the Boltzmann constant
/ BOLTS-mahn /
The bridge between temperature and energy for a single molecule. Temperature is ultimately about how much kinetic energy the molecules have, and the Boltzmann constant is the exchange rate that converts one into the other.
Precisely, k_B = 1.380649 x 10^-23 J/K, an exact defined value since 2019. For an ideal gas the average translational kinetic energy per molecule is (3/2) k_B T, and each degree of freedom gets (1/2) k_B T. It relates to the universal gas constant by R = N_A k_B.
It also appears in the entropy formula S = k_B ln W, engraved on Boltzmann's tombstone, and in the Maxwell-Boltzmann distribution. In short, it sets the scale of thermal energy, k_B T, which is about 4 x 10^-21 J at room temperature.
At room temperature (about 300 K) the average translational kinetic energy of a gas molecule is (3/2) k_B T, roughly 6 x 10^-21 J.
The constant converting temperature into single-molecule energy.
The Boltzmann constant is what makes temperature and energy interchangeable at the molecular level; it is essentially the universal gas constant divided by Avogadro's number.