ChemWiki: The Dynamic Chemistry E-textbook > Physical Chemistry > Thermodynamics > 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 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

T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}

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

Configurational temperature

[4] [5]

Non-equilibrium temperature

[6] [7]

Inverse temperature

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

\beta := \frac{1}{k_BT}

Negative temperature


You must to post a comment.
Last Modified
09:59, 2 Oct 2013

Page Rating

Was this article helpful?


Module Vet Level:
Module Target Level:

Creative Commons License UC Davis GeoWiki by University of California, Davis is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. Permissions beyond the scope of this license may be available at Terms of Use