Boltzmann constant

The Boltzmann constant kBk_{B} is a physical constant that commonly appears in thermodynamics and relates energy with temperature:

kB=RNA=1.38⋅10−23 J/K=1.38⋅10−16 erg/K=8.62⋅10−5 eV/K\begin{align} k_{B}=\frac{R}{N_{A}}&=1.38\cdot10^{-23}\text{ J/K}\\ &=1.38\cdot10^{-16}\text{ erg/K}\\ &=8.62\cdot10^{-5} \text{ eV/K} \end{align}

where RR is the ideal gas constant and NAN_{A} is the Avogadro number.

It is generally used in statistical mechanics, but it is occasionally employed in nuclear and particle physics to give a sense of scale for the energies found in those domains. This is done by arbitrarily converting between energy and temperature with E=kBTE=k_{B}T. Here's some examples:

  • room temperature (∼300 K\sim 300\text{ K}) shows energies in the order of ∼10−2 eV\sim 10^{-2}\text{ eV}, which is tiny.
  • the center of the sun (∼107 K\sim 10^{7}\text{ K}) gets around ∼1 keV\sim 1\text{ keV}.
  • the Rydberg energy (potential energy of the ground state of the hydrogen atom, 13.6 eV13.6\text{ eV}) gets about ∼105 K\sim 10^{5}\text{ K}.
  • modern collisions at the Large Hadron Collider at CERN can reach ∼10 TeV\sim 10\text{ TeV}, which is about ∼1017 K\sim 10^{17}\text{ K}. That's ten billion times the temperature of the core of the Sun!

Remember that temperature is only well-defined in complex systems with many interactions, such as macroscopic matter, so these numbers are just to give a sense of scale. Take them with a grain of salt.