Editing Gas constant (section)

== Specific gas constant ==
{| class="wikitable" style="float: right;"
! ''R''<sub>specific</sub><br />for dry air<ref>Based on a mean molar mass for [[Atmosphere of Earth#Composition|dry air]] of 28.964917&nbsp;g/mol.</ref>
! Unit
|-
| 287.052874
| J⋅kg<sup>−1</sup>⋅K<sup>−1</sup>
|-
| 53.3523
| ft⋅[[Pound-force|lbf]]⋅[[Pound (mass)|lb]]<sup>−1</sup>⋅°R<sup>−1</sup>
|-
| 1,716.46
| ft⋅[[Pound-force|lbf]]⋅[[slug (unit)|slug]]<sup>−1</sup>⋅°R<sup>−1</sup>
|}

The '''specific gas constant''' of a gas or a mixture of gases (''R''<sub>specific</sub>) is given by the molar gas constant divided by the [[molar mass]] (''M'') of the gas or mixture:
: <math> R_\text{specific} = \frac{R}{M}.</math>

Just as the molar gas constant can be related to the Boltzmann constant, so can the specific gas constant by dividing the Boltzmann constant by the molecular mass of the gas:
: <math> R_\text{specific} = \frac{k_\text{B}}{m}.</math>

Another important relationship comes from thermodynamics. [[Mayer's relation]] relates the specific gas constant to the specific heat capacities for a calorically perfect gas and a thermally perfect gas:
: <math> R_\text{specific} = c_p - c_V,</math>
where ''c<sub>p</sub>'' is the [[specific heat capacity]] for a constant pressure, and ''c<sub>V</sub>'' is the specific heat capacity for a constant volume.<ref>Anderson, ''Hypersonic and High-Temperature Gas Dynamics'', AIAA Education Series, 2nd ed., 2006.</ref>

It is common, especially in engineering applications, to represent the specific gas constant by the symbol ''R''. In such cases, the universal gas constant is usually given a different symbol such as ''{{overline|R}}'' to distinguish it. In any case, the context and/or unit of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to.<ref name="Moran2018">
{{cite book
 | last1 = Moran | first1 = Michael J.
 | last2 = Shapiro | first2 = Howard N.
 | last3 = Boettner | first3 = Daisie D.
 | last4 = Bailey | first4 = Margaret B.
 | title = Fundamentals of Engineering Thermodynamics
 | publisher = Wiley
 | location = Hoboken, New Jersey
 | edition = 9th
 | url = https://www.wiley.com/en-us/Fundamentals+of+Engineering+Thermodynamics%2C+9th+Edition-p-9781119391388
 | year = 2018
}}</ref>

In case of air, using the perfect gas law and the [[standard sea-level conditions]] (SSL) (air density ''ρ''<sub>0</sub> = 1.225&nbsp;kg/m<sup>3</sup>, temperature ''T''<sub>0</sub> = 288.15&nbsp;[[Kelvin|K]] and pressure ''p''<sub>0</sub> = {{val|101325|ul=Pa}}), we have that ''R''<sub>air</sub> = ''P''<sub>0</sub>/(''ρ''<sub>0</sub>''T''<sub>0</sub>) = {{val|287.052874247|u=J·kg<sup>−1</sup>·K<sup>−1</sup>}}. Then the molar mass of air is computed by ''M''<sub>0</sub> = ''R''/''R''<sub>air</sub> = {{val|28.964917|u=g/mol}}.<ref name="ICAO manual">{{cite book |title=Manual of the US Standard Atmosphere |date=1962 |publisher=National Aeronautics and Space Administration |pages=7–11 |edition=3 |url=https://ntrs.nasa.gov/api/citations/19630003300/downloads/19630003300.pdf}}</ref>