Editing Gas constant (section)

{{short description|Physical constant  equivalent to the Boltzmann constant, but in different units}}
{| class="wikitable" style="margin: 0 0 0 0.5em; float: right;"
! Value of {{math|''R''}}{{physconst|R|ref=only}}
! Unit
|-
| colspan="2" |'''[[International System of Units|SI units]]'''
|-
| {{val|8.31446261815324}}
| [[joule|J]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|8.31446261815324}}
| [[cubic metre|m<sup>3</sup>]]⋅[[pascal (unit)|Pa]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|8.31446261815324}}
| [[Kilogram|kg]]⋅[[Metre|m]]<sup>2</sup>⋅[[second|s]]<sup>−2</sup>⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| colspan="2" |'''Other common units'''
|-
| {{val|8314.46261815324}}
| [[litre|L]]⋅[[Pascal (unit)|Pa]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|8.31446261815324}}
| [[litre|L]]⋅[[pascal (unit)|kPa]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|0.0831446261815324}}
| [[litre|L]]⋅[[bar (unit)|bar]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|8.31446261815324|e=7}}
| [[erg (unit)|erg]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|0.730240507295273}}
| [[Atmosphere (unit)|atm]]⋅[[Foot (unit)|ft]]<sup>3</sup>⋅[[Mole (unit)#Similar units|lbmol]]<sup>−1</sup>⋅[[Rankine scale|°R]]<sup>−1</sup>
|-
| {{val|10.731577089016}}
| [[Pounds per square inch|psi]]⋅[[Foot (unit)|ft]]<sup>3</sup>⋅[[Mole (unit)#Similar units|lbmol]]<sup>−1</sup>⋅[[Rankine scale|°R]]<sup>−1</sup>
|-
| {{val|1.985875279009}}
| [[British thermal unit|BTU]]⋅[[Mole (unit)#Similar units|lbmol]]<sup>−1</sup>⋅[[Rankine scale|°R]]<sup>−1</sup>
|-
| {{val|297.031214}}
| [[Inch of water|inH<sub>2</sub>O]]⋅[[Foot (unit)|ft]]<sup>3</sup>⋅[[Mole (unit)#Similar units|lbmol]]<sup>−1</sup>⋅[[Rankine scale|°R]]<sup>−1</sup>
|-
| {{val|554.984319180}}
| [[torr]]⋅[[Foot (unit)|ft]]<sup>3</sup>⋅[[Mole (unit)#Similar units|lbmol]]<sup>−1</sup>⋅[[Rankine scale|°R]]<sup>−1</sup>
|-
| {{val|0.082057366080960}}
| [[litre|L]]⋅[[atmosphere (unit)|atm]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|62.363598221529}}
| [[litre|L]]⋅[[torr]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|1.98720425864083|end=...}}
| [[calorie|cal]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
| {{val|8.20573660809596|e=-5|end=...}}
| [[cubic metre|m<sup>3</sup>]]⋅[[atmosphere (unit)|atm]]⋅[[kelvin|K]]<sup>−1</sup>⋅[[mole (unit)|mol]]<sup>−1</sup>
|-
|}
[[File:Heating-gas-at-constant-pressure-and-constant-volume.svg|thumb|Heating gas at constant pressure and constant-volume]]
The '''molar gas constant''' (also known as the '''gas constant''', '''universal gas constant''', or '''ideal gas constant''') is denoted by the symbol {{math|''R''}} or {{math|{{overline|''R''}}}}. It is the molar equivalent to the [[Boltzmann constant]], expressed in units of [[energy]] per [[temperature|temperature increment]] per [[amount of substance]], rather than energy per temperature increment per ''particle''. The constant is also a combination of the constants from [[Boyle's law]], [[Charles's law]], [[Avogadro's law]], and [[Gay-Lussac's law]].  It is a [[physical constant]] that is featured in many fundamental equations in the physical  sciences, such as the [[ideal gas law]], the [[Arrhenius equation]], and the [[Nernst equation]].

The gas constant is the [[constant of proportionality]] that relates the energy scale in physics to the temperature scale and the scale used for [[amount of substance]].  Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The [[Boltzmann constant]] and the [[Avogadro constant]] were similarly determined, which separately relate energy to temperature and particle count to amount of substance.

The gas constant ''R'' is defined as the [[Avogadro constant]] ''N''<sub>A</sub> multiplied by the [[Boltzmann constant]] ''k'' (or ''k''<sub>B</sub>):
: <math>R = N_\text{A} k</math>
:: = {{physconst|NA|ref=no}} × {{physconst|k|ref=no}}
:: = {{val|8.31446261815324|u=J⋅K<sup>−1</sup>⋅mol<sup>−1</sup>}}.

Since the [[2019 revision of the SI]], both ''N''<sub>A</sub> and ''k'' are defined with exact numerical values when expressed in SI units.<ref name="SI2019">
{{cite book
 | last1 = Newell
 | first1 = David B.
 | last2 = Tiesinga
 | first2 = Eite
 | year = 2019
 | title = The International System of Units (SI)
 | series = NIST Special Publication 330
 | publisher = National Institute of Standards and Technology
 | location = Gaithersburg, Maryland
 | url = https://www.nist.gov/si-redefinition/meet-constants
 | doi = 10.6028/nist.sp.330-2019
 | s2cid = 242934226
}}</ref> As a consequence, the SI value of the molar gas constant is exact.

Some have suggested that it might be appropriate to name the symbol ''R'' the '''Regnault constant''' in honour of the [[French people|French]] [[chemist]] [[Henri Victor Regnault]], whose accurate experimental data were used to calculate the early value of the constant. However, the origin of the letter ''R'' to represent the constant is elusive. The universal gas constant was apparently introduced independently by [[August Friedrich Horstmann]] (1873)<ref name="Jensen">
{{cite journal
 |title=The Universal Gas Constant ''R''
 |last=Jensen |first=William B.
 |journal= J. Chem. Educ.
 |volume= 80
 |issue= 7
 |date=July 2003
 |pages=731
 |doi=10.1021/ed080p731|bibcode = 2003JChEd..80..731J 
 |author1-link=William B. Jensen}}</ref><ref name="JensenReprint">{{cite web
 |url= http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/100.%20Gas%20Constant.pdf
 |title=Ask the Historian: The Universal Gas Constant&nbsp;— Why is it represented by the letter ''R''?
}}</ref> and [[Dmitri Mendeleev]] who reported it first on 12 September 1874.<ref name="Mendeleev2">
{{cite journal
 |title=An exert from the Proceedings of the Chemical Society's Meeting on Sept. 12, 1874
 |last=Mendeleev |first=Dmitri I.
 |journal= Journal of Russian Chemical-Physical Society, Chemical Part
 |volume= VI
 |issue= 7
 |date=September 12, 1874
 |pages=208–209
}}</ref> Using his extensive measurements of the properties of gases,<ref name="Mendeleev3">
{{cite book
 |title=On the elasticity of gases [Объ упругости газовъ]
 |last=Mendeleev |first=Dmitri I.
 |date=1875
 | publisher = A. M. Kotomin, St.-Petersburg
}}</ref><ref>[http://gallica.bnf.fr/ark:/12148/bpt6k95208b/f12.image.r=mendeleev.langEN D. Mendeleev. On the elasticity of gases. 1875 (in Russian)] {{free access}}</ref>
Mendeleev also calculated it with high precision, within 0.3% of its modern value.<ref name="Mendeleev">
{{cite journal
 |title=Mendeleef's researches on Mariotte's law 1
 |last=Mendeleev |first=Dmitri I.
 |journal= Nature
 |volume= 15
 |issue= 388
 |date=March 22, 1877
 |pages=498–500
 |doi=10.1038/015498a0 |doi-access=free
 |bibcode=1877Natur..15..498D
}} {{free access}}</ref>

The gas constant occurs in the ideal gas law:
<math display="block">PV = nRT = m R_\text{specific} T,</math>
where ''P'' is the absolute [[pressure]], ''V'' is the volume of gas, ''n'' is the [[amount of substance]], ''m'' is the [[mass]], and ''T'' is the [[thermodynamic temperature]]. ''R''<sub>specific</sub> is the mass-specific gas constant. The gas constant is expressed in the same unit as [[molar heat]].