Critical point (thermodynamics)

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In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions (temperature, pressure and sometimes composition) at which a phaseboundary ceases to exist. There are multiple types of critical pointssuch as vapor-liquid critical points and liquid-liquid critical points.

Contents

• 1 Liquid-liquid critical point
  • 1.1 Mathematical definition
• 2 Vapor-liquid critical point
  • 2.1 Mathematical definition
  • 2.2 Principle of corresponding states
  • 2.3 Table of liquid-vapor critical temperature and pressure for selected substances
• 3 In renormalization group theory
• 4 See also
• 5 Footnotes
• 6 References
• 7 External links

[edit] Liquid-liquid critical point

The liquid-liquid critical point of a solution denotes the limit ofthe two-phase region of the phase diagram. In other words, this is thepoint at which an infinitesimal change in some thermodynamic variablesuch as temperature or pressure will lead to separation of the mixtureinto two distinct liquid phases, as shown in the polymer-solvent phasediagram to the right. Such points may also be denoted a critical solution temperature. Two types of liquid-liquid critical points are the upper critical solution temperature, or UCST, which denotes the warmest point at which cooling will induce phase separation, and the lower critical solution temperature, which denotes the coolest point at which heating will induce phase separation.

[edit] Mathematical definition

From a theory standpoint, as seen in the figure to the right theliquid-liquid critical point represents the temperature-concentrationextremum of the spinodal curve. Thus in a two-component system it mustsatisfy two conditions. First is the condition of the spinodal curve,which is that the second derivative of the free energy with respect toconcentration must equal zero. The second condition is the extremumcondition that the third derivative of the free energy withrespect to concentration must also equal zero, or that the derivativeof the spinodal temperature with respect to concentration must equalzero.

[edit] Vapor-liquid critical point

The term "critical point" is sometimes used to specificallydenote the vapor-liquid critical point of a material. The vapor-liquidcritical point denotes the conditions above which distinct liquid and gas phases do not exist.

As shown in the pure species phase diagram to the right, this is thepoint at which the phase boundary between liquid and gas terminates. Inwater, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa (3200 PSIA or 218 atm)^[1].

As the critical temperature is approached, the properties of the gasand liquid phases approach one another, resulting in only one phase atthe critical point : a homogeneous supercritical fluid. The heat of vaporizationis zero at and beyond this critical point, so there is no distinctionbetween the two phases. Above the critical temperature a liquid cannotbe formed by an increase in pressure, but with enough pressure a solid may be formed. The critical pressure is the vapor pressure at the critical temperature. On the diagram showing the thermodynamicproperties for a given substance, the point at critical temperature andcritical pressure is called the critical point of the substance. Thecritical molar volume is the volume of one mole of material at the critical temperature and pressure.

Critical properties vary from material to material, just as is the case for the melting point and boiling point.Critical properties for many pure substances are readily available inthe literature. Obtaining critical properties for mixtures is somewhatmore problematic.

[edit] Mathematical definition

For pure substances, there is an inflection point in the critical isotherm on a pV diagram. This means that at the critical point:

This relation can be used to evaluate two parameters for an equation of state in terms of the critical properties.

Sometimes a set of reduced properties are defined in terms of the critical properties, ie.:

[edit] Principle of corresponding states

Critical variables are useful for rewriting a varied equation of state into one that applies to all materials. The effect is similar to a normalizing constant. The principle of corresponding statesindicates that substances at equal reduced pressures and temperatureshave equal reduced volumes. This relationship is approximately true formany substances, but becomes increasingly inaccurate for large valuesof p_r

[edit] Table of liquid-vapor critical temperature and pressure for selected substances

Substance^[2][3]   Critical temperature   Critical pressure   °C K atm kPa Argon −122.4 151 48.1 4,870 Ammonia^[4] 132.4 405.5 111.3 11,280 Bromine 310.8 584.0 102 10,300 Cesium 1,664.85 1,938.00 94 9,500 Chlorine 143.8 417.0 76.0 7,700 Fluorine −128.85 144 51.5 5,220 Helium −267.96 5.19 2.24 227 Hydrogen −239.95 33.2 12.8 1,300 Krypton −63.8 209 54.3 5,500 Neon −228.75 44.4 27.2 2,760 Nitrogen −146.9 126 33.5 3,390 Oxygen −118.6 155 49.8 5,050 CO₂ 31.04 304.19 72.8 7,380 H₂SO₄ 654 927 45.4 4,600 Xenon 16.6 289.8 57.6 5,840 Lithium 2,950 3,220 652 66,100 Mercury 1,476.9 1,750.1 1,720 174,000 Sulfur 1,040.85 1,314.00 207 21,000 Iron 8,227 8,500 Gold 6,977 7,250 5,000 510,000 Aluminium 7,577 7,850 Water^[5][6] 373.946 647.096 217.7 22,060

[edit] In renormalization group theory

According to renormalization group theory, the defining property of criticality is that the natural length scale characteristic of the structure of the physical system, the so-called correlation length ξ, becomes infinite. There are also lines in phase space along which this happens: these are critical lines.

In equilibrium systems the critical point is reached only by tuning a control parameter precisely. However, in some non-equilibrium systems the critical point is an attractor of the dynamics in a manner that is robust with respect to system parameters, a phenomenon referred to as self-organized criticality.

The critical point is described by a conformal field theory.

[edit] See also

• Critical phenomena
• Phase transition
• Scale invariance
• Conformal field theory
• Critical exponents
• Percolation thresholds
• Self-organized criticality
• Triple point
• Supercritical fluid, Supercritical drying, Supercritical water oxidation
• Rushbrooke inequality
• Widom scaling
• Tricritical point
• Joback method, Klincewicz method, Lydersen method (Estimation of critical temperature, pressure, and volume from molecular structure)
• Lower critical solution temperature
• Upper critical solution temperature

[edit] Footnotes

1. ^ International Association for the Properties of Water and Steam, 2007.
2. ^ Emsley, John (1991). The Elements ((Second Edition) ed.). Oxford University Press. ISBN 0-19-855818-X. 
3. ^ Thermodynamics: An Engineering Approach ((Fourth Edition) ed.). McGraw-Hill. 2002. pp. 824. ISBN 0-07-238332-1. 
4. ^ http://www.engineeringtoolbox.com/ammonia-d_971.html
5. ^ International Association for the Properties of Water and Steam, 2007.
6. ^ "Critical Temperature and Pressure". Purdue University. http://www.chem.purdue.edu/gchelp/liquids/critical.html. Retrieved 2006-12-19. 

[edit] References

• "Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam" (PDF). International Association for the Properties of Water and Steam. August 2007. http://www.iapws.org/relguide/IF97-Rev.pdf. Retrieved 2009-06-09. 

[edit] External links

• "Critical points for some common solvents". ProSciTech. Archived from the original on 2008-01-31. http://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm. 
• "Critical Temperature and Pressure" (HTML). Department of Chemistry. Purdue University. http://www.chem.purdue.edu/gchelp/liquids/critical.html. Retrieved 2006-12-03. 
• Hagen Kleinert and Verena Schulte-Frohlinde, Critical Properties of φ⁴-Theories, World Scientific (Singapur, 2001); Paperback ISBN 981-02-4658-7 (readable online here)