Temperature: Difference between revisions

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The '''temperature''' of a system in [[classical thermodynamics]] is  intimately related to the [[zeroth law of thermodynamics]]; two systems having to have the same temperature if they are to be in thermal equilibrium (i.e. there is no net [[heat]] flow between them).
The '''temperature''' of a system in [[classical thermodynamics]] is  intimately related to the [[zeroth law of thermodynamics]]; two systems having to have the same temperature if they are to be in thermal equilibrium (i.e. there is no net [[heat]] flow between them).
However, it is most useful to have a temperature scale.
However, it is most useful to have a temperature scale.
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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>
==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]].
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>
====External links====
<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>.
*[http://physics.nist.gov/cuu/Units/kelvin.html NIST reference page]
==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>
<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>. The Rankine temperature scale is named after [[William John Macquorn Rankine]].


==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>
   
   
where <math>k_B</math> is the [[Boltzmann constant]].
where <math>k_B</math> is the [[Boltzmann constant]].  The kinematic temperature so defined is related to the [[equipartition]] theorem; for more details, see [http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29 Configuration integral].


==Configurational temperature==
==Configurational temperature==
*[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/10.1103/PhysRevLett.78.772 Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters ''' 78''' pp. 772-774 (1997)]</ref>
<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>
<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


:<math>\beta := \frac{1}{k_BT}</math>
:<math>\beta := \frac{1}{k_BT}</math>
==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==
*[[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)]
'''Related reading'''
#[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)]
*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]]

Latest revision as of 16:44, 29 March 2016

The temperature of a system in classical thermodynamics is intimately related to the zeroth law of thermodynamics; two systems having to have the same temperature if they are to be in thermal equilibrium (i.e. there is no net heat flow between them). However, it is most useful to have a temperature scale. By making use of the ideal gas law one can define an absolute temperature

however, perhaps a better definition of temperature is

where 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" [1]. For small systems, where fluctuations become significant, things become more complicated [2] [3].

Temperature scale[edit]

Temperature has the SI units (Système International d'Unités) of kelvin (K) (named in honour of William Thomson, Baron Kelvin of Largs [4]) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water[5] [6].

Non-SI temperature scales[edit]

Rankine temperature scale
0°R corresponds to 0 kelvin, and 1.8 degrees Rankine is equivalent to 1 kevlin [7]. The Rankine temperature scale is named after William John Macquorn Rankine.

Kinetic temperature[edit]

where is the Boltzmann constant. The kinematic temperature so defined is related to the equipartition theorem; for more details, see Configuration integral.

Configurational temperature[edit]

[8] [9]

Non-equilibrium temperature[edit]

[10] [11]

Inverse temperature[edit]

It is frequently convenient to define a so-called inverse temperature, , such that

Negative temperature[edit]

[12]

See also[edit]

References[edit]

  1. L. D. Landau and E. M. Lifshitz "Statistical Physics", Course of Theoretical Physics volume 5 Part 1 3rd Edition (1984) ISBN 0750633727 p. 35
  2. Richard McFee "On Fluctuations of Temperature in Small Systems", American Journal of Physics 41 pp. 230-234 (1973)
  3. 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)
  4. 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)
  5. H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 pp. 3-10 (1990)
  6. H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 p. 107 (1990)
  7. NIST guide to SI Units
  8. Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters 78 pp. 772-774 (1997)
  9. András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics 112 pp. 3964-3966 (2000)
  10. Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics 126 244506 (2007)
  11. J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics 129 044508 (2008)
  12. Norman F. Ramsey "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures", Physical Review 103 pp. 20-28 (1956)

Related reading