Difference between revisions of "Boltzmann constant"

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(Clarified the Equipartition Theorem reference...I think)
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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 Constant is illustrated in the equation for the [[translational kinetic energy]] of a particle in thermal [[equilibrium]] with its surroundings, the so-called equipartition theorem:<ref>http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html</ref>
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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 Constant, and ''T'' is the [[temperature]] in [[kelvin]].
 
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]].
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For more info on this see the [[equipartition theorem]]
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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
 
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

Revision as of 01:37, 1 January 2008

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

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