Boltzmann constant (redirected from Boltzmanns constant)

Boltzmann constant

Ratio of the universal gas constant (see gas laws) to Avogadro's number. It has a value of 1.380662 × 10⁻²³ joules per kelvin. Named after Ludwig Boltzmann, it is a fundamental constant of physics, occurring in nearly every statistical formulation of both classical and quantum physics.

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Boltzmann constant [′bōlts·mən ‚kän·stənt]

(statistical mechanics)

The ratio of the universal gas constant to the Avogadro number.

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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