Temperature

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

$T={\frac {pV}{Nk_{B}}}$

however, perhaps a better definition of temperature is

${\frac {1}{T(E,V,N)}}=\left.{\frac {\partial S}{\partial E}}\right\vert _{V,N}$

where $S$ 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" . For small systems, where fluctuations become significant, things become more complicated .

Temperature scale

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

Non-SI temperature scales

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

Kinetic temperature

$T={\frac {2}{3}}{\frac {1}{k_{B}}}{\overline {\left({\frac {1}{2}}m_{i}v_{i}^{2}\right)}}$

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

Inverse temperature

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

$\beta :={\frac {1}{k_{B}T}}$

See also

• Thermostats in molecular dynamics

References

Related reading

• Hasok Chang "Inventing Temperature: Measurement and Scientific Progress", Oxford University Press (2004) ISBN 978-0-19-517127-3
• M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert "Locality of Temperature" Physical Review X 4 031019 (2014)