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 ?
This is the goal of the present work: studying the global phase portrait of system (1) paying special attention to the existence, location and uniqueness of limit cycles surrounding 1, 7 or 13 critical points.
6 charts--when the vehicle enters the parking space, when it is in the critical point and when it leaves the parking space.
Trust Morris to find the best strip of ground, make the right move at the right time and kick-start a winning sequence for Critical Point, who is highly unlikely to be rated less than 60 in a month's time.
This "semi-cubical parabola" curve in the "control space" of all possible choices of u and v will separate the (u,v) choices that give functions with 3 critical points from those that give functions with 1 critical point.
As water approaches this critical point, the difference between water and steam grows increasingly smaller,' Stanley explains.
The critical point theory that we need is recalled in section 4, while section 5 is devoted to the proof of our uniqueness criterion in degree 1.
Data on the percentages of critical points and examples, as well as number of extra points, which were recorded in student notes were collected for each set of student notes produced in each condition.
That experiment also showed that xenon, when close to the critical point, is partly elastic; that is, it can "stretch" as well as flow.
Total quantity or scope: Feasibility study for alternative technical solutions / additional work to be performed on the critical point 01 Bala of the project Improving the navigation conditions on the Danube between Calarasi and Braila km 375 - km 175 in accordance with the requirements of the specification part of the tender documentation
As the sample temperature approaches the critical point, "those twinkles get slower and slower and more and more intense," Gammon says.
Hosted Solutions, the East Coast's premier data center and managed services provider announces today that Critical Point Group, the leading provider of marketing services for community banks and similar financial institutions has elected Hosted Solutions to provide its dedicated needs for the next three years.
It was a critical error at a critical point in the game, but he's a great kid that will build from this, and he showed a lot of guts and played well,'' Dorrell said.