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| == '''[[Ideal gas law]]''' ==
| | {{:{{FeaturedArticleTitle}}}} |
| ''by [[User:Milton Beychok|Milton Beychok]] and [[User:Paul Wormer|Paul Wormer]] (and [[User:Daniel Mietchen|Daniel Mietchen]] and [[User:David E. Volk|David E. Volk]])
| | <small> |
| | | ==Footnotes== |
| ----
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| {| class="wikitable" style="float: right;" | |
| ! Values of ''R''
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| ! Units
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| |-
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| | 8.314472
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| | [[Joule|J]]·[[Kelvin|K]]<sup>-1</sup>·[[Mole (unit)|mol]]<sup>-1</sup>
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| |-
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| | 0.082057
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| | [[Liter|L]]·[[atmosphere (unit)|atm]]·K<sup>-1</sup>·mol<sup>-1</sup>
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| |-
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| | 8.205745 × 10<sup>-5</sup>
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| | [[metre|m]]<sup>3</sup>·atm·K<sup>-1</sup>·mol<sup>-1</sup>
| |
| |-
| |
| | 8.314472
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| | L·k[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup>
| |
| |-
| |
| | 8.314472
| |
| | m<sup>3</sup>·Pa·K<sup>-1</sup>·mol<sup>-1</sup>
| |
| |-
| |
| | 62.36367
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| | L·[[mmHg]]·K<sup>-1</sup>·mol<sup>-1</sup>
| |
| |-
| |
| | 62.36367
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| | L·[[torr]]·K<sup>-1</sup>·mol<sup>-1</sup>
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| |-
| |
| | 83.14472
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| | L·m[[Bar (unit)|bar]]·K<sup>-1</sup>·mol<sup>-1</sup>
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| |-
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| | 10.7316
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| | [[Foot (unit)|ft]]<sup>3</sup>·[[Psi (unit)|psi]]· [[Rankine scale|°R]]<sup>-1</sup>·[[lb-mol]]<sup>-1</sup>
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| |-
| |
| | 0.73024
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| | ft<sup>3</sup>·atm·°R<sup>-1</sup>·lb-mol<sup>-1</sup>
| |
| |}
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| The '''[[ideal gas law]]''' is the [[equation of state]] of an '''ideal gas''' (also known as a '''perfect gas''') that relates its [[Pressure#Absolute pressure versus gauge pressure|absolute pressure]] ''p'' to its [[temperature|absolute temperature]] ''T''. Further parameters that enter the equation are the [[volume]] ''V'' of the container holding the gas and the [[amount of substance|amount]] ''n'' (in [[mole (unit)|moles]]) of gas contained in there. The law reads
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| :<math> pV = nRT \,</math>
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| where ''R'' is the [[molar gas constant]], defined as the product of the [[Boltzmann constant]] ''k''<sub>B</sub> and [[Avogadro's constant]] ''N''<sub>A</sub>
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| :<math>
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| R \equiv N_\mathrm{A} k_\mathrm{B}
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| </math> | |
| Currently, the most accurate value of R is:<ref>[http://physics.nist.gov/cgi-bin/cuu/Value?r Molar gas constant] Obtained from the [[NIST]] website. [http://www.webcitation.org/query?url=http%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fr&date=2009-01-03 (Archived by WebCite® at http://www.webcitation.org/5dZ3JDcYN on Jan 3, 2009)]</ref> 8.314472 ± 0.000015 J·K<sup>-1</sup>·mol<sup>-1</sup>.
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| The law applies to ''ideal gases'' which are hypothetical gases that consist of [[molecules]]<ref>Atoms may be seen as mono-atomic molecules.</ref> that do not interact, i.e., that move through the container independently of each other. In contrast to what is sometimes stated (see, e.g., Ref.<ref>[http://en.wikipedia.org/w/index.php?oldid=261421829 Wikipedia: Ideal gas law] Version of January 2, 2009</ref>) an ideal gas does not necessarily consist of [[point particle]]s without internal structure, but may be formed by polyatomic molecules with internal rotational, vibrational, and electronic [[degrees of freedom]]. The ideal gas law describes the motion of the [[center of mass|centers of mass]] of the molecules and, indeed, mass centers may be seen as structureless point masses. However, for other properties of ideal gases, such as [[entropy (thermodynamics)|entropy]], the internal structure may play a role.
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| The ideal gas law is a useful approximation for calculating temperatures, volumes, pressures or amount of substance for many gases over a wide range of values, as long as the temperatures and pressures are far from the values where [[condensation]] or [[sublimation]] occur.
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| Real gases deviate from ideal gas behavior because the intermolecular attractive and repulsive forces cause the motions of the molecules to be correlated. The deviation is especially significant at low temperatures or high pressures, i.e., close to condensation. A conventional measure for this deviation is the [[Compressibility factor (gases)|compressibility factor]].
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| There are many equations of state available for use with real gases, the simplest of which is the [[van der Waals equation]].
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| === Historic background ===
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| The early work on the behavior of gases began in pre-industrialized [[Europe]] in the latter half of the 17th century by [[Robert Boyle]] who formulated ''[[Boyle's law]]'' in 1662 (independently confirmed by [[Edme Mariotte]] at about the same time).<ref name=Savidge>[http://www.ceesi.com/docs_techlib/events/ishm2003/Docs/1040.pdf Compressibility of Natural Gas] Jeffrey L. Savidge, 78th International School for Hydrocarbon Measurement (Class 1040), 2003. From the website of the Colorado Engineering Experiment Station, Inc. (CEESI).</ref> Their work on air at low pressures established the inverse relationship between pressure and volume, ''V'' = constant / ''p'' at constant temperature and a fixed amount of air. ''Boyle's Law'' is often referred to as the ''Boyles-Mariotte Law''.
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| ''[[Ideal gas law|.... (read more)]]''
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| {| class="wikitable collapsible collapsed" style="width: 90%; float: center; margin: 0.5em 1em 0.8em 0px;"
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| ! style="text-align: center;" | [[Ideal gas law#References|notes]]
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| {{reflist|2}} | | {{reflist|2}} |
| |}
| | </small> |
Napoleon (Napoleon Bonaparte or, after 1804, Napoleon I, Emperor of the French) was a world historic figure and dictator of France from 1799 to 1814. He was the greatest general of his age--perhaps any age, with a sure command of battlefield tactics and campaign strategies, As a civil leader he played a major role in the French Revolution, then ended it when he became dictator in 1799 and Emperor of France in 1804 He modernized the French military, fiscal, political legal and religious systems. He fought an unending series of wars against Britain with a complex, ever-changing coalition of European nations on both sides. Refusing to compromise after his immense defeat in Russia in 1812, he was overwhelmed by a coalition of enemies and abdicated in 1814. In 1815 he returned from exile, took control of France, built a new army, and in 100 days almost succeeded--but was defeated at Waterloo and exiled to a remote island. His image and memory are central to French national identity, but he is despised by the British and Russians and is a controversial figure in Germany and elsewhere in Europe.
Rise to Power
Once the Revolution had begun, so many of the aristocratic officers turned against the Revolutionary government, or were exiled or executed, that a vacuum of senior leadership resulted. Promotions came very quickly now, and loyalty to the Revolution was as important as technical skill; Napoleon had both. His demerits were overlooked as he was twice reinstated, promoted, and allowed to collect his back pay. Paris knew him as an intellectual soldier deeply involved in politics. His first test of military genius came at Toulon in 1793, where the British had seized this key port. Napoleon, an acting Lieutenant-Colonel, used his artillery to force the British to abandon the city. He was immediately promoted by the Jacobin radicals under Robespierre to brigadier-general, joining the ranks of several brilliant young generals. He played a major role in defending Paris itself from counter-revolutionaries, and became the operational planner for the Army of Italy and planned two successful attacks in April 1794. He married Josephine (Rose de Beauharnais) in 1796, after falling violently in love with the older aristocratic widow.[1]
- ↑ Englund pp 63-73, 91-2, 97-8
