# Boltzmann constant

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## Boltzmann constant

A constant occurring in practically all statistical formulas and having a numerical value of 1.3807 × 10-23 joule/K. It is represented by the letter k. If the temperature T is measured from absolute zero, the quantity kT has the dimensions of an energy and is usually called the thermal energy. At 300 K (room temperature) kT = 0.0259 electronvolt.

The value of the Boltzmann constant may be determined from the ideal gas law. For 1 mole of an ideal gas Eq. (1a)

(1a)
(1b)
holds, where P is the pressure, V the volume, and R the universal gas constant. The value of R, 8.31 J/K mole, may be obtained from equation-of-state data. Statistical mechanics yields for the gas law Eq. (1b). Here N, the number of molecules in 1 mole, is called Avogadro's number and is equal to 6.02 × 1023 molecules/mole. Hence, comparing Eqs. (1a) and (1b), one obtains Eq. (2). (2) Almost any relation derived on the basis of the partition function or the Bose-Einstein, Fermi-Dirac, or Boltzmann distribution contains the Boltzmann constant. See Boltzmann statistics, Bose-Einstein statistics, Fermi-Dirac statistics, Kinetic theory of matter, Statistical mechanics

## Boltzmann constant

(bohlts -măn, -mahn) Symbol: k . A constant given by the ratio of the molar gas constant to the Avogadro constant and equal to 1.380 658 × 10–23 joules per kelvin. It is the constant by which the mean kinetic energy of a gas particle can be related to its thermodynamic temperature.

## Boltzmann Constant

one of the fundamental physical constants; equal to the ratio of the universal gas constant R to Avogadro’s number NA (the number of molecules in 1 mole of a substance): k = R/NA. It is named for L. Boltzmann. The Boltzmann constant enters into a number of the major relations of physics—the equation of the state of an ideal gas and the expression for the average energy of the thermal motion of particles (and thermal capacity itself). It also connects the entropy of a physical system with its thermodynamic probability.

The Boltzmann constant is k = (1.380622 ± 0.000059) x 10-23 joules per °K; this value corresponds to the most accurate data (as of 1969) on the constants R and NA. The value of the Boltzmann constant can be determined directly, for example, by the experimental verification of the laws of radiation. [3–1572–1; updated]

## Boltzmann constant

[′bōlts·mən ‚kän·stənt]
(statistical mechanics)
The ratio of the universal gas constant to the Avogadro number.
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As part of their work to precisely determine the Boltzmann constant, PTB needed to define absolute helium pressures.
0] (x) first kind of Bessel function k Boltzmann constant l cell length n number of particles T temperature u potential of interaction [u.
where k is the Boltzmann constant and W is the number of micro-states in an ensemble in the quantum-mechanical formulation [4].
B] is the Boltzmann constant, and T is the temperature, this will prevent a second electron from passing though, giving rise to the Coulomb block effect.
b] is the Boltzmann constant, [omega] (= 2[pi]f) is the ac frequency and [[tau].
s] is the activation energy for TEP, [alpha] is a constant and [alpha] < 1 suggests that the conductivity is small polaron hopping, whereas for [alpha] > 2, conductivity is due to large polarons, and k is the Boltzmann constant.
o] is the pre-exponential factor corresponding to 1/T = 0, E is the activation energy for electrical conductivity, k is the Boltzmann constant, and T is the temperature.
B] is the Boltzmann constant, T (K) is the absolute temperature, [eta] (cP) is the solvent viscosity (for [HCCl.
B], T, and [Eta], are the Boltzmann constant, the absolute temperature, and solvent viscosity, respectively.
B], T and [Eta] being the Boltzmann constant, the absolute temperature and the solvent viscosity, resp.

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