What is Boltzmann Constant?

by Alexander FufaeV

The Boltzmann constant is a physical constant and is denoted by $ k_{\text B} $. It has the following exact value:

Value of the Boltzmann constant

$$ \begin{align} k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} \end{align} $$

The unit of the Boltzmann constant is Joule per Kelvin:

$$ \begin{align} \frac{\mathrm{J}}{\mathrm{K}} ~=~ \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} \end{align} $$

The value 1 of the Boltzmann constant can also be expressed in electron-volts (eV) per kelvin. To do this, we need to convert 1 joule to electron-volts. This results in the following value of $k_{\text B}$ in electron-volts per kelvin:

$$ \begin{align} k_{\text B} ~=~ 8.617\,333\,2621 \, \frac{\mathrm{eV}}{\mathrm{K}} \end{align} $$

The Boltzmann constant occurs in the equations that describe systems with many particles. So you will often encounter the Boltzmann constant in statistical physics and solid state physics.

The Boltzmann constant links the molar gas constant $R_{\text m}$ with the Avogadro constant $N_{\text A}$:

$$ \begin{align} R_{\text m} ~&=~ N_{\text A} \, k_{\text B}\\
~&=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm{J}}{\mathrm{mol}\,\mathrm{K}} \end{align} $$

The Boltzmann constant links energy to temperature in our universe.

The Boltzmann constant can be determined, for example, by measuring the speed of sound in a gas.