Difference between revisions of "Boltzmann constant"
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The '''Boltzmann constant''' (symbol: '''''k''<sub>B</sub>''' or '''''k''''') is a [[physical constant]] which links [[energy]] and [[temperature]] on a molecular scale. It also appears in statistical definitions of [[entropy]]. It is named after the Austrian physicist [[Ludwig Boltzmann]]. The 2006 [[CODATA recommended value]] is {{nowrap|1.380 6504(24){{e|−23}} J K<sup>−1</sup>}}.<ref>{{CODATA 2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?k}}.</ref> | The '''Boltzmann constant''' (symbol: '''''k''<sub>B</sub>''' or '''''k''''') is a [[physical constant]] which links [[energy]] and [[temperature]] on a molecular scale. It also appears in statistical definitions of [[entropy]]. It is named after the Austrian physicist [[Ludwig Boltzmann]]. The 2006 [[CODATA recommended value]] is {{nowrap|1.380 6504(24){{e|−23}} J K<sup>−1</sup>}}.<ref>{{CODATA 2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?k}}.</ref> | ||
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| + | ==Determination== | ||
| + | The Boltzmann constant is currently determined from the [[molar gas constant]] ''R'' | ||
| + | :''k<sub>B</sub> = ''R''/''N''<sub>A</sub> | ||
| + | with ''R'' being determined from measurements of the [[speed of sound]] in [[argon]]. The current uncertainty in the value of ''k''<sub>B</sub> is entirely due to the uncertainty in the value of ''R'': modern measurements may push this below 10<sup>−6</sup>.<ref>{{citation | last = Moldover | first = Michael R. | title = Optimizing acoustic measurements of the Boltzmann constant | journal = C. R. Phys. | volume = 10 | issue = 9 | pages = 815–27 | doi = 10.1016/j.crhy.2009.10.007}}.</ref><ref>{{citation | first1 = Laurent | last1 = Pitre | first2 = Cécile | last2 = Guianvarc’h | first3 = Fernando | last3 = Sparasci | first4 = Arnaud | last4 = Guillou | first5 = Daniel | last5 = Truong | first6 = Yves | last6 = Hermier | first7 = Marc E. | last7 = Himbert | title = An improved acoustic method for the determination of the Boltzmann constant at LNE-INM/CNAM | journal = C. R. Phys. | volume = 10 | issue = 9 | pages = 835–48 | doi = 10.1016/j.crhy.2009.11.001}}.</ref> | ||
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| + | Direct methods for determining ''k''<sub>B</sub> have also been developed recently. | ||
| + | *Josephson noise thermometer<ref>{{citation | first1 = Samuel | last1 = Benz | first2 = D. Rod | last2 = White | first3 = JiFeng | last3 = Qu | first4 = Horst | last4 = Rogalla | first5 = Weston | last5 = Tew | title = Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer | journal = C. R. Phys. | volume = 10 | issue = 9 | pages = 849–58 | doi = 10.1016/j.crhy.2009.10.008}}.</ref> | ||
| + | *Doppler broadening<ref>{{citation | first1 = Khelifa | last1 = Djerroud | first2 = Cyril | last2 = Lemarchand | first3 = Alexandre | last3 = Gauguet | first4 = Christophe | last4 = Daussy | first5 = Stephan | last5 = Briaudeau | first6 = Benoît | last6 = Darquié | first7 = Olivier | last7 = Lopez | first8 = Anne | last8 = Amy-Klein | first9 = Christian | last9 = Chardonnet | first10 = Christian J. | last10 = Bordé | title = Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8{{e|−5}} accuracy level | journal = C. R. Phys. | volume = 10 | issue = 9 | pages = 883–93 | doi = 10.1016/j.crhy.2009.10.020}}.</ref> | ||
==Notes and references== | ==Notes and references== | ||
Latest revision as of 09:07, 5 September 2010
The Boltzmann constant (symbol: kB or k) is a physical constant which links energy and temperature on a molecular scale. It also appears in statistical definitions of entropy. It is named after the Austrian physicist Ludwig Boltzmann. The 2006 CODATA recommended value is 1.380 6504(24) × 10−23 J K−1.[1]
Determination
The Boltzmann constant is currently determined from the molar gas constant R
- kB = R/NA
with R being determined from measurements of the speed of sound in argon. The current uncertainty in the value of kB is entirely due to the uncertainty in the value of R: modern measurements may push this below 10−6.[2][3]
Direct methods for determining kB have also been developed recently.
Notes and references
Notes
References
- ↑ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. CODATA Recommended Values of the Fundamental Physical Constants: 2006. Rev. Mod. Phys. 2008, 80 (2), 633–730. doi:10.1103/RevModPhys.80.633, <http://physics.nist.gov/cuu/Constants/codata.pdf>. Direct link to value.
- ↑ Moldover, Michael R. Optimizing acoustic measurements of the Boltzmann constant. C. R. Phys., 10 (9), 815–27. DOI: 10.1016/j.crhy.2009.10.007.
- ↑ Pitre, Laurent; Guianvarc’h, Cécile; Sparasci, Fernando; Guillou, Arnaud; Truong, Daniel; Hermier, Yves; Himbert, Marc E. An improved acoustic method for the determination of the Boltzmann constant at LNE-INM/CNAM. C. R. Phys., 10 (9), 835–48. DOI: 10.1016/j.crhy.2009.11.001.
- ↑ Benz, Samuel; White, D. Rod; Qu, JiFeng; Rogalla, Horst; Tew, Weston Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer. C. R. Phys., 10 (9), 849–58. DOI: 10.1016/j.crhy.2009.10.008.
- ↑ Djerroud, Khelifa; Lemarchand, Cyril; Gauguet, Alexandre; Daussy, Christophe; Briaudeau, Stephan; Darquié, Benoît; Lopez, Olivier; Amy-Klein, Anne, et al. Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10−5 accuracy level. C. R. Phys., 10 (9), 883–93. DOI: 10.1016/j.crhy.2009.10.020.
Further reading
- Bormashenko, Edward; Sheshnev, Avigdor Measurable Values, Numbers and Fundamental Physcal Constants: Is the Boltzmann Constant kB a Fundamental Physical Constant?. Therm. Sci. 2009, 13 (4), 253–58. DOI: 10.2298/TSCI0904253B.
External links
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See also the corresponding article on Wikipedia. |
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