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As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380 649 × 10 −23 joules per kelvin. [1]
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 ...
Such wavenumbers were first used in the calculations of Johannes Rydberg in the 1880s. The Rydberg–Ritz combination principle of 1908 was also formulated in terms of wavenumbers. A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency.
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).
A quantum harmonic oscillator has an energy spectrum characterized by: , = (+) where j runs over vibrational modes and is the vibrational quantum number in the jth mode, is the Planck constant, h, divided by and is the angular frequency of the jth mode. Using this approximation we can derive a closed form expression for the vibrational ...
The constant of proportionality, , is called the Stefan–Boltzmann constant. It has the value It has the value σ = 5.670 374 419 ... × 10 −8 W⋅m −2 ⋅K −4 .
Planck was able to calculate the value of from experimental data on black-body radiation: his result, 6.55 × 10 −34 J⋅s, is within 1.2% of the currently defined value. [2] He also made the first determination of the Boltzmann constant from the same data and theory. [14]
This link is provided by Boltzmann's fundamental assumption written as S = k B ln Ω , {\displaystyle S=k_{\rm {B}}\ln \Omega ,} where k B is the Boltzmann constant , S is the classical thermodynamic entropy, and Ω is the number of microstates.