Critical point (thermodynamics)

 ( Conformal Field Theory ) 

[[File:CriticalPointMeasurementEthane.jpg|thumb|upright=1.5| ]]

In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas comes into a supercritical phase, and so cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature T_c and a critical pressure p_c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field.

The figure shows the schematic PT diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid, liquid and vapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At the triple point, all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at some critical temperature T_c and critical pressure p_c. This is the critical point.

The critical point of water occurs at and .

In the vicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming even more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high dielectric constant, and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor dielectric, a bad solvent for electrolytes, and mixes more readily with nonpolar gases and organic molecules.Anisimov, Jan Sengers, Levelt Sengers (2004): Near-critical behavior of aqueous systems. Chapter 2 in Aqueous System at Elevated Temperatures and Pressures Palmer et al., eds. Elsevier.

At the critical point, only one phase exists. The heat of vaporization is zero. There is a stationary point inflection point in the constant-temperature line ( critical isotherm) on a PV diagram. This means that at the critical point:P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.

$\backslash left(\backslash frac\{\backslash partial\; p\}\{\backslash partial\; V\}\backslash right)\_T\; =\; 0,$

$\backslash left(\backslash frac\{\backslash partial^2p\}\{\backslash partial\; V^2\}\backslash right)\_T\; =\; 0.$

Above the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called supercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by Michael Fisher and Benjamin Widom, who identified a p– T line that separates states with different asymptotic statistical properties (Fisher–Widom line).

Sometimes the critical point does not manifest in most thermodynamic or mechanical properties, but is "hidden" and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets, and a sudden enhancement in defect pair concentration.

 \quad V_\text{c} = 3nb,
 \quad p_\text{c} = \frac{a}{27b^2}.
     

 \quad p_\text{r} = \frac{p}{p_\text{c}},
 \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.