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Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1. The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
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).
For thermal noise, its spectral density is given by N 0 = kT, where k is the Boltzmann constant in joules per kelvin (J/K), and T is the receiver system noise temperature in kelvins. The noise amplitude spectral density is the square root of the noise power spectral density, and is given in units such as volts per square root of hertz, V / H z ...
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
The canonical ensemble is the only ensemble with constant N, V, and T that reproduces the fundamental thermodynamic relation. [9] Statistical equilibrium (steady state): A canonical ensemble does not evolve over time, despite the fact that the underlying system is in constant motion. This is because the ensemble is only a function of a ...
Boltzmann was born in Erdberg, a suburb of Vienna into a Catholic family. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg.
The energy and entropy of unpolarized blackbody thermal radiation, is calculated using the spectral energy and entropy radiance expressions derived by Max Planck [63] using equilibrium statistical mechanics, = (), = ((+) (+) ()) where c is the speed of light, k is the Boltzmann constant, h is the Planck constant, ν is frequency ...