# Gas constant

Values of R
[1]
Units
(V P T −1n−1)
8.3144598(48)kgm2 s−2 K−1mol−1
8.3144598(48)JK−1mol−1
8.3144598(48) ×103kJK−1mol−1
8.3144598(48)×107erg K−1mol−1
8.3144598(48)×103amu (km/s)2  K−1
8.3144598(48)m3Pa K−1mol−1
8.3144598(48)×106cm3Pa  K−1mol−1
8.3144598(48)LkPa K−1mol−1
8.3144598(48)×103cm3kPa K−1mol−1
8.3144598(48)×106m3MPa K−1mol−1
8.3144598(48)cm3MPa K−1mol−1
8.3144598(48)×105m3bar K−1mol−1
8.3144598(48)×102Lbar K−1mol−1
83.144598(48)cm3bar K−1mol−1
62.363577(36)LTorr K−1mol−1
1.9872036(11)×103kcal K−1mol−1
8.2057338(47)×105m3atm K−1mol−1
0.082057338(47)Latm K−1mol−1
82.057338(47)cm3atm K−1mol−1

The gas constant is also known as the molar, universal, or ideal gas constant, denoted by the symbol R or R and is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole, i.e. the pressure-volume product, 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 and the Nernst equation.

Physically, the gas constant is the constant of proportionality that happens to relate the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of the energy and temperature scales, plus similar historical setting of the value of the molar scale used for the counting of particles. The last factor is not a consideration in the value of the Boltzmann constant, which does a similar job of equating linear energy and temperature scales.

The gas constant value is

8.3144598(48) J⋅mol−1⋅K−1[1]

The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value. The relative uncertainty is 5.7×10−7. Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant; however, the exact reason for the original representation of the constant by the letter R is elusive.[2][3]

The gas constant occurs in the ideal gas law, as follows:

${\displaystyle PV=nRT=mR_{\rm {specific}}T\,\!}$

where P is the absolute pressure (SI unit pascals), V is the volume of gas (SI unit cubic metres), n is the amount of gas (SI unit moles), m is the mass (SI unit kilograms) contained in V, and T is the thermodynamic temperature (SI unit kelvins). The gas constant is expressed in the same physical units as molar entropy and molar heat capacity.

## Dimensions of R

From the general equation PV = nRT we get:

${\displaystyle R={\frac {PV}{nT}}}$

where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature.

As pressure is defined as force per unit area, the gas equation can also be written as:

${\displaystyle R={\frac$

Area and volume are (length)2 and (length)3 respectively. Therefore:

${\displaystyle R={\frac$

Since force × length = work:

${\displaystyle R={\frac {\mathrm {work} }{\mathrm {amount} \times \mathrm {temperature} }}}$

The physical significance of R is work per degree per mole. It may be expressed in any set of units representing work or energy (such as joules), other units representing degrees of temperature (such as degrees Celsius or Fahrenheit), and any system of units designating a mole or a similar pure number that allows an equation of macroscopic mass and fundamental particle numbers in a system, such as an ideal gas (see Avogadro's number).

Instead of a mole the constant can be expressed by considering the normal cubic meter.

Otherwise, we can also say that:

${\displaystyle \mathrm {force} ={\frac {\mathrm {mass} \times \mathrm {length} }{(\mathrm {time} )^{2}}}}$

Therefore, we can write "R" as:

${\displaystyle R={\frac {\mathrm {mass} \times \mathrm {length} ^{2}}{\mathrm {amount} \times \mathrm {temperature} \times (\mathrm {time} )^{2}}}}$

And so, in SI base units:

R = 8.3144598(48) kg m2 mol−1 K−1 s−2.
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