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Do ideal gases have a certain potential energy at a certain temperature?

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For an ideal gas there is no potential energy, by definition.

For a real gas there is a potential between the molecules, and the average value of the potential energy will have a (very complicated) dependency on temperature.

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From a kinetic theory of gases perspective, or equilibrium statistical mechanics perspective, potential of ideal gases will strictly be a function of the position of the particles (in fact the relative position of the particles). temperature is just one third of the mean square velocity. For ideal gases, in general

$U = f(\bar{r}_1,\bar{r}_2 ... \bar{r}_n)$

where $\bar{r}_i$ represent the relative positions of the particles to some reference frame. This can be translated into the relative distances between particles as well. For real gases this may be different though.

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  • $\begingroup$ "temperature is just one third of the mean square velocity" is that true for interacting gases? The energy stored as inter-atomic potential energy has no bearing on temperature? $\endgroup$
    – garyp
    Jan 28 '15 at 17:46

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