# Gas constant

Physical constant
Surname Universal gas constant
Formula symbol ${\ displaystyle R}$
value
SI 8th.314 462 618 153 24${\ displaystyle \ textstyle {\ frac {\ mathrm {kg \, m ^ {2}}} {\ mathrm {s ^ {2} \, mol \, K}}}}$
Uncertainty  (rel.) (exactly)
Relation to other constants
${\ displaystyle R = N _ {\ mathrm {A}} \ cdot k _ {\ mathrm {B}}}$
${\ displaystyle N _ {\ mathrm {A}}}$: Avogadro constant : Boltzmann constant
${\ displaystyle k _ {\ mathrm {B}}}$
Sources and Notes
Source SI value: CODATA 2018 ( direct link )

The gas constant , also molar , universal or general gas constant, is a physical constant from thermodynamics . It occurs in the thermal equation of state of ideal gases . This equation establishes a relationship between pressure , volume , temperature and amount of substance of an ideal gas : The product of pressure and volume is proportional to the product of amount of substance and temperature. The ideal gas constant is the proportionality constant${\ displaystyle R}$ ${\ displaystyle p}$ ${\ displaystyle V}$ ${\ displaystyle T}$ ${\ displaystyle n}$

${\ displaystyle pV = nRT \ Leftrightarrow R = {\ frac {pV} {nT}}.}$

Since the ideal gas equation can also be expressed with the number of particles instead of the amount of substance and the Boltzmann constant then appears as a constant of proportionality, there is a simple relationship between the gas constant, Boltzmann constant and the Avogadro constant , which links the number of particles and the amount of substance: ${\ displaystyle N}$ ${\ displaystyle k _ {\ mathrm {B}}}$ ${\ displaystyle N _ {\ mathrm {A}}}$

${\ displaystyle R = N _ {\ mathrm {A}} k _ {\ mathrm {B}}}$

Since both constants have been given by definition since the revision of the International System of Units (SI) in 2019 , the numerical value of the gas constant is also exact:

${\ displaystyle R = 8 {,} 314 \; 462 \; 618 \; 153 \; 24 \ \ mathrm {\ frac {J} {mol \, K}}}$

## meaning

The general gas constant was determined empirically . It is by no means obvious that the molar gas constant has the same value for all ideal gases and that there is thus a universal or general gas constant. One could assume that the gas pressure depends on the molecular mass of the gas, but this is not the case for ideal gases. Amadeo Avogadro first found in 1811 that the molar gas constant is the same for different ideal gases, known as Avogadro's Law .

The gas constant as the product of Avogadro and Boltzmann constants occurs in various areas of thermodynamics, mainly in the description of ideal gases. Such is the internal energy of ideal gases ${\ displaystyle U}$

${\ displaystyle U = {\ frac {1} {2}} fRT}$

with the number of degrees of freedom of the gas and derived from this the molar heat capacity at constant volume${\ displaystyle f}$${\ displaystyle C_ {V}}$

${\ displaystyle C_ {V} = {\ frac {1} {2}} fR}$

and the molar heat capacity at constant pressure ${\ displaystyle C_ {p}}$

${\ displaystyle C_ {p} = {\ frac {3} {2}} fR \ ,.}$

The gas constant also plays a role outside of the thermodynamics of gases, for example in the Dulong-Petit law for the heat capacity of solids and liquids :

${\ displaystyle C_ {p _ {\, \ mathrm {fixed}}} \ approx C_ {V _ {\, \ mathrm {fixed}}} = 3R}$

## Specific gas constant

Specific gas constant and molar mass
gas ${\ displaystyle R _ {\ mathrm {s}}}$
in J kg −1 K −1
${\ displaystyle M}$
in g mol −1
Argon , ar 208.1 39.950
Helium , he 2077.1 4.003
Carbon dioxide , CO 2 188.9 44.010
Carbon monoxide , CO 296.8 28.010
dry air 287.1 28.960
Methane , CH 4 518.4 16.040
Propane , C 3 H 8 188.5 44.100
Oxygen , O 2 259.8 32.000
Sulfur dioxide , SO 2 129.8 64.060
Nitrogen , N 2 296.8 28.010
Water vapor , H 2 O 461.4 18.020
Hydrogen , H 2 4124.2 2.016

Division of the universal gas constant by the molar mass of a certain gas provides the specific ( related to the mass ) and for the gas special or individual gas constant, formula symbols : ${\ displaystyle M}$

${\ displaystyle R _ {\ rm {s}}, R _ {\ rm {i}}, R _ {\ rm {spec}} = {\ frac {R} {M}}.}$

### Example in air

The molar mass for dry air is 0.028 964 4 kg / mol. This results in the specific gas constant of air:

${\ displaystyle R _ {\ mathrm {s, air}} = {\ frac {8 {,} 314 \; 46 \; \ mathrm {J} / (\ mathrm {mol} \ cdot \ mathrm {K})} { 0 {,} 028 \; 964 \; 4 \ \ mathrm {kg} / \ mathrm {mol}}} = 287 {,} 058 \ \ mathrm {\ frac {J} {kg \ cdot K}}}$

The thermal equation of state for ideal gases is then:

${\ displaystyle p \; V = m \; R _ {\ mathrm {s}} \; T}$

where m is the mass.

## Individual evidence

1. The value is also exact as the product of two exact values, but in CODATA it is only given with the first ten valid digits, followed by periods. The numbers given in the info box are all valid.
2. Wolfgang Demtröder: Experimentalphysik 1: Mechanics and heat . 6th edition. Springer, 2013, ISBN 978-3-642-25465-9 , pp. 266 .
3. ^ Langeheinecke: Thermodynamics for Engineers. Vieweg + Teubner, Wiesbaden 2008, ISBN 978-3-8348-0418-1
4. ^ Günter Warnecke: Meteorology and Environment: An Introduction. Google eBook, p. 14, limited preview in Google Book search.