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MindTouch
http://mindtouch.com

This file and accompanying files are licensed under the MindTouch Master Subscription Agreement (MSA).

At any time, you shall not, directly or indirectly: (i) sublicense, resell, rent, lease, distribute, market, commercialize or otherwise transfer rights or usage to: (a) the Software, (b) any modified version or derivative work of the Software created by you or for you, or (c) MindTouch Open Source (which includes all non-supported versions of MindTouch-developed software), for any purpose including timesharing or service bureau purposes; (ii) remove or alter any copyright, trademark or proprietary notice in the Software; (iii) transfer, use or export the Software in violation of any applicable laws or regulations of any government or governmental agency; (iv) use or run on any of your hardware, or have deployed for use, any production version of MindTouch Open Source; (v) use any of the Support Services, Error corrections, Updates or Upgrades, for the MindTouch Open Source software or for any Server for which Support Services are not then purchased as provided hereunder; or (vi) reverse engineer, decompile or modify any encrypted or encoded portion of the Software.

A complete copy of the MSA is available at http://www.mindtouch.com/msa

# 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.

### 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

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

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

### Inverse temperature

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

$\beta := \frac{1}{k_BT}$

### Contributions

09:59, 2 Oct 2013

## Classifications

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### Textbook Maps

An NSF funded Project