Gas constant: Difference between revisions
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! Values of ''R'' |
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! Units <br /> [[Ideal gas law|(V·P·T<sup>-1</sup>·n<sup>-1</sup>)]] |
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|- [[International Organization for Standardization | ISO]] |
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| 8.314472 |
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| [[Joule|J]]·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 0.0820574587 |
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| [[Liter|L]]·[[atmosphere (unit)|atm]]·[[Kelvin|K]]<sup>-1</sup>·[[Mole (unit)|mol]]<sup>-1</sup> |
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|- |
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| 83.14472 |
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| [[centimeter|cm]]<sup>3</sup>·[[bar (unit)|bar]]·[[mole (unit)|mol]]<sup>-1</sup>·[[Kelvin|K]]<sup>-1</sup> |
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|- |
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| 8.20574587 × 10<sup>-5</sup> |
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| m<sup>3</sup>·atm·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 8.314472 |
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| cm<sup>3</sup>·MPa·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 8.314472 |
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| L·k[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 8.314472 |
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| m<sup>3</sup>·[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 62.36367 |
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| L·[[mmHg]]·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 62.36367 |
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| L·Torr·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 83.14472 |
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| L·mbar·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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|- |
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| 0.08314472 |
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| L·bar·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 1.987 |
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| [[calorie|cal]]·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 6.132440 |
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| [[foot-pound|lbf]]·ft·K<sup>-1</sup>·g-mol<sup>-1</sup> |
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|- |
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| 10.73159 |
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| ft<sup>3</sup>·psi· [[Rankine scale|°R]]<sup>-1</sup>·[[lb-mol]]<sup>-1</sup> |
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|- |
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| 0.7302413 |
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| ft<sup>3</sup>·atm·°R<sup>-1</sup>·lb-mol<sup>-1</sup> |
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|- |
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| 998.9701 |
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| ft<sup>3</sup>·mmHg·K<sup>-1</sup>·lb-mol<sup>-1</sup> |
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|- |
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| 8.314472 × 10<sup>7</sup> |
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| erg·K<sup>-1</sup>·mol<sup>-1</sup> |
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|- |
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| 1716 '''(Air only)''' |
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| ft·lb·°R<sup>-1</sup>·[[slug (unit)|slug]]<sup>-1</sup> |
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|- |
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| 286.9 '''(Air only)''' |
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| N·m·kg<sup>-1</sup>·K<sup>-1</sup> |
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|- |
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| 286.9 '''(Air only)''' |
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| J·kg<sup>-1</sup>·K<sup>-1</sup> |
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|} |
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The '''gas constant''' (also known as the '''molar''', '''universal''', or '''ideal gas constant''', usually denoted by symbol '''''R''''') is a [[physical constant]] which is featured in a large number of fundamental equations in the physical sciences, such as the [[ideal gas law]] and the [[Nernst equation]]. It is equivalent to the [[Boltzmann constant]], but expressed in units of [[energy]] (i.e. the pressure-volume product) per [[kelvin]] per ''[[mole (unit)|mole]]'' (rather than energy per kelvin per ''particle''). |
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Its value is: |
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:'''''R'' = 8.314472(15) J · K<sup>-1</sup> · mol<sup>-1</sup>''' |
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The two digits in [[Bracket|parentheses]] are the uncertainty ([[standard deviation]]) in the last two digits of the value. |
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The gas constant occurs in the simplest [[equation of state]], the [[ideal gas law]], as follows: |
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:<math>P = \frac{nRT}{V} = \frac{RT}{V_{\rm m}}</math> |
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where: |
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: <math>P\,\!</math> is the absolute [[pressure]] |
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: <math>T\,\!</math> is absolute [[thermodynamic temperature|temperature]] |
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: <math>V\,\!</math> is the volume the gas occupies |
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: <math>n\,\!</math> is the amount of gas (the number of gas molecules, usually in [[mole (unit)|mole]]s) |
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: <math>V_{\rm m}\,\!</math> is the [[molar volume]] |
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The gas constant has the same units as specific [[entropy]]. |
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===Relationship with the Boltzmann constant=== |
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The [[Boltzmann constant]] ''k<sub>B</sub>'' (often abbreviated ''k'') may be used in place of the gas constant by working in pure particle count, ''N'', rather than number of moles, ''n'', since |
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:<math>\qquad R=N_A k_B\,\!</math>, |
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where <math>N_A</math> is [[Avogadro constant|Avogadro's number]]. |
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For example, the ideal gas law in terms of Boltzmann's constant is <math>PV=Nk_BT\,\!</math>. |
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===Specific gas constant=== |
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The '''specific gas constant''' of a gas or a mixture of gases (<math>R</math>) is given by the universal gas constant, divided by the [[molar mass]] (<math>M</math>) of the gas/mixture. |
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:<math> R = \frac{\bar{R}}{M} </math> |
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It is common to represent the specific gas constant by the symbol <math>R</math>. In such cases the context and/or units of <math>R</math> should make it clear as to which gas constant is being referred to. For example, the equation for the [[speed of sound#speed in ideal gases and in air|speed of sound]] is usually written in terms of the specific gas constant. |
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The specific gas constant of dry [[air]] is |
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:<math>R_\mathrm{dry\,air} = 287.05 \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}</math> |
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==US Standard Atmosphere== |
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The [[US Standard Atmosphere]], 1976 (USSA1976) defines the Universal Gas Constant as:<ref>{{cite web |url=http://www.sworld.com.au/steven/space/atmosphere/ |title=Standard Atmospheres |accessdate=2007-01-07}}</ref><ref name="USSA1976">[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf U.S. Standard Atmosphere], 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MiB).</ref> |
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:<math>\bar{R} = 8.31432\times 10^3 \frac{\mathrm{N \cdot m}}{\mathrm{kmol \cdot K}} </math> |
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The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant.<ref name="USSA1976"/> This disparity is not a significant departure from accuracy, and USSA1976 uses this value of ''R'' for all the calculations of the standard atmosphere. When using the [[International Organization for Standardization|ISO]] value of ''R'', the calculated pressure increases by only 0.62 pascals at 11,000 meters (the equivalent of a difference of only 0.174 meters – or 6.8 inches) and an increase of 0.292 pascals at 20,000 meters (the equivalent of a difference of only 0.338 meters – or 13.2 inches). |
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== See also == |
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* [[Boltzmann constant]] |
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* [[measurement uncertainty|Standard measurement uncertainty]] |
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==References== |
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<!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags--> |
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<references/> |
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== External links == |
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* [http://physics.nist.gov/cgi-bin/cuu/Value?r|search_for=gas+constant Gas Constant CODATA Value] at [[NIST]] |
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* [http://physics.nist.gov/cgi-bin/cuu/Value?k|search_for=boltzmann Boltzmann Constant CODATA Value] at [[NIST]] |
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[[Category:Gases|Constant]] |
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[[Category:Physical constants]] |
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[[Category:Amount of substance]] |
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[[ar:ثابت الغازات العام]] |
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[[bs:Univerzalna gasna konstanta]] |
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[[bg:Универсална газова константа]] |
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[[cs:Molární plynová konstanta]] |
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[[da:Gaskonstant]] |
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[[de:Universelle Gaskonstante]] |
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[[et:Universaalne gaasikonstant]] |
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[[es:Constante universal de los gases ideales]] |
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[[eo:Universala gaskonstanto]] |
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[[fa:ثابت عمومی گازها]] |
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[[fr:Constante universelle des gaz parfaits]] |
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[[ko:기체 상수]] |
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[[it:Costante dei gas]] |
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[[he:קבוע הגזים]] |
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[[lt:Dujų konstanta]] |
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[[hu:Egyetemes gázállandó]] |
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[[nl:Gasconstante]] |
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[[ja:気体定数]] |
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[[mr:वैश्विक वायू एकक]] |
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[[no:Gasskonstant]] |
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[[nn:Gasskonstant]] |
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[[pl:Stała gazowa]] |
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[[pt:Constante universal dos gases perfeitos]] |
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[[ru:Универсальная газовая постоянная]] |
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[[sk:Univerzálna plynová konštanta]] |
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[[sl:Splošna plinska konstanta]] |
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[[fi:Kaasuvakio]] |
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[[sv:Allmänna gaskonstanten]] |
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[[th:ค่าคงตัวของแก๊ส]] |
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[[vi:Hằng số khí]] |
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[[uk:Газова стала]] |
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[[zh:氣體常數]] |
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Revision as of 00:40, 13 October 2008
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