Boltzmann constant

The Boltzmann constant K (or K B) was introduced by Ludwig Boltzmann at the time of his definition of the Entropie in 1873. The system being with macroscopic, but free balance to evolve/move on a microscopic scale between \ Omega different microphone-states, its Entropie S is given by:

This Constante fundamental physics is equal to R/NA

  • R is the constant of perfect gas: R = 8,314 J.K-1.mol-1

  • NA is the Nombre of Avogadro equal to NA =6,022 X 1023 mol-1

from where K B ≈ 1,3806 × 10-23 J. K-1

K B can be interpreted like the factor of proportionality connecting the temperature of a system to its thermal energy. Indeed, the Température of an object is before a a whole Sensation, in fact of heat or cold. The Kelvin noted K' allows a quantitative measurement of the temperature. During the 19th century, the physicists become aware that the feeling of heat or cold is in fact a transfer of energy of a body towards another, in the form of Chaleur. The perception of the temperature is thus anything else only the demonstration of a transfer of energy, the thermal energy via a constant of proportionality which is being kB :

Ethermique = 1/2 kBT (It is the expression of energy in the simplest cases with only one degree of freedom, more generally Ethermique = f/2 kBT , where F is the number of degree of freedom, equal to 3 in a space with three dimensions).

This constant is thus used in all the physique utilizing a nonnull temperature. Is used it to convert a measurable size: the Temperature in Kelvin, an energy. It is a common language to all the physical phenomena and thus intervenes for example in:

  • the calculation of the electromagnetic spectrum of the black body;

  • systems according to a Statistical of Maxwell-Boltzmann (or Distribution of Maxwell-Boltzmann), in particular the Law of Arrhenius;
  • the Constant of Stefan-Boltzmann;
  • the Constant of radiation;
  • the energy interns of a Perfect gas.

Value

In the units IF, CODATA () of 2006 recommends the following value:

k_B \ simeq 1,380 \ 6504 \ times 10^ {- 23} \ mbox {J}. \ mbox {K} ^ {- 1}

With a standard uncertainty of:

\ plusmn 0,000 \ 0024 \ times 10^ {- 23} \ mbox {J}. \ mbox {K} ^ {- 1}

That is to say a relative uncertainty of: 1,7 \ times 10^ {- 6}

Value in eV/K

k_B \ simeq 8,617 343 \ times 10^ {- 5} \ mbox {eV}. \ mbox {K} ^ {- 1}

With a standard uncertainty of:

\ plusmn 0,000 015 \ times 10^ {- 5} \ mbox {eV}. \ mbox {K} ^ {- 1}

Value in Hz/K

k_B/h \ simeq 2,083 6644 \ times 10^ {10} \ mbox {Hz}. \ mbox {K} ^ {- 1}

With a standard uncertainty of:

\ plusmn 0,000 0036 \ times 10^ {10} \ mbox {Hz}. \ mbox {K} ^ {- 1}

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