Temperature: Difference between revisions

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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]]

Revision as of 11:48, 8 October 2010

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

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

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

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

Configurational temperature

[8] [9]

Non-equilibrium temperature

[10] [11]

Inverse temperature

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

Negative temperature

See also

References