Difference between revisions of "Gas constant" - New World Encyclopedia
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{| class="wikitable" style="float: right;" | {| class="wikitable" style="float: right;" | ||
! Values of ''R'' | ! Values of ''R'' | ||
− | ! Units | + | ! Units <br /> [[Ideal gas law|(V·P·T<sup>-1</sup>·n<sup>-1</sup>)]] |
|- [[International Organization for Standardization | ISO]] | |- [[International Organization for Standardization | ISO]] | ||
| 8.314472 | | 8.314472 | ||
− | | | + | | [[Joule|J]]·K<sup>-1</sup>·mol<sup>-1</sup> |
|- | |- | ||
− | | 0. | + | | 0.0820574587 |
− | | | + | | [[Liter|L]]·[[atmosphere (unit)|atm]]·[[Kelvin|K]]<sup>-1</sup>·[[Mole (unit)|mol]]<sup>-1</sup> |
|- | |- | ||
| 8.20574587 × 10<sup>-5</sup> | | 8.20574587 × 10<sup>-5</sup> | ||
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|- | |- | ||
| 8.314472 | | 8.314472 | ||
− | | | + | | L·k[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup> |
|- | |- | ||
| 8.314472 | | 8.314472 | ||
− | | m<sup>3</sup> | + | | m<sup>3</sup>·[[Pascal (unit)|Pa]]·K<sup>-1</sup>·mol<sup>-1</sup> |
|- | |- | ||
− | | 62. | + | | 62.36367 |
− | | | + | | L·[[mmHg]]·K<sup>-1</sup>·mol<sup>-1</sup> |
|- | |- | ||
− | | 62. | + | | 62.36367 |
| L·Torr·K<sup>-1</sup>·mol<sup>-1</sup> | | L·Torr·K<sup>-1</sup>·mol<sup>-1</sup> | ||
|- | |- | ||
Line 32: | Line 31: | ||
|- | |- | ||
| 1.987 | | 1.987 | ||
− | | cal | + | | [[calorie|cal]]·K<sup>-1</sup>·mol<sup>-1</sup> |
|- | |- | ||
| 6.132440 | | 6.132440 | ||
− | | | + | | [[foot-pound|lbf]]·ft·K<sup>-1</sup>·g-mol<sup>-1</sup> |
|- | |- | ||
− | | 10. | + | | 10.73159 |
− | | ft<sup>3</sup> | + | | ft<sup>3</sup>·psi· [[Rankine scale|°R]]<sup>-1</sup>·[[lb-mol]]<sup>-1</sup> |
|- | |- | ||
− | | 8. | + | | 0.7302413 |
− | | | + | | ft<sup>3</sup>·atm·°R<sup>-1</sup>·lb-mol<sup>-1</sup> |
+ | |- | ||
+ | | 998.9701 | ||
+ | | ft<sup>3</sup>·mmHg·K<sup>-1</sup>·lb-mol<sup>-1</sup> | ||
+ | |- | ||
+ | | 8.314472 × 10<sup>7</sup> | ||
+ | | erg·K<sup>-1</sup>·mol<sup>-1</sup> | ||
+ | |- | ||
+ | | 1716 '''(Air only)''' | ||
+ | | ft·lb·°R<sup>-1</sup>·[[slug (unit)|slug]]<sup>-1</sup> | ||
+ | |- | ||
+ | | 286.9 '''(Air only)''' | ||
+ | | N·m·kg<sup>-1</sup>·K<sup>-1</sup> | ||
|- | |- | ||
− | | | + | | 286.9 '''(Air only)''' |
− | | | + | | J·kg<sup>-1</sup>·K<sup>-1</sup> |
|} | |} | ||
− | The '''gas constant''' (also known as the '''universal''' or '''ideal gas constant''', usually denoted by symbol '''''R''''') is a [[physical constant]] | + | 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: | Its value is: | ||
:'''''R'' = 8.314472(15) J · K<sup>-1</sup> · mol<sup>-1</sup>''' | :'''''R'' = 8.314472(15) J · K<sup>-1</sup> · mol<sup>-1</sup>''' | ||
− | The two digits | + | The two digits in [[Bracket|parentheses]] are the uncertainty ([[standard deviation]]) in the last two digits of the value. |
− | + | The gas constant occurs in the simplest [[equation of state]], the [[ideal gas law]], as follows: | |
− | + | :<math>P = \frac{nRT}{V} = \frac{RT}{V_{\rm m}}</math> | |
− | :<math> | + | where: |
+ | : <math>P\,\!</math> is the absolute [[pressure]] | ||
+ | : <math>T\,\!</math> is absolute [[thermodynamic temperature|temperature]] | ||
+ | : <math>V\,\!</math> is the volume the gas occupies | ||
+ | : <math>n\,\!</math> is the amount of gas (the number of gas molecules, usually in [[mole (unit)|mole]]s) | ||
+ | : <math>V_{\rm m}\,\!</math> is the [[molar volume]] | ||
− | + | The gas constant has the same units as specific [[entropy]]. | |
− | + | ||
+ | ===Relationship with the Boltzmann constant=== | ||
+ | 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 | ||
+ | :<math>\qquad R=N_A k_B\,\!</math>, | ||
+ | where <math>N_A</math> is [[Avogadro constant|Avogadro's number]]. | ||
+ | For example, the ideal gas law in terms of Boltzmann's constant is <math>PV=Nk_BT\,\!</math>. | ||
===Specific gas constant=== | ===Specific gas constant=== | ||
− | The '''specific gas constant''' of a gas or a mixture of gases ( | + | The '''specific gas constant''' of a gas or a mixture of gases (R)is given by the universal gas constant, divided by the [[molar mass]] (<math>M</math>) of the gas/mixture. |
− | :<math> | + | :<math> R = \frac{\bar{R}}{M} </math> |
− | 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]] | + | 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. |
The specific gas constant of dry [[air]] is | The specific gas constant of dry [[air]] is | ||
Line 82: | Line 91: | ||
==US Standard Atmosphere== | ==US Standard Atmosphere== | ||
− | The [[US Standard Atmosphere]], 1976 (USSA1976) defines the Universal Gas Constant | + | 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> |
− | :<math>R = 8.31432\ | + | :<math>\bar{R} = 8.31432\times 10^3 \frac{\mathrm{N \cdot m}}{\mathrm{kmol \cdot K}} </math> |
− | 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"/> | + | 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). |
== See also == | == See also == | ||
* [[Boltzmann constant]] | * [[Boltzmann constant]] | ||
− | == | + | ==References== |
<!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags—> | <!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags—> | ||
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== External links == | == 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]] | * [http://physics.nist.gov/cgi-bin/cuu/Value?r|search_for=gas+constant Gas Constant CODATA Value] at [[NIST]] | ||
* [http://physics.nist.gov/cgi-bin/cuu/Value?k|search_for=boltzmann Boltzmann Constant CODATA Value] at [[NIST]] | * [http://physics.nist.gov/cgi-bin/cuu/Value?k|search_for=boltzmann Boltzmann Constant CODATA Value] at [[NIST]] | ||
− | [[Category: | + | [[Category:Gases|Constant]] |
− | [[Category: | + | [[Category:Physical constants]] |
− | + | [[ar:ثابت الغازات العام]] | |
+ | [[bs:Univerzalna gasna konstanta]] | ||
+ | [[bg:Универсална газова константа]] | ||
+ | [[cs:Molární plynová konstanta]] | ||
+ | [[da:Gaskonstant]] | ||
+ | [[de:Universelle Gaskonstante]] | ||
+ | [[et:Universaalne gaasikonstant]] | ||
+ | [[es:Constante universal de los gases ideales]] | ||
+ | [[eo:Universala gaskonstanto]] | ||
+ | [[fa:ثابت عمومی گازها]] | ||
+ | [[fr:Constante universelle des gaz parfaits]] | ||
+ | [[ko:기체 상수]] | ||
+ | [[it:Costante dei gas]] | ||
+ | [[he:קבוע הגזים]] | ||
+ | [[lt:Dujų konstanta]] | ||
+ | [[hu:Egyetemes gázállandó]] | ||
+ | [[nl:Gasconstante]] | ||
+ | [[ja:気体定数]] | ||
+ | [[mr:वैश्विक वायू एकक]] | ||
+ | [[no:Gasskonstant]] | ||
+ | [[nn:Gasskonstant]] | ||
+ | [[pl:Stała gazowa]] | ||
+ | [[pt:Constante universal dos gases perfeitos]] | ||
+ | [[ru:Универсальная газовая постоянная]] | ||
+ | [[sk:Univerzálna plynová konštanta]] | ||
+ | [[sl:Splošna plinska konstanta]] | ||
+ | [[fi:Kaasuvakio]] | ||
+ | [[sv:Allmänna gaskonstanten]] | ||
+ | [[th:ค่าคงตัวของแก๊ส]] | ||
+ | [[vi:Hằng số khí]] | ||
+ | [[uk:Газова стала]] | ||
+ | [[zh:氣體常數]] |
Revision as of 18:52, 15 July 2008
Values of R | Units (V·P·T-1·n-1) |
---|---|
8.314472 | J·K-1·mol-1 |
0.0820574587 | L·atm·K-1·mol-1 |
8.20574587 × 10-5 | m3·atm·K-1·mol-1 |
8.314472 | cm3·MPa·K-1·mol-1 |
8.314472 | L·kPa·K-1·mol-1 |
8.314472 | m3·Pa·K-1·mol-1 |
62.36367 | L·mmHg·K-1·mol-1 |
62.36367 | L·Torr·K-1·mol-1 |
83.14472 | L·mbar·K-1·mol-1 |
1.987 | cal·K-1·mol-1 |
6.132440 | lbf·ft·K-1·g-mol-1 |
10.73159 | ft3·psi· °R-1·lb-mol-1 |
0.7302413 | ft3·atm·°R-1·lb-mol-1 |
998.9701 | ft3·mmHg·K-1·lb-mol-1 |
8.314472 × 107 | erg·K-1·mol-1 |
1716 (Air only) | ft·lb·°R-1·slug-1 |
286.9 (Air only) | N·m·kg-1·K-1 |
286.9 (Air only) | J·kg-1·K-1 |
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 (rather than energy per kelvin per particle).
Its value is:
- R = 8.314472(15) J · K-1 · mol-1
The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value.
The gas constant occurs in the simplest equation of state, the ideal gas law, as follows:
where:
- is the absolute pressure
- is absolute temperature
- is the volume the gas occupies
- is the amount of gas (the number of gas molecules, usually in moles)
- is the molar volume
The gas constant has the same units as specific entropy.
Relationship with the Boltzmann constant
The Boltzmann constant kB (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
- ,
where is Avogadro's number. For example, the ideal gas law in terms of Boltzmann's constant is .
Specific gas constant
The specific gas constant of a gas or a mixture of gases (R)is given by the universal gas constant, divided by the molar mass () of the gas/mixture.
It is common to represent the specific gas constant by the symbol . In such cases the context and/or units of should make it clear as to which gas constant is being referred to. For example, the equation for the speed of sound is usually written in terms of the specific gas constant.
The specific gas constant of dry air is
US Standard Atmosphere
The US Standard Atmosphere, 1976 (USSA1976) defines the Universal Gas Constant as:[1][2]
The USSA1976 does recognize, however, that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant.[2] 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 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).
See also
- Boltzmann constant
ReferencesISBN links support NWE through referral fees
- ↑ Standard Atmospheres. Retrieved 2007-01-07.
- ↑ 2.0 2.1 U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MiB).
External links
- Gas Constant CODATA Value at NIST
- Boltzmann Constant CODATA Value at NIST
ar:ثابت الغازات العام bs:Univerzalna gasna konstanta bg:Универсална газова константа cs:Molární plynová konstanta da:Gaskonstant de:Universelle Gaskonstante et:Universaalne gaasikonstant es:Constante universal de los gases ideales eo:Universala gaskonstanto fa:ثابت عمومی گازها fr:Constante universelle des gaz parfaits ko:기체 상수 it:Costante dei gas he:קבוע הגזים lt:Dujų konstanta hu:Egyetemes gázállandó nl:Gasconstante ja:気体定数 mr:वैश्विक वायू एकक no:Gasskonstant nn:Gasskonstant pl:Stała gazowa pt:Constante universal dos gases perfeitos ru:Универсальная газовая постоянная sk:Univerzálna plynová konštanta sl:Splošna plinska konstanta fi:Kaasuvakio sv:Allmänna gaskonstanten th:ค่าคงตัวของแก๊ส vi:Hằng số khí uk:Газова стала zh:氣體常數