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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
| |
| | 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
| |
| | L·[[torr]]·K<sup>-1</sup>·mol<sup>-1</sup>
| |
| |-
| |
| | 83.14472
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| | L·m[[Bar (unit)|bar]]·K<sup>-1</sup>·mol<sup>-1</sup>
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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;" | [[Volatility (chemistry)#References|notes]]
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| {{reflist|2}} | | {{reflist|2}} |
| |}
| | </small> |
Paramhansa Yogananda circa 1920.
Paramhansa Yogananda (5 Jan 1893–7 Mar 1952) was one of the first Indian teachers from the Hindu spiritual tradition to reside permanently in the West, and in particular, he was the first to teach yoga to Americans. He emphasized the universality of the great religions, and ceaselessly taught that all religions, especially Hinduism and Christianity, were essentially the same in their essence. The primary message of Yogananda was to practice the scientific technique of kriya yoga to be released from all human suffering.
He emigrated from India to the United States in 1920 and eventually founded the Self-Realization Fellowship there in Los Angeles, California. He published his own life story in a book called Autobiography of a Yogi, first published in 1946. In the book, Yogananda provided some details of his personal life, an introduction to yoga, meditation, and philosophy, and accounts of his world travels and encounters with a wide variety of saints and colorful personalities, including Therese Neumann, Mohandas K. Gandhi, Luther Burbank, and Jagadis C. Bose.
Paramhamsa, also spelled Paramahamsa, is a Sanskrit title used for Hindu spiritual teachers who have become enlightened. The title of Paramhansa originates from the legend of the swan. The swan (hansa) is said to have a mythical ability to sip only the milk from a water-and-milk mixture, separating out the more watery part. The spiritual master is likewise said to be able to live in a world like a supreme (param) swan, and only see the divine, instead of all the evil mixed in there too, which the worldly person sees.
Yogananda is considered by his followers and many religious scholars to be a modern avatar.
In 1946, Yogananda published his Autobiography of a Yogi. It has since been translated into 45 languages, and in 1999 was designated one of the "100 Most Important Spiritual Books of the 20th Century" by a panel of spiritual authors convened by Philip Zaleski and HarperCollins publishers.
Awake: The Life of Yogananda is a 2014 documentary about Paramhansa Yogananda, in English with subtitles in seventeen languages. The documentary includes commentary by George Harrison and Ravi Shankar, among others.[1][2]
