critical point


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critical point

[′krid·ə·kəl ′pȯint]
(mathematics)
A point at which the first derivative of a function is either 0 or does not exist.
(petroleum engineering)
A location on the drilling line which is subject to strain when the pipe is run into or pulled out of the drill hole.
(physical chemistry)
The temperature and pressure at which two phases of a substance in equilibrium with each other become identical, forming one phase.
The temperature and pressure at which two ordinarily partially miscible liquids are consolute.

Critical Point

 

a point on a phase diagram corresponding to the critical state. The critical point of two-phase liquid-vapor equilibrium is the end point on the equilibrium curve and is characterized by the critical values of the temperature Tc, pressure Pc, and volume Vc (see Table 1).

Table 1. Parameters of the liquid-vapor critical point of some substances
 Tc
(oK)
>
pc
(atm)*
Vc × 106
(m3 /mole)
* 1 atm = 1.01 × 106 N/m2
Helium...........5.32.2657.8
Hydrogen...........33.012.861.8
Oxygen.................154.850.174.4
Nitrogen...........126.233.590.1
Carbon dioxide.........304.272.994.0
Propane............369.942.0200
Alcohol (ethyl)............516.363.0167
Bromine..............584102144
Water...........647218.356
Iodine...........785116
Sulfur...........1313116
Mercury...........17501,50044
Cesium...........2030115332

The critical point is a particular case of the phase transition point and is characterized by the loss of thermodynamic stability with respect to the density or composition of the substance. On one side of the critical point the substance is homogeneous (usually when T > Tc); on the other it separates into phases. For mixtures or solutions a distinction should be made between the critical point of liquid-vapor equilibrium and the critical point of equilibrium of phases of different composition that are in the same state of aggregation (liquid-liquid or gas-gas). In this connection the critical point of mixtures (or solutions) is also characterized by the critical concentration xc. As a result of the increased number of parameters determining the system’s state, mixtures have not a critical point but rather a critical curve, whose points differ in the values of Tc, pc, Vc, and xc. Critical phenomena are observed in the region of the critical point.

critical point

critical pointclick for a larger image
The point between two bases from which it will take the same time to fly to either base.
An aircraft flying at flight level 350 has pressurization failure and is forced to descend to flight level 130. At critical point, it can either proceed to its destination airport or it can return to the airport of departure. It would take the same time to the either airport. The value of critical point will change if the aircraft is not incapacitated and can fly at the same altitude and speed.
References in periodicals archive ?
As similar as the discussions in Section 3, one can find that only four-, five-, and six-dimensional HL AdS black holes with spherical horizon have physical critical point, as shown in Table 3.
For any positive y and O there is exactly one critical point of the form (x, x) .
Z(5): Critical Point Symmetry for the Prolate to Oblate Nuclear Shape Phase Transition.
Consequently the critical point ([r.sub.-], [[theta].sub.-]) is a saddle.
The sign of difference integration is not an indication of the critical point, whereas the integral value could be--near the critical point, it is bigger.
Section 3 is devoted to the analysis of the critical points, which will be useful in Section 5 to obtain the parameter planes.
This step up to 1m2f seems sure to suit Critical Point and the opposition is moderate.
Two particular examples of polynomial functions give a good idea of the critical point behavior for functions of two variables.
In a series of experiments in recent years, scientists have begun to close in on this critical point. These advances offer a glimpse of possible explanations for water's unusual behaviors, and suggest that Stanley and Poole may have been on to something.
In [15], it was applied to Markov functions: for such functions, it was shown in essence that uniqueness of a critical point holds if the Green capacity of the support of the defining measure is less than an absolute constant.
Palaeoclimate reconstructions suggest that when atmospheric loading of greenhouse gases exceeds an unknown threshold (a "critical point" or "tipping point"), a dramatic avalanche of change may be triggered.
The negotiations between Northwest Airlines Corp (NWACQ.PK) and its pilots are at a critical point.