A constant occurring in practically all statistical formulas and having a numerical value of 1.3807 × 10−23 joule/K. It is represented by the letter k. If the temperature T is measured from absolute zero, the quantity kT has the dimensions of an energy and is usually called the thermal energy. At 300 K (room temperature), kT = 0.0259 eV.
The value of the Boltzmann constant may be determined from the ideal gas law. For 1 mole of an ideal gas Eq. (1a)
holds, where P is the pressure, V the volume, and R the universal gas constant. The value of R, 8.31 J/K mole, may be obtained from equation-of-state data. Statistical mechanics yields for the gas law Eq. (1b).
Since k occurs explicitly in the distribution formula, Eq. (2), any quantity calculated using the Boltzmann distribution depends explicitly on k. Examples are specific heat, viscosity, conductivity, and the velocity of sound. Perhaps the most unusual relation involving k is the one between the probability of a state W and the entropy S, given by Eq. (3),
which is obtained by a process of identification similar to the one just described.
Almost any relation derived on the basis of the partition function or the Bose-Einstein, Fermi-Dirac, or Boltzmann distribution contains the Boltzmann constant. See also: Avogadro's number; Boltzmann statistics; Bose-Einstein statistics; Fermi-Dirac statistics; Kinetic theory of matter; Statistical mechanics