# Boltzmann Constant

Written by Jerry Ratzlaff on . Posted in Thermodynamics

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 $$\large{ \frac{kg-m^2}{s^2} }$$)