Temperature: Difference between revisions
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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> | ||
<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>. | |||
==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== | ||
<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== | ||
<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 | ||
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*[[Thermostats | Thermostats in molecular dynamics]] | *[[Thermostats | Thermostats in molecular dynamics]] | ||
==References== | ==References== | ||
<references/> | |||
[[category: Classical thermodynamics]] | [[category: Classical thermodynamics]] | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||
[[category: Non-equilibrium thermodynamics]] | [[category: Non-equilibrium thermodynamics]] | ||
Revision as of 11:12, 9 March 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.
Units
Temperature has the SI units of kelvin (K) (named in honour of William Thomson [1]) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water[2] [3].
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
Non-equilibrium temperature
Inverse temperature
It is frequently convenient to define a so-called inverse temperature, , such that
Negative temperature
See also
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)
- ↑ H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 pp. 3-10 (1990)
- ↑ H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia 27 p. 107 (1990)
- ↑ Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters 78 pp. 772-774 (1997)
- ↑ András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics 112 pp. 3964-3966 (2000)
- ↑ Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics 126 244506 (2007)
- ↑ J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics 129 044508 (2008)