Boltzmann’s constant (symbol: k), denoted as kB​, is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It is a crucial constant in statistical mechanics and thermodynamics and is named after the Austrian physicist Ludwig Boltzmann.

The value of Boltzmann’s constant is approximately:

kB≈1.380649×10−23 J/K

or

kB≈8.617333262145×10−5 eV/K

where:

J is the joule, the SI unit of energy,
K is the kelvin, the SI unit of temperature,
eV is the electronvolt, a unit of energy commonly used in physics.

Boltzmann’s constant appears in various equations related to the statistical behavior of particles, such as the Boltzmann distribution, the Maxwell-Boltzmann distribution, and the entropy formula in statistical mechanics. It relates the macroscopic quantity of temperature to the microscopic behavior of particles in a system.

The Boltzmann constant is used in the context of the ideal gas law, the definition of entropy, and the expression for thermal energy, among other thermodynamic and statistical physics formulas. Its value is fundamental to the understanding of thermal phenomena and provides a bridge between macroscopic thermodynamics and microscopic statistical mechanics.

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