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 ?
In the coexistence region, the critical point is at the situation in which both minima of spherical point is at the situation in which both minima of spherical and deformed are degenerate.
Totally, we conclude that only four-, five-, and six-dimensional HL AdS black holes with spherical horizon have physical critical points, as shown in Table 1.
The critical points of system (3.2) are solutions ([x.sub.1], [x.sub.2]) of the system
These shape phase transitions were considered in the framework of the geometric collective model [12], resulting in the introduction of the critical point symmetries E(5) [13] X(5) [14].
As we have already mentioned in the introductory section, our goal in this work is to apply the methodology developed in [1] to study conditions for existence, location and unicity of the limit cycles surrounding 1, 7 and 13 critical points.
The similar dependencies of the vehicle entering the parking space, while in the critical point and leaving the parking place are shown in Fig.
The expressions of the other critical points come from the roots of the 6-degree symmetric polynomial Q(z,a,c) given in the following result.
-We explained how to control such critical points to protect people health.
How does an interactive geometry program make it possible to treat a broad subject like critical points of functions in a unified sway, across a wide range of courses at different levels?
However, from first principles in differential topology, local minima turn out to be difficult to analyse independently from other critical points, namely saddles and local maxima.
He calls for a "properly risk-managed approach to critical infrastructure" and "an integrated, sensible, systems-based approach." And according to Dana Milbank of The Washington Post, to whom I am indebted for these examples, he speaks of "the critical points of triangulation" and of "better information about the constituents of the supply chain." At DHS, he aims for "internal integration into a unified command structure:" I have to say that I have never known anyone who talked this way who was also an effective leader.
In its written comments on this rulemaking, the Canadian Council of Motor Transport Administrators (CCMTA) expressed disappointment that some of the directions proposed by the FMCSA "ran counter to critical and fundamental points of consensus which had been built over the previous 10 years through the research and standard development phases." What are the critical points of difference that could jeopardize regulatory uniformity between the United States and Canada?