Critical temperature

File:Phase-diag2.svg

A typical phase diagram. The dotted green line gives the anomalous behaviour of water

The critical temperature, T_c, of a material is the temperature above which distinct liquid and gas phases do not exist. As the critical temperature is approached, the properties of the gas and liquid phases become the same resulting in only one phase: the supercritical fluid. Above the critical temperature a liquid cannot be 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 thermodynamic properties for a given substance, the point at critical temperature and critical pressure is called the critical point of the substance. The critical 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 in the literature. Obtaining critical properties for mixtures is somewhat more problematic.

Two immiscible liquids, such as oil and water, will also have a critical temperature and pressure at which the two phases will become consolute.

Table of critical temperature and pressure for selected substances

Element	Critical temperature	Critical pressure
Argon	−122.4°C (150.8 K)	48.1 atm (4870 kPa)
Bromine	310.8°C (584 K)	102 atm (10340 kPa)
Chlorine	143.8°C (417 K)	76.0 atm (7700 kPa)
Fluorine	−128.85°C (144.3 K)	51.5 atm (5220 kPa)
Helium	−267.96°C (5.19 K)	2.24 atm (227 kPa)
Hydrogen	-239.95°C (33.2 K)	12.8 atm (1297 kPa)
Krypton	−63.8°C (209.4 K)	54.3 atm (5500 kPa)
Neon	−228.75°C (44.4 K)	27.2 atm (2760 kPa)
Nitrogen	−146.9°C (126.2 K)	33.5 atm (3390 kPa)
Oxygen	−118.6°C (154.6 K)	49.8 atm (5050 kPa)
CO2	31.04°C (304.1 K)	72.8 atm (7377 kPa)
Xenon	16.6°C (289.7 K)	57.6 atm (5840 kPa)
Water	~ 374°C (647.096 K)	217.7 atm (22059 kPa)

Other uses

Superconductivity

In superconductivity applications, critical temperature refers to the temperature below which a given material becomes superconductive.

Construction

In construction, critical temperature refers to the temperature above which structural steel loses its strength and is no longer fully capable of loadbearing support. Maintaining structural and important process steel building components below this critical temperature, which varies from country to country but is generally between 500 and 560°C, is an important function of passive fire protection.

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:

<math>\left(\frac{\partial p}{\partial V}\right)_T = \left(\frac{\partial^2p}{\partial V^2}\right)_T = 0</math>

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.:

<math>T_r = T/T_c</math>

<math>p_r = p/p_c</math>

<math>V_r = V/V_c</math>

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 p_r

See also

• Critical phenomena
• Critical exponent
• Critical point
• Aerogel

Further reading

• "Critical Temperature and Pressure" (HTML). Department of Chemistry. Purdue University. 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)

Template:WikiDoc Sources