Formula Specific Gas Constant Mass Boltzmann Constant
$$R_{\text s} ~=~ \frac{k_{\text B}}{\class{brown}{m}}$$ $$R_{\text s} ~=~ \frac{k_{\text B}}{\class{brown}{m}}$$ $$\class{brown}{m} ~=~ \frac{k_{\text B}}{R_{\text s}}$$ $$k_{\text B} ~=~ \class{brown}{m} \, R_{\text s}$$
Specific gas constant
$$ R_{\text s} $$ Unit $$ \frac{\mathrm{J}}{\mathrm{kg} \, \mathrm{K}} = \frac{\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$ The specific gas constant depends on the gas under consideration and, by definition, gives the ratio of the molar gas constant \(R\) to the molar mass \(M_{\text n}\) of a gas.
| Gas | Specific gas constant \(R_{\text s}\) |
|---|---|
| Helium (He) | \( 2077.1 \, \frac{\mathrm J}{ \mathrm{kg}\, \mathrm{K} } \) |
| Methane (CH4) | \( 518.4 \, \frac{\mathrm J}{ \mathrm{kg}\, \mathrm{K} } \) |
| Nitrogen (N2) | \( 296.8 \, \frac{\mathrm J}{ \mathrm{kg}\, \mathrm{K} } \) |
| Oxygen (O2) | \( 259.8 \, \frac{\mathrm J}{ \mathrm{kg}\, \mathrm{K} } \) |
| Carbon dioxide (CO2) | \( 188.9 \, \frac{\mathrm J}{ \mathrm{kg}\, \mathrm{K} } \) |
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$ Mass of a gas particle (e.g. a He atom, when dealing with a helium gas).
Boltzmann Constant
$$ k_{\text B} $$ Unit $$ \frac{\mathrm J}{\mathrm K} = \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$ Boltzmann constant is a physical constant from many-particle physics and has the following exact value:$$ k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} $$