# Boltzmann constant

*13 January 2011*.

The **Boltzmann constant** *k* (also *k*_{B}) is the ratio of the molar gas constant *R* to Avogadro's constant *N*_{A}. It can be thought of as the gas constant for a single molecule (or even for an arbitrary particle in a colloidal solution) rather than for a mole^{[1]}.

The Boltzmann constant is illustrated here in the equation for the translational kinetic energy of a simple particle in thermal equilibrium with its surroundings:^{[2]}

Where KE_{avg} is the average kinetic energy of the particle, *k* is the Boltzmann constant, and *T* is the temperature in kelvin.

For more info on this see the equipartition theorem.

According to NIST^{[3]} the Boltzmann constant has a value of 1.3806504 x 10^{-23} J/K with a standard uncertainty of 0.0000024 x 10^{-23} J/K and a relative uncertainty of 1.7 x 10^{-6} (this is represented by the concise form 1.380 6504(24) x 10^{-23} J/K

The Boltzmann constant can also be represented in alternative units as 8.617385 x 10^{-5} eV/K

## [edit] References

- ↑ Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p582
- ↑ http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
- ↑ http://physics.nist.gov/cgi-bin/cuu/CCValue?k%7CShowFirst=Browse

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