# Difference between revisions of "Boltzmann constant"

Paul Wormer (Talk | contribs) m (R and k italic; kelvin not capitalized; no footnotes in equations) |
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− | The '''Boltzmann constant''' ''k'' (also ''k''<sub></sub>) is the ratio of the [[molar gas constant]] ''R'' to [[Avogadro's constant]] ''N''<sub>A</sub>. 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]]<ref>Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p582</ref>. | + | The '''Boltzmann constant''' ''k'' (also ''k''<sub>B</sub>) is the ratio of the [[molar gas constant]] ''R'' to [[Avogadro's constant]] ''N''<sub>A</sub>. 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]]<ref>Fundamentals of Physics, Fourth Edition by David Halliday, Robert Resnick, and Jearl Walker p582</ref>. |

The Boltzmann Constant is illustrated in the equation for the [[translational kinetic energy]] of a particle in thermal [[equilibrium]] with its surroundings,<ref>http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html</ref> | The Boltzmann Constant is illustrated in the equation for the [[translational kinetic energy]] of a particle in thermal [[equilibrium]] with its surroundings,<ref>http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html</ref> |

## Revision as of 15:40, 31 December 2007

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 in the equation for the translational kinetic energy of a particle in thermal equilibrium with its surroundings,^{[2]}
the so-called equipartition theorem,

KE_{avg} = 3/2 *kT*

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

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

- ↑ 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