Boltzmann constant

The Boltzmann constant is the physical constant relating temperature to energy. Despite its name, this constant wasn't introduced by Boltzmann himself, but rather named in honour of him.

For a huge ensemble of objects, such as the billions of trillions of hot molecules propelling a piston in a steam engine, a dominant technology of Boltzmann's era, there is no possible way to determine the state of each independent molecule as they are all moving at different velocities with a range of different energies. Nonetheless, understanding the physics of heat engines and analogous systems demands some way to make mathematically useful statements about collections of enormous numbers of objects. Thus, Boltzmann and other scientists showed that it can be done in terms of statistics and probabilities, i.e. statistical mechanics. The collective thermodynamic properties of ensembles derive from the sum of the energies of each individual object.

Given a thermodynamic system at an absolute temperature \[T\], by equipartition theorem, the average thermal energy carried by each microscopic degrees of freedom in the system is \[\frac{1}{2}k_{\text{B}}T\]. In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases. Monatomic ideal gases possess three degrees of freedom per atom, corresponding to the three spatial directions. According to the equipartition of energy this means that there is a thermal energy of ⁠\[\frac{3}{2}k_{\text{B}}T\] per atom. This corresponds very well with experimental data.

The Boltzmann constant is defined as \[k_{B}=\frac{R}{N_{\text{A}}}\], where \[R\] is the molar gas constant and \[N_{\text{A}}\] is the Avogadro constant. In November 2018, the Boltzmann constant has been revised using measurements collected via acoustic thermometry, dielectric-constant gas thermometry and Johnson Noise Thermometry to be exactly \[1.380649\times10^{-23}\] joules per kelvin.