Critical point (thermodynamics)

In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent 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 cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature Tc and a critical pressure pc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

1. Subcritical ethane, liquid and gas phase coexist
2. Critical point (32.17 °C, 48.72 bar), opalescence
3. Supercritical ethane, fluid[1]

Liquid-vapor critical point


The liquid-vapor critical point in a pressure–temperature phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.

For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid-vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.

The figure to the right 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 Tc and critical pressure pc. This is the critical point.

In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa (3200 psia or 218 atm).[2]

In the vicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever 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 prefers to mix with nonpolar gases and organic molecules.[3]

At the critical point, only one phase exists. The heat of vaporization is zero. There is a stationary inflection point in the constant-temperature line (critical isotherm) on a PV diagram. This means that at the critical point:[4][5][6]

Real Gas Isotherms
The critical isotherm with the critical point K

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 Fisher and Widom[7] who identified a p,T-line that separates states with different asymptotic statistical properties (Fisher-Widom line).


Critical carbon dioxide
Carbon dioxide exuding fog while cooling from supercritical to critical temperature

The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822[8][9] and named by Dmitri Mendeleev in 1860[10] and Thomas Andrews in 1869.[11] Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3,000 atm.


Solving the above condition for the van der Waals equation, one can compute the critical point as


However, the van der Waals equation, based on a mean field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws.

To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties[12]


The principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of pr.

For some gases, there is an additional correction factor, called Newton's correction, added to the critical temperature and critical pressure calculated in this manner. These are empirically derived values and vary with the pressure range of interest.[13]

Table of liquid–vapor critical temperature and pressure for selected substances

Substance[14][15] Critical temperature Critical pressure (absolute)
Argon −122.4 °C (150.8 K) 48.1 atm (4,870 kPa)
Ammonia (NH3)[16] 132.4 °C (405.5 K) 111.3 atm (11,280 kPa)
R-134a 101.06 °C (374.21 K) 40.06 atm (4,059 kPa)
R-410A 72.8 °C (345.9 K) 47.08 atm (4,770 kPa)
Bromine 310.8 °C (584.0 K) 102 atm (10,300 kPa)
Caesium 1,664.85 °C (1,938.00 K) 94 atm (9,500 kPa)
Chlorine 143.8 °C (416.9 K) 76.0 atm (7,700 kPa)
Ethanol (C2H5OH) 241 °C (514 K) 62.18 atm (6,300 kPa)
Fluorine −128.85 °C (144.30 K) 51.5 atm (5,220 kPa)
Helium −267.96 °C (5.19 K) 2.24 atm (227 kPa)
Hydrogen −239.95 °C (33.20 K) 12.8 atm (1,300 kPa)
Krypton −63.8 °C (209.3 K) 54.3 atm (5,500 kPa)
Methane (CH4) −82.3 °C (190.8 K) 45.79 atm (4,640 kPa)
Neon −228.75 °C (44.40 K) 27.2 atm (2,760 kPa)
Nitrogen −146.9 °C (126.2 K) 33.5 atm (3,390 kPa)
Oxygen −118.6 °C (154.6 K) 49.8 atm (5,050 kPa)
Carbon dioxide (CO2) 31.04 °C (304.19 K) 72.8 atm (7,380 kPa)
Nitrous oxide (N2O) 36.4 °C (309.5 K) 71.5 atm (7,240 kPa)
Sulfuric acid (H2SO4) 654 °C (927 K) 45.4 atm (4,600 kPa)
Xenon 16.6 °C (289.8 K) 57.6 atm (5,840 kPa)
Lithium 2,950 °C (3,220 K) 652 atm (66,100 kPa)
Mercury 1,476.9 °C (1,750.1 K) 1,720 atm (174,000 kPa)
Sulfur 1,040.85 °C (1,314.00 K) 207 atm (21,000 kPa)
Iron 8,227 °C (8,500 K)
Gold 6,977 °C (7,250 K) 5,000 atm (510,000 kPa)
Aluminium 7,577 °C (7,850 K)
Water (H2O)[2][17] 373.946 °C (647.096 K) 217.7 atm (22,060 kPa)

Mixtures: liquid–liquid critical point

A plot of typical polymer solution phase behavior including two critical points: an LCST and a UCST.

The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) will lead to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature (UCST), which is the hottest point at which cooling will induce phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating will induce phase separation.

Mathematical definition

From a theoretical standpoint, the liquid–liquid critical point represents the temperature-concentration extremum of the spinodal curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the second derivative of the free energy with respect to concentration must equal zero), and the extremum condition (the third derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero).

See also


  1. ^ Horstmann, Sven (2000). Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung [Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the PSRK group contribution equation of state] (Ph.D.) (in German). Carl-von-Ossietzky Universität Oldenburg. ISBN 3-8265-7829-5.
  2. ^ a b International Association for the Properties of Water and Steam, 2007.
  3. ^ Anisimov, 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.
  4. ^ P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W.H. Freeman 2006), p.21
  5. ^ K.J. Laidler and J.H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p.27
  6. ^ P.A. Rock, Chemical Thermodynamics (MacMillan 1969), p.123
  7. ^ Fisher, Widom: Decay of Correlations in Linear Systems, J. Chem Phys 50, 3756 (1969)
  8. ^ Charles Cagniard de la Tour (1822). "Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée" [Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether (i.e., diethyl ether), and distilled petroleum spirit]. Annales de chimie et de physique (in French). 21: 127–132.
  9. ^ Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1-3001-4.
  10. ^ Landau, Lifshitz, Theoretical Physics Vol V, Statistical Physics, Ch. 83 [German edition 1984]
  11. ^ Andrews, Thomas (1869). "The Bakerian lecture: On the continuity of the gaseous and liquid states of matter". Philosophical Transactions of the Royal Society. London. 159: 575–590. The term "critical point" appears on page 588.
  12. ^ Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93. ISBN 0-07-121688-X.
  13. ^ Maslan, Frank D.; Littman, Theodore M. (1953). "Compressibility Chart for Hydrogen and Inert Gases". Ind. Eng. Chem. 45 (7): 1566–1568. doi:10.1021/ie50523a054.
  14. ^ Emsley, John (1991). The Elements (Second ed.). Oxford University Press. ISBN 0-19-855818-X.
  15. ^ Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: An Engineering Approach (Fourth ed.). McGraw-Hill. p. 824. ISBN 0-07-238332-1.
  16. ^ "Ammonia - NH3 - Thermodynamic Properties". Retrieved 2017-04-07.
  17. ^ "Critical Temperature and Pressure". Purdue University. Retrieved 2006-12-19.


External links

Boiling point

The boiling point of a substance is the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a higher boiling point than when that liquid is at atmospheric pressure. For example, water boils at 100 °C (212 °F) at sea level, but at 93.4 °C (200.1 °F) at 1,905 metres (6,250 ft) altitude. For a given pressure, different liquids will boil at different temperatures.

The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar.The heat of vaporization is the energy required to transform a given quantity (a mol, kg, pound, etc.) of a substance from a liquid into a gas at a given pressure (often atmospheric pressure).

Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid.

Critical point

Critical point may refer to:

Critical phenomena in physics

Critical point (mathematics), in calculus, the points of an equation where the derivative is zero

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

Critical point (network science)

Construction point, in skiing, a line the represents the steepest point on a hill

Gibbs free energy

In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy to distinguish it from Helmholtz free energy) is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric). The Gibbs free energy (ΔGº = ΔHº-TΔSº) (J in SI units) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter); this maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.The Gibbs energy (also referred to as G) is also the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. Its derivative with respect to the reaction coordinate of the system vanishes at the equilibrium point. As such, a reduction in G is a necessary condition for the spontaneity of processes at constant pressure and temperature.

The Gibbs free energy, originally called available energy, was developed in the 1870s by the American scientist Josiah Willard Gibbs. In 1873, Gibbs described this "available energy" as

the greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition.

The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical free energy in full.

Index of physics articles (C)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.


In anthropology, liminality (from the Latin word līmen, meaning "a threshold") is the quality of ambiguity or disorientation that occurs in the middle stage of rites, when participants no longer hold their preritual status but have not yet begun the transition to the status they will hold when the rite is complete. During a rite's liminal stage, participants "stand at the threshold" between their previous way of structuring their identity, time, or community, and a new way, which completing the rite establishes.

The concept of liminality was first developed in the early twentieth century by folklorist Arnold van Gennep and later taken up by Victor Turner. More recently, usage of the term has broadened to describe political and cultural change as well as rites. During liminal periods of all kinds, social hierarchies may be reversed or temporarily dissolved, continuity of tradition may become uncertain, and future outcomes once taken for granted may be thrown into doubt. The dissolution of order during liminality creates a fluid, malleable situation that enables new institutions and customs to become established. The term has also passed into popular usage and has been expanded to include liminoid experiences that are more relevant to post-industrial society.

List of refrigerants

Chemical refrigerants are assigned an R number which is determined systematically according to molecular structure. Common refrigerants are frequently referred to as Freon (a registered trademark of DuPont). The following is a list of refrigerants with their Type/Prefix, ASHRAE designated numbers, IUPAC chemical name, molecular formula, CAS registry number / Blend Name, Atmospheric Lifetime in years, Semi-Empirical Ozone depletion potential, net Global warming potential over a 100-year time horizon, Occupational exposure limit/Permissible exposure limit in parts per million (volume per volume) over a time-weighted average (TWA) concentration for a normal eight-hour work day and a 40-hour work week, ASHRAE 34 Safety Group in Toxicity & Flammability (in Air @ 60 °C & 101.3 kPa) classing, Refrigerant Concentration Limit / Immediately Dangerous to Life or Health in parts per million (volume per volume) & grams per cubic meter, Molecular mass in Atomic mass units, Normal Boiling Point (or Bubble & Dew Points for the Zeotrope(400)-series)(or Normal Boiling Point & Azeotropic Temperature for the Azeotrope(500)-series) at 101,325 Pa (1 atmosphere) in degrees Celsius, Critical Temperature in degrees Celsius and Critical Pressure (absolute) in kiloPascals.


Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre; similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as ​1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Supercritical fluid

A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It can effuse through solids like a gas, and dissolve materials like a liquid. In addition, close to the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be "fine-tuned".

Supercritical fluids occur in the atmospheres of the gas giants Jupiter and Saturn, and probably in those of the ice giants Uranus and Neptune. In a range of industrial and laboratory processes, they are used as a substitute for organic solvents. Carbon dioxide and water are the most commonly used supercritical fluids, being used for decaffeination and power generation, respectively.


This article is about the phenomenon where a liquid can exist in a metastable state above its boiling point. See superheated water for pressurized water above 100 °C. See superheater for the device used in steam engines.In physics, superheating (sometimes referred to as boiling retardation, or boiling delay) is the phenomenon in which a liquid is heated to a temperature higher than its boiling point, without boiling. This is a so-called metastable state or metastate, where boiling might occur at any time, induced by external or internal effects. Superheating is achieved by heating a homogeneous substance in a clean container, free of nucleation sites, while taking care not to disturb the liquid.

Triple point

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.

In addition to the triple point for solid, liquid, and gas phases, a triple point may involve more than one solid phase, for substances with multiple polymorphs. Helium-4 is a special case that presents a triple point involving two different fluid phases (lambda point).The triple point of water was used to define the kelvin, the base unit of thermodynamic temperature in the International System of Units (SI). The value of the triple point of water was fixed by definition, rather than measured, but that changed with the 2019 redefinition of SI base units. The triple points of several substances are used to define points in the ITS-90 international temperature scale, ranging from the triple point of hydrogen (13.8033 K) to the triple point of water (273.16 K, 0.01 °C, or 32.018 °F).

The term "triple point" was coined in 1873 by James Thomson, brother of Lord Kelvin.

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