Temperature - Revision history

Carl McBride: /* References */ Added a publication

2016-03-29T15:44:16Z

References: Added a publication

← Older revision		Revision as of 17:44, 29 March 2016
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	'''Related reading'''		'''Related reading'''
	*Hasok Chang "Inventing Temperature: Measurement and Scientific Progress", Oxford University Press (2004) ISBN 978-0-19-517127-3		*Hasok Chang "Inventing Temperature: Measurement and Scientific Progress", Oxford University Press (2004) ISBN 978-0-19-517127-3
			*[http://dx.doi.org/10.1103/PhysRevX.4.031019 M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert "Locality of Temperature" Physical Review X '''4''' 031019 (2014)]


	[[category: Classical thermodynamics]]		[[category: Classical thermodynamics]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: /* Negative temperature */ Added a reference

2010-10-08T11:01:21Z

Negative temperature: Added a reference

← Older revision		Revision as of 13:01, 8 October 2010
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	:<math>\beta := \frac{1}{k_BT}</math>		:<math>\beta := \frac{1}{k_BT}</math>
	==Negative temperature==		==Negative temperature==
			<ref>[http://dx.doi.org/10.1103/PhysRev.103.20 Norman F. Ramsey "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures", Physical Review '''103''' pp. 20-28 (1956)]</ref>

	==See also==		==See also==
	*[[Thermostats \| Thermostats in molecular dynamics]]		*[[Thermostats \| Thermostats in molecular dynamics]]

Carl McBride: /* References */ Added a book reference

2010-10-08T10:56:19Z

References: Added a book reference

← Older revision		Revision as of 12:56, 8 October 2010
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	==References==		==References==
	<references/>		<references/>
			'''Related reading'''
			*Hasok Chang "Inventing Temperature: Measurement and Scientific Progress", Oxford University Press (2004) ISBN 978-0-19-517127-3
	[[category: Classical thermodynamics]]		[[category: Classical thermodynamics]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: Added another reference

2010-10-08T10:48:07Z

Added another reference

← Older revision		Revision as of 12:48, 8 October 2010
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	:<math>\frac{1}{T(E,V,N)} = \left. \frac{\partial S}{\partial E}\right\vert_{V,N}</math>		:<math>\frac{1}{T(E,V,N)} = \left. \frac{\partial S}{\partial E}\right\vert_{V,N}</math>

	where <math>S</math> is the [[entropy]].		where <math>S</math> is the [[entropy]]. That said, in the words of Landau and Lifshitz "''Like the entropy, the temperature is seen to be a purely statistical quantity, which has meaning only for macroscopic bodies''" <ref>L. D. Landau and E. M. Lifshitz "Statistical Physics", Course of Theoretical Physics volume 5 Part 1 3rd Edition (1984) ISBN 0750633727 p. 35</ref>. For small systems, where fluctuations become significant, things become more complicated <ref>[http://dx.doi.org/10.1119/1.1987181 Richard McFee "On Fluctuations of Temperature in Small Systems", American Journal of Physics '''41''' pp. 230-234 (1973)]</ref>
			<ref>[http://dx.doi.org/10.1063/1.3486557 Grey Sh. Boltachev and Jürn W. P. Schmelzer "On the definition of temperature and its fluctuations in small systems", Journal of Chemical Physics '''133''' 134509 (2010)]</ref>.
	==Temperature scale==		==Temperature scale==
	Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]], Baron Kelvin of Largs <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>		Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]], Baron Kelvin of Largs <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>
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	==References==		==References==
	<references/>		<references/>
	~~'''Related reading'''~~
	*[http://dx.doi.org/10.1063/1.3486557 Grey Sh. Boltachev and Jürn W. P. Schmelzer "On the definition of temperature and its fluctuations in small systems", Journal of Chemical Physics '''133''' 134509 (2010)]
	[[category: Classical thermodynamics]]		[[category: Classical thermodynamics]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: /* References */ Added a recent publication

2010-10-08T09:13:30Z

References: Added a recent publication

← Older revision		Revision as of 11:13, 8 October 2010
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	==References==		==References==
	<references/>		<references/>
			'''Related reading'''
			*[http://dx.doi.org/10.1063/1.3486557 Grey Sh. Boltachev and Jürn W. P. Schmelzer "On the definition of temperature and its fluctuations in small systems", Journal of Chemical Physics '''133''' 134509 (2010)]
	[[category: Classical thermodynamics]]		[[category: Classical thermodynamics]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: /* Temperature scale */ Added a historical note

2010-09-28T14:49:53Z

Temperature scale: Added a historical note

← Older revision		Revision as of 16:49, 28 September 2010
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	where <math>S</math> is the [[entropy]].		where <math>S</math> is the [[entropy]].
	==Temperature scale==		==Temperature scale==
	Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]] <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>		Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]], Baron Kelvin of Largs <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>
	<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.		<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.
	====Non-SI temperature scales====		====Non-SI temperature scales====

Carl McBride: /* Non-SI temperature scales */ Added historical note

2010-09-28T14:45:56Z

Non-SI temperature scales: Added historical note

← Older revision		Revision as of 16:45, 28 September 2010
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	====Non-SI temperature scales====		====Non-SI temperature scales====
	'''Rankine temperature scale''' <br>		'''Rankine temperature scale''' <br>
	0°R corresponds to 0 kelvin, and 1.8 degrees Rankine is equivalent to 1 kevlin <ref>[http://pml.nist.gov/Pubs/SP811/appenB9.html#TEMPERATURE NIST guide to SI Units]</ref>		0°R corresponds to 0 kelvin, and 1.8 degrees Rankine is equivalent to 1 kevlin <ref>[http://pml.nist.gov/Pubs/SP811/appenB9.html#TEMPERATURE NIST guide to SI Units]</ref>. The Rankine temperature scale is named after [[William John Macquorn Rankine]].

	==Kinetic temperature==		==Kinetic temperature==

Carl McBride: Changed units to temperature scales

2010-09-28T14:44:48Z

Changed units to temperature scales

← Older revision		Revision as of 16:44, 28 September 2010
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	where <math>S</math> is the [[entropy]].		where <math>S</math> is the [[entropy]].
	==~~Units~~==		==Temperature scale==
	Temperature has the SI units of ''kelvin'' (K) (named in honour of [[William Thomson]] <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>		Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]] <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>
	<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.		<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.
			====Non-SI temperature scales====
			'''Rankine temperature scale''' <br>
			0°R corresponds to 0 kelvin, and 1.8 degrees Rankine is equivalent to 1 kevlin <ref>[http://pml.nist.gov/Pubs/SP811/appenB9.html#TEMPERATURE NIST guide to SI Units]</ref>

	==Kinetic temperature==		==Kinetic temperature==
	:<math>T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}</math>		:<math>T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}</math>

Carl McBride: Changed references to Cite format.

2010-03-09T10:12:58Z

Changed references to Cite format.

← Older revision		Revision as of 12:12, 9 March 2010
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	where <math>S</math> is the [[entropy]].		where <math>S</math> is the [[entropy]].
	==Units==		==Units==
	Temperature has the SI units of ''kelvin'' (K) (named in honour of [[William Thomson]]) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]].		Temperature has the SI units of ''kelvin'' (K) (named in honour of [[William Thomson]] <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]</ref>
	~~====External links====~~		<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.
	*[http://~~physics~~.~~nist~~.~~gov~~/~~cuu~~/~~Units~~/~~kelvin~~.~~html NIST reference page~~]

	==Kinetic temperature==		==Kinetic temperature==
	:<math>T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}</math>		:<math>T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}</math>
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	==Configurational temperature==		==Configurational temperature==
	*[http://dx.doi.org/10.1103/PhysRevLett.78.772 Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters ''' 78''' pp. 772-774 (1997)]		<ref>[http://dx.doi.org/10.1103/PhysRevLett.78.772 Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters ''' 78''' pp. 772-774 (1997)]</ref>
	*[http://dx.doi.org/10.1063/1.480995 András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics '''112''' pp. 3964-3966 (2000)]		<ref>[http://dx.doi.org/10.1063/1.480995 András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics '''112''' pp. 3964-3966 (2000)]</ref>

	==Non-equilibrium temperature==		==Non-equilibrium temperature==
	*[http://dx.doi.org/10.1063/1.2743032 Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics '''126''' 244506 (2007)]		<ref>[http://dx.doi.org/10.1063/1.2743032 Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics '''126''' 244506 (2007)]</ref>
	*[http://dx.doi.org/10.1063/1.2958913 J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics '''129''' 044508 (2008)]		<ref>[http://dx.doi.org/10.1063/1.2958913 J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics '''129''' 044508 (2008)]</ref>

	==Inverse temperature==		==Inverse temperature==
	It is frequently convenient to define a so-called [[inverse temperature]], <math>\beta</math>, such that		It is frequently convenient to define a so-called [[inverse temperature]], <math>\beta</math>, such that
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	*[[Thermostats \| Thermostats in molecular dynamics]]		*[[Thermostats \| Thermostats in molecular dynamics]]
	==References==		==References==
	#William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp. (1848)		<references/>
	~~#[http:~~/~~/dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10 (1990)]~~
	~~#[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]~~
	[[category: Classical thermodynamics]]		[[category: Classical thermodynamics]]
	[[category: statistical mechanics]]		[[category: statistical mechanics]]
	[[category: Non-equilibrium thermodynamics]]		[[category: Non-equilibrium thermodynamics]]

Carl McBride: Added a section heading

2010-03-09T10:00:05Z

Added a section heading

← Older revision		Revision as of 12:00, 9 March 2010
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	:<math>\beta := \frac{1}{k_BT}</math>		:<math>\beta := \frac{1}{k_BT}</math>
			==Negative temperature==
	==See also==		==See also==
	*[[Thermostats \| Thermostats in molecular dynamics]]		*[[Thermostats \| Thermostats in molecular dynamics]]