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.

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

• 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)