Fukushima Critical point (thermodynamics)

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For other uses, see Critical point.

Carbon dioxide exuding fog while cooling from supercritical to critical temperature

In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also known as a critical state, occurs under conditions (such as specific values of temperature, pressure or composition) at which no phase boundaries exist. There are multiple types of critical points, including vapor–liquid critical points and liquid–liquid critical points.

Pure substances: vapor–liquid critical point

1. Subcritical ethane, liquid and gas phase coexist
2. Critical point, opalescence
3. Supercritical ethane, fluid^[1]

The vapor–liquid 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.

The term critical point is sometimes used to specifically denote the vapor–liquid critical point of a material, above which distinct liquid and gas phases do not exist. As shown in the phase diagram to the right, this is the point at which the phase boundary between liquid and gas terminates. In water, the critical point occurs at around 647 K (374 °C; 705 °F) and 22.064 MPa (3200 PSIA or 218 atm).^[2]
As the substance approaches critical temperature, the properties of its gas and liquid phases converge, resulting in only one phase at the critical point: a homogeneous supercritical fluid. The heat of vaporization is zero at and beyond this critical point, and so no distinction exists between the two phases. On the PT diagram, the point at which critical temperature and critical pressure meet is called the critical point of the substance. Above the critical temperature, a liquid cannot be formed by an increase in pressure, even though a solid may be formed under sufficient pressure. 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.
Critical properties vary from material to material, and for many pure substances are readily available in the literature. Nonetheless, obtaining critical properties for mixtures is more challenging.

Mathematical definition

The critical isotherm with the critical point K

For pure substances, there is an inflection point in the critical isotherm (constant temperature line) on a PV diagram. This means that at the critical point:^[3]^[4]^[5]

$\left(\frac{\partial p}{\partial V}\right)_T = \left(\frac{\partial^2p}{\partial V^2}\right)_T = 0$

That is, the first and second partial derivatives of the pressure p with respect to the volume V are both zero, with the partial derivatives evaluated at constant temperature T. This relation can be used to evaluate two parameters for an equation of state in terms of the critical properties, such as the parameters a and b in the van der Waals equation.^[3]
Sometimes a set of reduced properties is defined in terms of the critical properties, i.e.:^[6]

$T_r = T/T_c\,$

$p_r = p/p_c\,$

$V_r = \frac{V}{RT_c/p_c}\,$

$T_c = 8a/27Rb,$

$V_c = 3nb\,$

$P_c = a/27b^2,$

where $T_r$ is the reduced temperature, $p_r$ is the reduced pressure, $V_r$ is the reduced volume, and $R$ is the universal gas constant.

Principle of corresponding states

Critical variables are useful for writing a varied equation of state that applies to all materials, similar to normalization. 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.

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

Substance^[7]^[8]	Critical temperature	Critical pressure (absolute)
Argon	−122.4 °C (150.8 K)	48.1 atm (4,870 kPa)
Ammonia^[9]	132.4 °C (405.5 K)	111.3 atm (11,280 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	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)
CH₄ (methane)	−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)
CO₂	31.04 °C (304.19 K)	72.8 atm (7,380 kPa)
N₂O	36.4 °C (309.5 K)	71.5 atm (7,240 kPa)
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^[2]^[10]	373.946 °C (647.096 K)	217.7 atm (22.06 MPa)

History

The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822^[11] ^[12] and named by Thomas Andrews in 1869.^[13] He 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.

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.