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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.
The compressibility factor at the critical point, which is defined as =, where the subscript indicates physical quantities measured at the critical point, is predicted to be a constant independent of substance by many equations of state.
In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point.These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states.
The critical point is described by a conformal field theory. According to the renormalization group theory, the defining property of criticality is that the characteristic length scale of the structure of the physical system, also known as the correlation length ξ, becomes infinite. This can happen along critical lines in phase space.
Critical point (set theory), an elementary embedding of a transitive class into another transitive class which is the smallest ordinal which is not mapped to itself; Critical point (thermodynamics), a temperature and pressure of a material beyond which there is no longer any difference between the liquid and gas phases; Quantum critical point ...
So for temperatures above the critical temperature (126.2 K), there is no phase transition; as pressure increases the gas gradually transforms into something more like a liquid. Just above the critical point there is a range of pressure for which Z drops quite rapidly (see the 130 K curve), but at higher temperatures the process is entirely ...
Boca Raton, Florida, 2003; Section 6, Fluid Properties; Critical Constants. Also agrees with Celsius values from Section 4: Properties of the Elements and Inorganic Compounds, Melting, Boiling, Triple, and Critical Point Temperatures of the Elements Estimated accuracy for Tc and Pc is indicated by the number of digits.
Anisimov et al. (2004), [11] without referring to Frenkel, Fisher, or Widom, reviewed thermodynamic derivatives (specific heat, expansion coefficient, compressibility) and transport coefficients (viscosity, speed of sound) in supercritical water, and found pronounced extrema as a function of pressure up to 100 K above the critical temperature.