteria existed approximately 3.3 billion years ago and were the first oxygen-producing evolving phototropic organisms. They were responsible for the initial conversion of the earth’s atmosphere from an anoxic state to an oxic state (that is, from a state without oxygen to a state with oxygen). Being the first to carry out oxygenic photosynthesis, they were able to convert carbon dioxide into oxygen, playing a major role in oxygenating the atmosphere. Photosynthesizing plants would later evolve and convert more carbon dioxide into oxygen. Over time, excess carbon became locked in fossil fuels, sedimentary rocks (notably limestone), and animal shells. As oxygen was released, it reacted with ammonia to create nitrogen; in addition, bacteria would also convert ammonia into nitrogen. As more plants appeared, the levels of oxygen increased significantly, while carbon dioxide levels dropped. At first the oxygen combined with various elements (such as iron), but eventually oxygen accumulated in the atmosphere, resulting in mass extinctions and further evolution. With the appearance of an ozone layer (ozone is an allotrope of oxygen) lifeforms were better protected from ultraviolet radiation. This oxygen-nitrogen atmosphere is the "third atmosphere".

References

- [http://www.oma.be/BIRA-IASB/Public/Research/Thermo/Thermotxt.en.html The thermosphere: a part of the heterosphere], by J. Vercheval (viewed 1 Apr 2005)

External links

- [http://nssdc.gsfc.nasa.gov/space/model/models_home.html#atmo NASA atmosphere models]
- [http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html NASA's Earth Fact Sheet]
- [http://atmospheres.agu.org/ American Geophysical Union: Atmospheric Sciences]
- [http://www.srh.noaa.gov/srh/jetstream/atmos/layers.htm Layers of the Atmosphere] Category:Atmospheric sciences Category:Atmosphere Category:Environments ko:대기권 ms:Atmosfera ja:大気

Membrane

A membrane is a thin, typically planar structure or material that separates two environments. Because it sits between environments or phases and has a finite volume, it can be referred to as an interphase rather than an interface. Membranes selectively control mass transport between the phases or environments. Biological membranes include:
- Cell membrane and intracellular membranes
- mucous membrane
- S-layer Artificial membranes are used in:
- Reverse osmosis
- Filtration (Microfiltration, Ultrafiltration)
- Pervaporation
- Dialysis
- Electrodialysis
- Emulsion liquid membranes
- Membrane-based solvent extraction
- Membrane reactors
- Gas permeation
- supported liquid membranes Theoretical membranes are used in:
- M-theory (simplified) simple:Membranes

Volume

Volume, also called capacity, is a quantification of how much space an object occupies. The international unit for volume is the cubic meter. The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squares) are assigned zero volume in the three-dimensional space. Mathematically, volumes are defined by means of integral calculus, by approximating the given body with a large amount of small cubes, and adding the volumes of those cubes. The generalization of volume to arbitrarily many dimensions is called content. In differential geometry, volume is expressed by means of the volume form. Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units). Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.

Volume formula

Common equations for volume: :A cube:

s^3 = s \cdot s \cdot s

(where s is the length of a side) : :A rectangular prism:

l \cdot w \cdot h

(length, width, height) : :A cylinder:

\pi \cdot r^2 h

(r = radius of circular face, h = distance between faces) : :A sphere:

\frac \pi r^3

(r = radius of sphere) : :An ellipsoid:

\frac \pi abc

(a, b, c = semi-axes of ellipsoid) : :A pyramid:

\frac A h

(A = area of base, h = height from base to apex) : :A cone (circular-based pyramid):

\frac \pi r^2 h

(r = radius of circle at base, h = distance from base to tip) : :Any prism that has a constant cross sectional area along the height
- :

A \cdot h

(A = area of the base, h = height) : :Any figure (calculus required) :

\int A(h) dh

where h is any dimension of the figure, and A(h) is the area of the cross-sections perpendicular to h described as a function of the position along h; this will work for any figure (no matter if the prism is slanted or the cross-sections change shape). The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix. The volume of any tetrahedron, given its vertices a, b, c and d, is (1/6)·|det(a−b, b−c, c−d)|, or any other combination of pairs of vertices that form a simply connected graph.

Volume measures: other metric units

A commonly used metric unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre (American spelling cubic meter), which was formerly termed a stere and often called a "cube" in engineering slang. A cubic centimetre (American spelling cubic centimeter) is the same volume as a millilitre.

Volume measures: USA

U.S. customary units of volume:
- U.S. fluid ounce, about 29.6 mL
- U.S. liquid pint = 16 fluid ounces, or about 473 mL
- U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
- U.S. liquid quart = 32 fluid ounces or two U.S. pints, or about 946 mL
- U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
- U.S. gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
- U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
- U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L The acre foot is often used in measuring the volume of water in a reservoir or an aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot. It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³.
- cubic inch = 16.387 064 cm³
- cubic foot = 1,728 in³ ≈ 28.317 dm³
- cubic yard = 27 ft³ ≈ 0.7646 m³
- cubic mile = 5,451,776,000 yd³ = 3,379,200 acre-feet ≈ 4.168 km³

Volume measures: UK

Imperial units of volume:
- UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
- UK pint = 20 fluid ounces, or about 568 mL
- UK quart = 40 ounces or two pints, or about 1.137 L
- UK gallon = 160 ounces or four quarts, or exactly 4.546 09 L May it be noted that due to metrication within the UK, the quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol & diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer & cider (bottled & canned beer is sold in SI units) and for milk (this too is increasingly being sold in SI units).

Volume measures: cooking

Traditional cooking measures for volume also include:
- teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
- teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL) (Canada)
- teaspoon = 5 mL (metric)
- tablespoon = 1/2 U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
- tablespoon = 1/2 Imperial fluid ounce or 3 teaspoons (about 14.21 mL) (Canada)
- tablespoon = 15 mL or 3 teaspoons (metric)
- tablespoon = 5 fluidrams (about 17.76 mL) (British)
- cup = 8 U.S. fluid ounces or 1/2 U.S. liquid pint (about 237 mL)
- cup = 8 Imperial fluid ounces or 1/2 fluid pint (about 227 mL) (Canada)
- cup = 250 mL (metric)

Relationship to density

The volume of an object is equal to its mass divided by its average density. This is a rearrangement of the calculation of density as mass per unit volume. The term specific volume is used for volume divided by mass. This is the reciprocal of the mass density, expressed in units such as cubic meters per kilogram (m³/kg).

Volume comparisons

To help compare different volumes, see orders of magnitude (volume)

External links

- [http://www.unitconversion.org/unit_converter/volume.html Online Volume Converter - convert between various units of volume, such as cubic meter, liter, barrel, tablespoon, cup, and so on]
- [http://www.unitconversion.org/unit_converter/volume-v.html Interactive Volume Conversion Table - convert selected unit to all other units of volume]
- [http://www.unitconversion.org/unit_converter/volume-dry-v.html Volume - Dry Online Interactive Unit Converter]
- [http://jumk.de/calc/volume.shtml Volume or capacity conversion of English and American units to metric units]
- [http://calc.skyrocket.de/en/ Online Unit Converter - Conversion of many different units]
- [http://www.ex.ac.uk/trol/scol/ccvol.htm Conversion Calculator for Units of Volume for many units (Cleave Books)]
- ko:부피 ja:体積 simple:Volume

Bourdon gauge

Many techniques have been developed for the measurement of reduced or increased pressures. Gauges are either direct- or indirect-reading. Those that measure pressure by calculating the force exerted on the surface by incident particle flux are called direct reading gauges. Indirect gauges record the pressure by measuring a gas property that changes in a predictable manner with gas density.

Bourdon Tube Type

In 1849 the Bourdon tube pressure gauge was patented in France by Eugene Bourdon. A pressure or vacuum gauge usually consists of a closed coiled tube connected to the chamber or pipe in which pressure is to be sensed. As the pressure increases the tube will tend to uncoil, while a reduced pressure will cause the tube to coil more tightly. This motion is transferred through a link to a gear train connected to an indicating needle. The needle is presented in front of a card face inscribed with the pressure indications associated with particular needle deflections. In the following pictures the transparent cover face has been removed and the mechanism removed from the case. This particular gauge is a combination vacuum and pressure gauge used for automotive diagnosis. The left side of the face, used for measuring manifold vacuum, is calibrated in centimeters of mercury vacuum on its inner scale and inches of mercury vacuum in its outer scale. The right portion of the face is used to measure fuel pump pressure and is calibrated in kilograms per square centimeter on its inner scale and pounds per square inch on its outer scale.

Mechanical details

pounds per square inch Stationary parts:
- A: Receiver block. This joins the inlet pipe to the fixed end of the Bourdon tube (1) and secures the chassis plate (B). The two holes receive screws that secure the case.
- B: Chassis Plate. The face card is attached to this. It contains bearing holes for the axles.
- C: Secondary Chassis Plate. It supports the outer ends of the axles.
- D: Posts to join and space the two chassis plates. Moving Parts: # Stationary end of Bourdon tube. This communicates with the inlet pipe through the receiver block. # Moving end of Bourdon tube. This end is sealed. # Pivot and pivot pin. # Link joining pivot pin to lever (5) with pins to allow joint rotation. # Lever. This an extension of the sector gear (7). # Sector gear axle pin. # Sector gear. # Indicator needle axle. This has a spur gear that engages the sector gear (7) and extends through the face to drive the indicator needle. Due to the short distance between the lever arm link boss and the pivot pin and the difference between the effective radius of the sector gear and that of the spur gear, any motion of the Bourdon tube is greatly amplified. A small motion of the tube results in a large motion of the indicator needle. # Hair spring to preload the gear train to eliminate gear lash and hysteresis.

Aneroid chamber (bellows) type

hysteresis In gauges intended to sense small pressures or pressure differences, or require that an absolute pressure be measured, the gear train and needle may be driven by an enclosed and sealed bellows chamber, called an aneroid, which means "without liquid". (Early barometers used a column of liquid such as water or the liquid metal mercury suspended by a vacuum.) This bellows configuration is used in aneroid barometers (barometers with an indicating needle and dial card), altimeters, altitude recording barographs, and the altitude telemetry instruments used in weather balloon radiosondes. These devices use the sealed chamber as a reference pressure and are driven by the external pressure. Other sensitive aircraft instruments such as air speed indicators and rate of climb indicators (variometers) have connections both to the internal part of the aneroid chamber and to an external enclosing chamber.

External links

http://www.finecontrols.co.uk/pressure_gauges.htm Category:Measuring instruments

Atmosphere (unit)

When expressed as a measurement, an atmosphere (symbol: atm) or standard atmosphere is a unit of pressure roughly equal to the average atmospheric pressure at sea level on Earth. It is defined as 101.325 kPa and equal to the pressure under 760 mm of mercury. ; 1 atm : = 1013.25 hPa = 1013.25 mbar : = 101.325 kPa : = 760 mm of mercury (mmHg) : = 29.92126 inches of mercury

Applications

In chemistry, standard temperature and pressure (STP) is defined as a reference temperature of 0 °C (273.15 K) and pressure of 101.325 kPa (1 atm). In the United Kingdom, scuba divers and others often use the word atmosphere loosely to mean 1 bar (1000 millibars, or 100000 Pa). The unit technical atmosphere (at) is roughly equal to the gauge pressure under 10 m of water; 1 at = 98066.5 Pa. Category:Atmosphere ko:기압

Vacuum

For other uses, see vacuum cleaner and Vacuum (musical group). The root of the word vacuum is the Latin word vacuum (pl. vacua) which means a space devoid of matter. In physics, a vacuum is the absence of matter in a volume of space.

Vacuum ranges

Vacuum ranges are defined as follows:

Perfect vacuum

A perfect vacuum is an ideal state that cannot practically be obtained in a laboratory, nor even in outer space, where there are a few hydrogen atoms per cubic centimeter at 10⁻¹⁴ pascal or 10⁻¹⁶ torr. In modern day usage vacuum is considered to exist in an enclosed space or chamber, when the pressure of gaseous environment is lower than atmospheric pressure (760 Torr or 101 kPa), or has been reduced as much as necessary to prevent the influence of some gas on a process being carried out in that space.

Partial vacuum

Physicists use the term partial vacuum to describe real-life non-ideal vacuum. A complete characterization of the physical state would require further parameters, such as temperature. The antithesis of a vacuum, which is also an ideal unachievable state, is called a plenum. In engineering, a vacuum is any region where the gas pressure is less than atmospheric pressure. Engineers measure the degree of vacuum in units of pressure. The SI unit of pressure is the pascal (abbreviation Pa), but vacuum is usually measured in millimeters of mercury (mmHg) or torr, with 1 mmHg or 1 torr equaling 133.3223684 pascals. It is often also measured using the barometric scale, or as a percentage of atmospheric pressure in bars or atms. For commercial purposes, vacuum is often measured in inches of mercury (inHg). This means that the pressure in vacuum, when specified in inches of mercury, is equal to the specified inches of mercury subtracted from 29.92. Thus a vacuum of 26 inHg is equivalent to a pressure of (29.92 - 26) or 3.92 inHg. Here, 29.92 inHg means perfect vacuum.

Degrees of vacuum

- Atmospheric pressure = variable, but standardised at 101.325 kPa (760 Torr) or 760 mm of mercury
- Vacuum cleaner = approximately 80 kPa (600 Torr)
- Mechanical vacuum pump = approximately 100 Pa to 100 μPa (1 Torr to 10⁻⁶ Torr)
- Near earth outer space = approximately 100 μPa (10⁻⁶ Torr)
- Cryopumped MBE chamber = 100 nPa to 1 nPa (10⁻⁹ Torr to 10⁻¹¹ Torr)
- Pressure on the Moon = approximately 1 nPa (10⁻¹¹ Torr)
- Interstellar space = approximately 1 fPa (10⁻¹⁷ Torr)
- [http://www-ssg.sr.unh.edu/ism/what1.html Source for interstellar vacuum] As gas pressure decreases, the mean free path (MFP) of the gas molecules increases. When the MFP is greater than the chamber, pump, spacecraft, or other objects present, the continuum assumptions of fluid mechanics do not apply. This vacuum state is called high vacuum, and the study of fluid flows in this regime is called particle gas dynamics. In interplanetary and interstellar space, isotropic gas pressure is insignificant when compared to solar pressure, solar wind, and dynamic pressure. Astrophysicists prefer to use density to describe these environments, in units of particles per cubic metre.

Creating a vacuum

The easiest way to create an artificial vacuum is to expand the volume of a container. For example, your muscles expand your lungs to create a partial vacuum inside them, and air rushes in to fill the vacuum. By repeatedly closing off a compartment of the vacuum and exhausting it, it is possible to pump air out of a chamber of fixed size in a manner analogous to pumping a milkshake out of a glass. This is the principle behind most mechanical vacuum pumps. Inside the pump, a mechanism expands a small sealed cavity to create a deep vacuum. Because of the pressure differential, some air from the chamber is pushed into the pump's small cavity. The pump's cavity is then sealed from the chamber, opened to the atmosphere, and squeezed back to a minute size. A mechanical vacuum pump moves the same volume of gas with each cycle, but as the chamber's pressure drops, this volume contains less and less mass. So although the pumping speed remains constant when measured in litres/second, it drops exponentially when measured in kilograms/second. Meanwhile, the leakage rates, evaporation rates, and sublimation rates produce a constant mass flow into the system. When the pump's mass flow drops to the same level as the mass flows into the chamber, the system asymptotically approaches a constant pressure called the base pressure. Evaporation and sublimation into a vacuum is called outgassing, and the most common source is water absorbed by materials in the chamber. Outgassing can be reduced by desiccation prior to vacuum pumping. The base pressure of a rubber- and plastic-sealed piston pump system is typically 1 to 50 kPa, while a scroll pump might reach 10 Pa and a rotary vane oil pump with a clean and empty metallic chamber can easily achieve 0.1 Pa. If the dominant mass flow into the vacuum system is chamber leakage or outgassing of materials under vacuum, then the vacuum can be improved simply by installing bigger pumps. However, there is a point where backstream leakage through the pump and outgassing of the pump oils become the dominant mass flows into the chamber. In this situation, the vacuum will approach the pump's ultimate pressure - the best vacuum that this type of pump can achieve under ideal conditions. Adding more pumps in parallel or bigger pumps of the same type can still improve the pump-down speed, but they will not reduce the base pressure below ultimate. Better pumping technologies must be used to go beyond this barrier.

High vacuum

Fortunately, once the pressure has dropped below 1 kPa or so, another vacuum pumping technique becomes possible. Matter flows differently at different pressures based on the laws of fluid dynamics. At atmospheric pressure and mild vacuums, molecules interact with each other and push on their neighboring molecules in what is known as viscous flow. When the distance between the molecules increases, the molecules interact with the walls of the chamber more often than the other molecules, and molecular pumping becomes more effective than compression pumping. This regime is generally called high vacuum. One such method to create a high vacuum to ultra high vacuum is by the use of cryopumps. Cryopumping incorporates the use of introducing cryogenics and a vacuum system. On a larger scale, the principles are the same as in a Cryomodule Molecular pumps sweep out a larger area than mechanical pumps, and do so more frequently, making them capable of much higher pumping speeds as measured in volume per time. They do this at the expense of the seal between the vacuum and their exhaust. Since there is no seal, a small pressure at the exhaust can easily force flow backstream through the pump; this is called stall. In high vacuum, however, pressure gradients have little effect on fluid flows, and molecular pumps can attain their full potential. The two main types of molecular pumps are the diffusion pump and the turbomolecular pump. Both types of pumps blow out gas molecules that diffuse into the pump. Diffusion pumps blow out molecules with jets of oil, while turbomolecular pumps use high speed fans. Both of these pumps will stall and fail to pump if exhausted directly to atmospheric pressure, so they must be exhausted to a lower grade vacuum created by a mechanical pump. As with mechanical pumps, the base pressure will be reached when leakage, outgassing, and backstreaming equal the pump speed, but now minimizing leakage and outgassing to a level comparable to backstreaming becomes much more difficult. High vacuum systems generally require metal chambers with metal O-ring seals such as Klein flanges or ISO flanges. The system must be clean and free of organic matter to minimize outgassing. All materials, solid or liquid, have a small vapour pressure, and their outgassing becomes important when the vacuum pressure falls below this vapour pressure. As a result, many materials that work well in low vacuums, such as epoxy, will become a problematic source of outgassing when attempting to achieve high vacuums. With these standard precautions, vacuums of 1 mPa are easily achieved with off-the-shelf molecular pumps. With careful design and operation, 1μPa is possible.

Ultra-high vacuum

:Main article: Ultra high vacuum Even higher vacuums are possible, but they generally require custom-built equipment, strict operational procedures, and a fair amount of trial-and-error. Yet more specialized pumps become useful: # Converting the molecules of gas to their solid phase by freezing them, called cryopumping or cryotrapping # Converting them to solids by electrically combining them with other materials, called ion pumping Ultra-high vacuum systems are usually made of stainless steel with metal-gasketed conflat flanges. The system is usually baked, preferably under vacuum, to temporarily raise the vapour pressure of all outgassing materials in the system and boil them off. If necessary, this outgassing of the system can also be performed at room temperature, but this takes much more time. Once the bulk of the outgassing materials are boiled off and evacuated, the system may be cooled to lower vapour pressures and minimize residual outgassing during actual operation. Some systems are cooled well below room temperature by liquid nitrogen to shut down residual outgassing and simultaneously cryopump the system. In ultra-high vacuum systems, some very odd leakage paths and outgassing sources must be considered. The water absorption of aluminium and palladium becomes an unacceptable source of outgassing, and even the absorptivity of hard metals such as stainless steel or titanium must be considered. Some oils and greases will boil off in extreme vacuums. The porosity of the metallic chamber walls may have to be considered, and the grain direction of the metallic flanges should be parallel to the flange face. The impact of molecular size must be considered. Smaller molecules can leak in more easily and are more easily absorbed by certain materials, and molecular pumps are less effective at pumping gases with lower molecular weights. Your system may be able to evacuate nitrogen, (the main component of air,) to the desired vacuum, but your chamber could still be full of residual atmospheric hydrogen and helium. Vessels lined with a highly gas-permeable material such as palladium (which is a high-capacity hydrogen sponge) create special outgassing problems. The lowest pressures currently achievable in laboratory are about 10^-13 Pa.

Vacuum in space

Pa Much of outer space has the density and pressure of an almost perfect vacuum. It is cold and has no friction. The properties of the vacuum remain largely unknown. A perfect vacuum is an ideal state that cannot practically be obtained in a laboratory, nor even in outer space, where there are a few hydrogen atoms per cubic centimeter at 10−14 pascal or 10−16 torr. All of the observable universe is also filled with large numbers of photons, the so-called cosmic background radiation, and quite likely a correspondingly large number of neutrinos. The current temperature is about 3 K, being merely 3 degrees above the absolute zero of temperature. Neither these photons nor the neutrinos produce a significant interaction with matter, so stars, planets and spacecraft move freely in this near perfect vacuum of interstellar space. Stars, planets and moons keep their atmosphere by gravitational attraction, so atmospheres have no firm boundary. The density of gas decreases with distance from the object. In Low Earth Orbit (about 300 km altitude) the atmospheric density is still sufficient to produce significant drag on satellites. Most Earth satellites operate in this region, and they need to fire their engines every few days to maintain orbit. The atmosphere in Low Earth Orbit is increasingly being polluted with man-made debris. Studies have discovered that some satellites retrieved from orbit are coated with a very thin layer of urine and fecal matter evidently released from Russian and US space missions. [http://see.msfc.nasa.gov/sparkman/Section_Docs/article_1.htm] Beyond planetary atmospheres, the pressure from photons and other particles from the sun become significant. Spacecraft can be buffeted by solar winds, but planets are too massive to be affected. The idea of using this wind with a solar sail has been proposed for interplanetary travel. The deep vacuum of space could make it an attractive environment for certain processes, for instance those that require ultraclean surfaces. In 1913, Norwegian explorer and physicist Kristian Birkeland may have been the first to predict that space is not only a plasma, but also contains "dark matter". He wrote: "It seems to be a natural consequence of our points of view to assume that the whole of space is filled with electrons and flying electric ions of all kinds. We have assumed that each stellar system in evolutions throws off electric corpuscles into space. It does not seem unreasonable therefore to think that the greater part of the material masses in the universe is found, not in the solar systems or nebulae, but in "empty" space. (See "Polar Magnetic Phenomena and Terrella Experiments", in The Norwegian Aurora Polaris Expedition 1902-1903 (publ. 1913, p.720)

The quantum-mechanical vacuum

Even an ideal vacuum, thought of as the complete absence of anything, will not in practice remain empty. One reason is that the walls of a vacuum chamber emit light in the form of black-body radiation: visible light if they are at a temperature of thousands of degrees, infrared light if they are cooler. If this soup of photons is in thermodynamic equilibrium with the walls, it can be said to have a particular temperature, as well as a pressure. More fundamentally, quantum mechanics predicts that vacuum energy can never be exactly zero. The lowest possible energy state is called the zero-point energy and consists of a seething mass of virtual particles that have brief existence. This is called vacuum fluctuation. While most agree that this represents a significant part of particle physics, it is a concept that would benefit from a deeper understanding than currently available. Vacuum fluctuations may also be related to the so-called cosmological constant in the theory of gravitation, if indeed this entity were to be observed in nature on a macroscopic scale. The best support for vacuum fluctuations is the Casimir effect. In quantum field theory and string theory, the term "vacuum" is used to represent the ground state in the Hilbert space, that is, the state with the lowest possible energy. In free (non-interacting) quantum field theories, this state is analogous to the ground state of a quantum harmonic oscillator. If the theory is obtained by quantization of a classical theory, each stationary point of the energy in the configuration space gives rise to a single vacuum. String theory is believed to be analogous to quantum field theory but one with a huge number of vacua - with the so-called anthropic landscape.

Historical interpretation

Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers did not like to admit the existence of a vacuum, asking themselves "how can 'nothing' be something?". Plato found the idea of a vacuum inconceivable. He believed that all physical things were instantiations of an abstract Platonic ideal, and could not imagine an "ideal" form of a vacuum. Similarly, Aristotle considered the creation of a vacuum impossible—nothing could not be something. Later Greek philosophers thought that a vacuum could exist outside the cosmos, but not inside it. In the Middle Ages, the idea of a vacuum was thought to be immoral or even heretical. The absence of anything implied the absence of God, and hearkened back to the void prior to the story of creation in the book of Genesis. Medieval thought experiments into the idea of a vacuum considered whether a vacuum was present, if only for an instant, between two flat plates when they were rapidly separated. There was much discussion of whether the air moved in quickly enough as the plates were separated, or, following William Burley whether a 'celestial agent' prevented the vacuum arising—that is, whether nature abhorred a vacuum. This speculation became irrelevant after the Paris condemnations of Bishop Tempier, which required there to be no restrictions on the powers of God, which led to the conclusion that God could create a vacuum if he so wished. Following work by Galileo, Evangelista Torricelli argued in 1643 that there was a vacuum at the top of a mercury barometer. Some people believe that although Torricelli produced the first vacuum, it was Blaise Pascal who recognized it for what it was. Robert Boyle later conducted experiments on the effects of a vacuum. For example, a canary exposed to vacuum would rupture open due to the lack of pressure. In 1654, Otto von Guericke conducted his famous Magdeburg hemispheres experiment, showing that teams of horses could not separate two hemispheres from which the air had been evacuated. Concurrently, theories of the nature of light had proposed the idea of a aethereal medium which would be the medium to convey waves of light (Newton relied on this idea to explain refraction and radiated heat). This evolved into the luminiferous aether idea of the 19th century, but it was known to have significant shortcomings. In 1887 the Michelson-Morley experiment, using an interferometer to attempt to detect the change in the speed of light caused by the Earth moving with respect to the aether, was a famous null result, showing that there really was no static, pervasive medium throughout space and through which the Earth moved as though through a wind. (Of course, if the aether were the medium in which light waves traveled and electromagnetic and gravitational fields manifest, then it would be exceedingly difficult to distinguish the characteristics of such medium from those of the field or fields one was in. It would no more be possible to show that the Earth moved in relation to such an aether than it would be to illustrate that it moved in relation to its own electromagnetic and gravitational fields.)

External links

- [http://www.avs.org/ American Vacuum Society]
- [http://scitation.aip.org/jvsta/ Journal of Vacuum Science and Technology A]
- [http://scitation.aip.org/jvstb/ Journal of Vacuum Science and Technology B]
- [http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970603.html Discussion of the effects on humans of exposure to hard vacuums].
- [http://www.arXiv.org/abs/hep-th/0012062 Vacuum Energy in High Energy Physics]
- [http://vacuumscientists.com/ Scientist of vacuum]
- http://www.mcallister.com/vacuum.html (Short History of Vacuum Terminology and Technology) Category:Industrial processes ja:真空

Capacitor

:See Capacitor (component) for a discussion of specific types. A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. A capacitor is occasionally referred to using the older term condenser. condenser condenser

History

In circa 600 BC, Thales of Miletus recorded that the Ancient Greeks could generate sparks by rubbing balls of amber on spindles. This is the triboelectric effect, the mechanical separation of charge in a dielectric. This effect is the basis of the capacitor. In October 1745, Ewald Georg von Kleist of Pomerania invented the first recorded capacitor: a glass jar coated inside and out with metal. The inner coating was connected to a rod that passed through the lid and ended in a metal sphere. By layering the insulator between two metal plates, von Kleist dramatically increased charge density. Before Kleist's discovery became widely known, a Dutch physicist Pieter van Musschenbroek independently invented a very similar capacitor in January 1746. It was named the Leyden jar, after the University of Leyden where van Musschenbroek worked. Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. Originally, the units of capacitance were in 'jars'. A jar is equivalent to about 1 nF. Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Volta in 1782 (derived from the Italian condensatore), with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor. Most non-English languages still use a word derived from "condensatore", like the French condensateur or the German kondensator. 1782

Physics

Overview

A capacitor consists of two electrodes or plates, each of which stores an opposite charge. These two plates are conductive and are separated by an insulator or dielectric. The charge is stored at the surface of the plates, at the boundary with the dielectric. Because each plate stores an equal but opposite charge, the total charge in the capacitor is always zero. dielectric dielectric

Capacitance

The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates: :

C = \frac

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge causes a potential difference of one volt across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (µF), nanofarads (nF) or picofarads (pF). The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates. The capacitance of a parallel-plate capacitor is given by: :

C \approx \frac; A >> d^2

[http://www.ttc-cmc.net/~fme/captance.html] where ε is the permittivity of the dielectric, A is the area of the plates and d is the spacing between them.

Stored energy

As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor owing to the electric field of these charges. Ever increasing work must be done against this ever increasing electric field as more charge is separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across the capacitor, and therefore the electric field. The energy stored is given by: :

E_\mathrm =  C V^2

where V is the voltage across the capacitor.

Hydraulic model

As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics: the pressure across the unit is proportional to the integral of the current, a steady-state current cannot pass through it but a pulse or alternating current can be transmitted, the capacitance of units connected in parallel is equivalent to the sum of their individual capacitances; etc.

In electric circuits

Circuits with DC sources

Electrons cannot directly pass across the dielectric from one plate of the capacitor to the other. When there is a current through a capacitor, electrons accumulate on one plate and electrons are removed from the other plate. This process is commonly called 'charging' the capacitor even though the capacitor is at all times electrically neutral. In fact, the current through the capacitor results in the separation rather than the accumulation of electric charge. This separation of charge causes an electric field to develop between the plates of the capacitor giving rise to voltage across the plates. This voltage V is directly proportional to the amount of charge separated Q. But Q is just the time integral of the current I through the capacitor. This is expressed mathematically as: :

I = \frac = C\frac

where :I is the current flowing in the conventional direction, measured in amperes :dV/dt is the time derivative of voltage, measured in volts / second. :C is the capacitance in farads For circuits with a constant (DC) voltage source, the voltage across the capacitor cannot exceed the voltage of the source. Thus, an equilibrium is reached where the voltage across the capacitor is constant and the current through the capacitor is zero. For this reason, it is commonly said that capacitors block DC current.

Circuits with AC sources

The capacitor current due to an AC voltage or current source reverses direction periodically. That is, the AC current alternately charges the plates in one direction and then the other. With the exception of the instant that the current changes direction, the capacitor current is non-zero at all times during a cycle. For this reason, it is commonly said that capacitors 'pass' AC current. However, at no time do electrons actually cross between the plates. Since the voltage across a capacitor is the integral of the current, as shown above, with sine waves in AC or signal circuits this results in a phase difference of 90 degrees, the current leading the voltage phase angle. It can be shown that the AC voltage across the capacitor is in quadrature with the AC current through the capacitor. That is, the voltage and current are 'out-of-phase' by a quarter cycle. The amplitude of the voltage depends on the amplitude of the current divided by the product of the frequency of the current with the capacitance, C. The ratio of the voltage amplitude to the current amplitude is called the reactance of the capacitor. This capacitive reactance is given by: :

X_C = -\frac = -\frac

where : $\omega = 2 \pi f$ , the angular frequency measured in radians per second :X_C = capacitive reactance, measured in ohms :f = frequency of AC in hertz :C = capacitance in farads and is analogous to the resistance of a resistor. Clearly, the reactance is inversely proportional to the frequency. That is, for very high-frequency alternating currents the reactance approaches zero so that a capacitor is nearly a short circuit to a very high frequency AC source. Conversely, for very low frequency alternating currents, the reactance increases without bound so that a capacitor is nearly an open circuit to a very low frequency AC source. Reactance is so called because the capacitor doesn't dissipate power, but merely stores energy. In electrical circuits, as in mechanics, there are two types of load, resistive and reactive. Resistive loads (analogous to an object sliding on a rough surface) dissipate energy that enters them, ultimately by electromagnetic emission (see Black body radiation), while reactive loads (analogous to a spring or frictionless moving object) retain the energy. The impedance of a capacitor is given by: :

Z_C = \frac = \frac

Hence, capacitive reactance is the negative imaginary component of impedance. The negative sign indicates that the current leads the voltage by 90° for a sinusoidal signal, as opposed to the inductor, where the current lags the voltage by 90°. Also significant is that the impedance is inversely proportional to the capacitance, unlike resistors and inductors for which impedances are linearly proportional to resistance and inductance respectively. This is why the series and shunt impedance formulae (given below) are the inverse of the resistive case. In series, impedances sum. In shunt, conductances sum. In a tuned circuit such as a radio receiver, the frequency selected is a function of the inductance (L) and the capacitance (C) in series, and is given by: :

f = \frac

This is the frequency at which resonance occurs in an RLC series circuit. For an ideal capacitor, the capacitor current is proportional to the time rate of change of the voltage across the capacitor where the constant of proportionality is the capacitance, C: :

i(t) = C \frac

The impedance in the frequency domain can be written as :

Z = \frac = - j X_C

. This shows that a capacitor has a high impedance to low-frequency signals (when ω is small) and a low impedance to high-frequency signals (when ω is large). This frequency dependent behaviour accounts for most uses of the capacitor (see "Applications", below). When using the Laplace transform in circuit analysis, the capacitive impedance is represented in the s domain by: :

Z(s)=\frac

Capacitors and displacement current

The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating as in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid.

Capacitor networks

A capacitor can be used to block the DC Current flowing within the circuit and therefore have important applications in coupling of ac signals between amplifier stages, whilst preventing dc from passing.

Series or parallel arrangements

Capacitors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent capacitance (C_eq): :A diagram of several capacitors, side by side, both leads of each connected to the same wires :

C_ = C_1  + C_2 + \cdots + C_n  \,

The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total capacitance: :A diagram of several capacitors, connected end to end, with the same amount of current going through each :

\frac = \frac + \frac + \cdots +  \frac

In parallel, the total charge stored is the sum of the charge in each capacitor. While in series, the charge on each capacitor is the same. One possible reason to connect capacitors in series is to increase the overall voltage rating. In practice, a very large resistor might be connected across each capacitor to ensure that the total voltage is divided appropriately for the individual ratings, rather than by minute differences in the capacitance values. Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity, so that at any given time one of the capacitors is not conducting.

Capacitor/inductor duality

In mathematical terms, the ideal capacitor can be considered as an inverse of the ideal inductor, because the voltage-current equations of the two devices can be transformed into one another by exchanging the voltage and current terms. Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time.

Applications

Energy storage

A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery. The recent commercial availability of very large value capacitors, close to one farad in size, has enabled such components to allow batteries to be changed in electronic devices without the memory being lost, for instance, or for energy storage for delivery during extreme peak demands, as often found in the enormously powerful car audio systems now seen.

Signal processing

The energy stored in a capacitor can be used to represent information, either in binary form, as in computers, or in analogue form, as in switched-capacitor circuits and bucket-brigade delay lines. Capacitors can be used in analog circuits as components of integrators or more complex filters and in negative feedback loop stabilization. Signal processing circuits also use capacitors to integrate a current signal.

Power supply applications

Capacitors are commonly used in power supplies where they smooth the output of a full or half wave rectifier. They can also be used in charge pump circuits as the energy storage element in the generation of higher voltages than the input voltage. Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. Capacitors are used in power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in Volt-Amperes reactive (VAr). The purpose is to match the inductive loading of machinery which contains motors, to make the load appear to be mostly resistive. Capacitors are also used in parallel to interrupt units of a high-voltage circuit breaker in order to distribute the voltage between these units. In this case they are called grading capacitors. In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see electrolytic capacitor). Non-polarized electrolytic capacitors used for signal filtering are typically drawn with two curved plates. Other non-polarized capacitors are drawn with two straight plates.

Tuned circuits

Capacitors and inductors are applied together in tuned circuits to select information in particular frequency bands. For example, radio receivers rely on variable capacitors to tune the station frequency. Speakers use passive analog crossovers, and analog equalizers use capacitors to select different audio bands.

Signal coupling

Because capacitors pass AC but block DC signals (when charged up to the applied dc voltage), they are often used to separate the AC and DC components of a signal. This method is known as AC coupling. (Sometimes transformers are used for the same effect.) Here, a large value of capacitance, whose value need not be accurately controlled, but whose reactance is small at the signal frequency, is employed. Capacitors for this purpose designed to be fitted through a metal panel are called feed-through capacitors, and have a slightly different schematic symbol.

Transducer applications

Although capacitors usually maintian a fixed physical structure and utilization varies the electrical voltage and current, the effects of varying the physical and/or electrical characteristics of the dielectric with a fixed electrical supply can also be of use. Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors with a flexible plate can be used to measure strain or pressure. Capacitors are used as the transducer in condenser microphones, where one plate is moved by air pressure, relative to the fixed position fo the other plate.

Noise filters, motor starters, and snubbers

When an inductive circuit is opened, the energy stored in the magnetic field of the inductance collapses quickly, creating a large voltage across the open circuit of the switch or relay. If the inductance is large enough, the energy will generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A snubber capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in contact breaker ignition systems, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but will still radiate undesirable radio frequency interference (RFI), which a filter capacitor absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy more slowly and minimize RFI. Such resistor-capacitor combinations are available in a single package. In an inverse fashion, to initiate current quickly through an inductive circuit requires a greater voltage than required to maintain it; in uses such as large motors, this can cause undesirable startup characteristics, and a motor starting capacitor is used to store enough energy to give the current the initial push required to start the motor up.

Weapons applications

An obscure military application of the capacitor is in an EMP weapon. A plastic explosive is used for the dielectric. The capacitor is charged up and the explosive is detonated. The capacitance becomes smaller, but the charge on the plates stays the same. This creates a high-energy electromagnetic shock wave capable of destroying unprotected electronics for miles around. These devices are rumored to have been employed by the US in the 2003 invasion of Iraq, though this is highly unlikely. See Explosively pumped flux compression generator. Large high-voltage low-inductance capacitors are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons, and are also used as power supplies for electromagnetic guns such as railguns or coilguns.

Ideal and nonideal capacitors

In practice, this ideal model of the capacitor often has to be modified to reflect real world capacitor construction and operation. The most obvious example is electrolytic capacitors, where the capacitor is polarized such that when the voltage is connected in reversed fashion, the capacitor acts as a resistor. Similar problems of dielectric leakage are a constant complication of all capacitor design however, and have led to constant improvements in capacitor design, as the material used for dielectrics has changed from oiled paper to mylar and from ceramic to Teflon. This also addresses the related problem of dielectric stability; oiled or electrolyte soaked paper dries out over time, reducing the capacitance and increasing leakage, a problem reduced in modern components. On the other hand, the requirements of large plate area for reasonably useful capacitor values as well as reasonable packaging resulted in the universal practice of rolling the plate/dielectric sandwich into a cylinder, which was then encapsulated. However, this process also creates an inductance in series with