Boltzmann constant: Difference between revisions
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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''' ''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 | The Boltzmann constant is illustrated here in the equation for the [[translational kinetic energy]] of a simple particle in thermal [[equilibrium]] with its surroundings:<ref>http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html</ref> | ||
<math> KE_\mathrm{avg} = \left(\frac{3}{2}\right) kT</math><br /> | <math> KE_\mathrm{avg} = \left(\frac{3}{2}\right) kT</math><br /> | ||
Where KE<sub>avg</sub> is the average [[kinetic energy]] of the particle, ''k'' is the Boltzmann | Where KE<sub>avg</sub> is the average [[kinetic energy]] of the particle, ''k'' is the Boltzmann constant, and ''T'' is the [[temperature]] in [[kelvin]]. | ||
According to [[NIST]]<ref>http://physics.nist.gov/cgi-bin/cuu/CCValue?k|ShowFirst=Browse</ref> the Boltzmann | For more info on this see the [[equipartition theorem]]. | ||
According to [[NIST]]<ref>http://physics.nist.gov/cgi-bin/cuu/CCValue?k|ShowFirst=Browse</ref> the Boltzmann constant has a value of 1.3806504 x 10<sup>-23</sup> J/K with a [[standard uncertainty]] of 0.0000024 x 10<sup>-23</sup> J/K and a [[relative uncertainty]] of 1.7 x 10<sup>-6</sup> (this is represented by the [[concise form]] 1.380 6504(24) x 10<sup>-23</sup> J/K | |||
The Boltzmann constant can also be represented in alternative units as 8.617385 x 10<sup>-5</sup> eV/K | |||
==References== | ==References== | ||
<references/> | <references/>[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 11:00, 20 July 2024
The Boltzmann constant k (also kB) is the ratio of the molar gas constant R to Avogadro's constant NA. 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 KEavg 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
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