Boltzmann constant
The Boltzmann constant (kB or k), named after Ludwig Boltzmann, is a physical constant relating energy at the individual particle level with temperature. It is the gas constant R divided by the Avogadro constant NA:
The Boltzmann constant has the dimension energy divided by temperature, the same as entropy. The accepted value in SI units is 6977138064851999999♠1.38064852(79)×10−23 J/K.
Bridge from macroscopic to microscopic physics
Boltzmann's constant, k, is a bridge between macroscopic and microscopic physics. Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure p and volume V is proportional to the product of amount of substance n (in moles) and absolute temperature T:
where R is the gas constant (7000831446210000000♠8.3144621(75) J⋅K−1⋅mol−1). Introducing the Boltzmann constant transforms the ideal gas law into an alternative form:
where N is the number of molecules of gas. For n = 1 mol, N is equal to the number of particles in one mole (Avogadro's number).
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