**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. (1*a*)

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. (1*b*).

Here *N*, the number of molecules in 1 mole, is called the Avogadro number and is equal to 6.02 × 10^{23} molecules/mole. Hence, comparing Eqs. (1*a*) and (1*b*), one obtains Eq. (2).

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**