# Boltzmann Constant

Boltzmann constant, abbreviated as \(k\) or \(k_b\), is a porportionality factor which compares the average relative kinetic energy of particales in a gas with the temperature of the gas.

## Boltzmann constant Formula

\(\large{ k_b = \frac{ p \; V }{ T_a \; n } }\) |

### Where:

Units |
English |
Metric |

\(\large{ k_b }\) = Boltzmann constant | \(\large{ \frac{lbm-ft^2}{sec^2} }\) | \(\large{ \frac{kJ}{molecule-K} }\) |

\(\large{ T_a }\) = absolute temperature | \(\large{ F}\) | \(\large{ K }\) |

\(\large{ n }\) = number of molecules of gas | dimensionless | |

\(\large{ p }\) = pressure | \(\large{ \frac{lbf}{in^2} }\) | \(\large{ Pa }\) |

\(\large{ V }\) = volume | \(\large{ in^3}\) | \(\large{ mm^3 }\) |

## Boltzmann constant

\(\large{ k_b = 1.3807\;x\;10^{-23} \; \frac{kJ}{molecule-K} }\) | (these units are the same as \(\large{ \frac{kg-m^2}{s^2} }\)) |