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.
References in periodicals archive ?
6], which may well contribute to decreasing the measurement uncertainty for the Boltzmann constant as a whole, Mahr Federal says.
0] coefficient matrix of V of the modified G"-T method B mobility of the end of a sub-molecule b molecular structure constant d end-to-end distance of a molecule E" loss modulus G" imaginary parts of the complex shear modulus i ith representative point k Boltzmann constant (1.
o] is the characteristic relaxation time, and k is the Boltzmann constant.
o] is relaxation time at infinite temperature, k is the Boltzmann constant, and T is the temperature.
a] is the temperature parameter (1/K) which is the resultant of the activation energy divided by the Boltzmann constant.
4 for two separate temperatures, it is possible to calculate the activation energy divided by Boltzmann constant (activation energy/k = [zeta]) as follows:
Thus the Boltzmann constant is a negative quantity in the negative universe.
B], T, and [Eta], are the Boltzmann constant, the absolute temperature, and solvent viscosity, respectively.
2] is the principal polarizability difference of the chain-link parallel and transverse to the link, k is the Boltzmann constant, and T is the absolute temperature.
is the critical free energy change, k is the Boltzmann constant, and [[Beta].
0] the atomic vibrational period, E the bond energy, e the extension ratio, d the bond strength, [Sigma] the applied stress, T the absolute temperature, k the Boltzmann constant, and [N.