Boltzmann constant
/ BOLT-smahn KON-stunt /
Temperature is something you feel; energy is something you count in joules. The Boltzmann constant is the exchange rate between the two — the small number that converts a thermometer reading into the average jiggling energy of a single molecule. It is the personal, per-particle version of the gas constant that chemists use for whole moles.
More precisely, the Boltzmann constant (symbol k or kB) has the fixed value 1.380649 times ten to the minus twenty-three joules per kelvin. Multiply it by an absolute temperature and you get the characteristic thermal energy kT available to each degree of freedom of a molecule. It also equals the gas constant divided by Avogadro's number — the same quantity, just shrunk from a mole down to one particle.
Why it matters: this tiny constant ties the microscopic and macroscopic worlds together. It appears in the Boltzmann factor, in the entropy formula S = k ln W, in the equipartition theorem, and wherever temperature meets atoms. Since 2019 it is no longer measured but defined exactly, which is in fact how the kelvin itself is now pinned down.
At 300 kelvin the thermal energy kT is about 4.1 times ten to the minus twenty-one joules — a quantity so small it is awkward in joules, which is why chemists multiply by Avogadro's number to get the more familiar RT of about 2.5 kilojoules per mole.
kT per molecule scales up to RT per mole via Avogadro's number.
Do not mix up the Boltzmann constant k (per molecule) with the gas constant R (per mole): R = k times Avogadro's number. They carry the same physics on different head-counts.