Critical points

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The critical point is a point found at the end of the liquid-vapour coexistence curve (the red point shown on the pressure-temperature plot on the right). At this point the temperature is known as the critical temperature and the pressure is known as the critical pressure . For an interesting discourse on the "discovery" of the liquid-vapour critical point, the Bakerian Lecture of Thomas Andrews makes good reading [1]. Critical points are singularities in the partition function. In the critical point vicinity (Ref. [2] Eq. 17a)

and

For a review of the critical region see the work of Michael E. Fisher [3]

"... Turning now to the question of specific heats, it has long been known that real gases exhibit a large ``anomalous" specific-heat maximum above which lies near the critical isochore and which is not expected on classical theory..."

also

"... measurements (Ref. [4] ) of for argon along the critical isochore suggest strongly that . Such a result is again inconsistent with classical theory."

Thus in the vicinity of the liquid-vapour critical point, both the isothermal compressibility and the heat capacity at constant pressure diverge to infinity.

Liquid-liquid critical point

Solid-liquid critical point

It is widely held that there is no solid-liquid critical point. The reasoning behind this was given on the grounds of symmetry by Landau and Lifshitz [5]. However, recent work using the Z2 potential suggests that this may not be the last word on the subject. [6].

Tricritical points

Critical exponents

Main article: Critical exponents

See also

References

Related reading