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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 .
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).
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).
where σ is the Stefan–Boltzmann constant, σ ≈ 5.67 × 10 −8 W⋅m −2 ⋅K −4 [53] To remain in thermal equilibrium at constant temperature T, the black body must absorb or internally generate this amount of power P over the given area A.
The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting: [11] =, where A is the surface area, T is the temperature (in kelvins) and σ is the Stefan–Boltzmann constant, with a value of 5.670 374 419... × 10 −8 W⋅m −2 ⋅K −4.
The law was formulated by Josef Stefan in 1879 and later derived by Ludwig Boltzmann. The formula E = σT 4 is given, where E is the radiant heat emitted from a unit of area per unit time, T is the absolute temperature, and σ = 5.670 367 × 10 −8 W·m −2 ⋅K −4 is the Stefan–Boltzmann constant. [28]
So in what Planck called "an act of desperation", [91] he turned to Boltzmann's atomic law of entropy as it was the only one that made his equation work. Therefore, he used the Boltzmann constant k and his new constant h to explain the blackbody radiation law which became widely known through his published paper. [92] [93]
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 ...