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Critical points

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Press temp.png

The critical point, discovered in 1822 by Charles Cagniard de la Tour [1][2] , 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 (T_c) and the pressure is known as the critical pressure (P_c). For an interesting discourse on the "discovery" of the liquid-vapour critical point, the Bakerian Lecture of Thomas Andrews makes good reading [3]. Critical points are singularities in the partition function. In the critical point vicinity (Ref. [4] Eq. 17a)

 \left.\frac{\partial P}{\partial n}\right\vert_{T}   \simeq 0


n \int_0^{\infty} c(r) ~4 \pi r^2 ~{\rm d}r \simeq  1

For a review of the critical region see the work of Michael E. Fisher [5]

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


"... measurements (Ref. [6] ) of C_V(T) for argon along the critical isochore suggest strongly that C_V(T) \rightarrow \infty ~{\rm as} ~ T  \rightarrow  T_c \pm. 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[edit]

Solid-liquid critical point[edit]

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 [7]. However, recent work using the Z2 potential suggests that this may not be the last word on the subject. [8].

Tricritical points[edit]

Critical exponents[edit]

Main article: Critical exponents

Yang-Yang anomaly[edit]

Main article: Yang-Yang anomaly

See also[edit]


Related reading

  • H. Eugene Stanley "Introduction to Phase Transitions and Critical Phenomena", Oxford University Press (1971) ISBN 9780195053166
  • Cyril Domb "The Critical Point: A Historical Introduction To The Modern Theory Of Critical Phenomena", Taylor and Francis (1996) ISBN 9780748404353