Critical temperature

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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. Above the critical temperature, there is only one phase. The critical pressure is the vapor pressure at the critical temperature. The critical molar volume is the volume of one mole of material at the critical temperature and pressure. On diagrams showing thermodynamic properties for a given substance, the point at critical temperature and critical pressure is called the critical point of the substance. Above its critical temperature, a gas cannot be liquefied.

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.

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

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

Contents 1 Critical temperature of selected elements 2 Critical temperature of selected molecules 3 In Superconductivity 4 In Construction and Passive Fire Protection 5 See also 6 Literature

Critical temperature of selected elements

Element Critical temperature (°C) Argon -122.29 Arsenic 1400 Bromine 315 Chlorine 143.8 Fluorine -128.85 Helium -267.96 Hydrogen -240.17 Iodine 546 Krypton -63.7 Mercury 1477 Neon -228.75 Nitrogen -146.9 Oxygen -118.57 Phosphorus 721 Radon 105 Selenium 1493 Sulfur 1041 Xenon 16.58

Critical temperature of selected molecules

Compound Critical temperature (°C) Critical pressure (atm) Ammonia (NH3) 132 115 Carbon dioxide (CO2) 31.2 77 Carbon monoxide (CO) -141 35.9 Ethanol (C2H6O) 216 65 Methane (CH4) -82 45.8 Propane (C3H8) 97 42 Sulfur dioxide (SO2) 157 77.8 Water (H2O) 374 217.8

In Superconductivity

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

In Construction and Passive Fire Protection

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.

See also

• Critical phenomena
• Critical exponent
• critical point

Literature

• Hagen Kleinert and Verena Schulte-Frohlinde, Critical Properties of φ⁴-Theories, World Scientific (Singapur, 2001); Paperback ISBN 981-02-4658-76 (readable online here)

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