Boltzmann constant

Definition (SI, 2022)

The Boltzmann constant is defined as $k = 1.380649 \times 10^{-23} \, \text{J} \cdot \text{K}^{-1}$.

(a fundamental physical constant in the system of SI units, i.e. the "metric system")

Notes

• also denoted as $k_B$
• The Boltzmann constant defines temperature (in kelvins) in terms of joules, viz. every $1\, \text{K}$ change of thermodynamic temperature corresponds to a thermal energy change of exactly $1.380649 \times 10^{-23} \, \text{J}$
• In the statistical definition of entropy, where $W$ refers to the number of distinct microscopic states available to the system given macroscopic constraints,
  • $S = k \ln W$
  • $k$ therefore scales the value of entropy by physical units
  • this definition of entropy is related to information entropy via Gibbs entropy

See also

• Shannon entropy

References

1. https://physics.nist.gov/cgi-bin/cuu/Value?k
2. https://en.wikipedia.org/wiki/Boltzmann_constant
3. https://en.wikipedia.org/wiki/Kelvin