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The Boltzmann constant sets up a relationship between wavelength and temperature (dividing hc/k by a wavelength gives a temperature) with one micrometer being related to 14 387.777 K, and also a relationship between voltage and temperature (kT in units of eV corresponds to a voltage) with one volt being related to 11 604.518 K.
The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale: / = = , where k B is the Boltzmann constant. The k B is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kiloelectronvolt), which is equal to 174 MK (megakelvin).
The Stefan–Boltzmann constant, σ, is derived from other known physical constants: = where k is the Boltzmann constant, the h is the Planck constant, and c is the speed of light in vacuum. [19] [4]: 388
kT (also written as k B T) is the product of the Boltzmann constant, k (or k B), and the temperature, T.This product is used in physics as a scale factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT, that is, on E ...
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
k B, the Boltzmann constant. ... In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 10 28 eV (the Planck energy, ...
The SI unit of temperature is the kelvin (K), but using the above relation the electron temperature is often expressed in terms of the energy unit electronvolt (eV). Each kelvin (1 K) corresponds to 8.617 333 262... × 10 −5 eV; this factor is the ratio of the Boltzmann constant to the elementary charge. [6]
For a classical system (e.g. Boltzmann gas), it reads: = where: k B is the Boltzmann constant; T is the absolute temperature; e is the electric charge of an electron; For a metal, described by a Fermi gas (Fermi liquid), quantum version of the Einstein relation should be used.