临界点（热力学）

液-汽临界点

总览

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

理论

$\displaystyle{ T_\text{c} = \frac{8a}{27Rb}, \quad V_\text{c} = 3nb, \quad p_\text{c} = \frac{a}{27b^2}. }$

$\displaystyle{ T_\text{r} = \frac{T}{T_\text{c}}, \quad p_\text{r} = \frac{p}{p_\text{c}}, \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}. }$

部分物质的液-气临界温度和压力表

Substance[15][16] Critical temperature Critical pressure (absolute)

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)
310.8 °C (584.0 K) 102 atm (10,300 kPa)
1,664.85 °C (1,938.00 K) 94 atm (9,500 kPa)

−128.85 °C (144.30 K) 51.5 atm (5,220 kPa)

−63.8 °C (209.3 K) 54.3 atm (5,500 kPa) 54.3 atm (5,500 kPa)

−228.75 °C (44.40 K) 27.2 atm (2,760 kPa) 27.2 atm (2,760 kPa)

2,950 °C (3,220 K) 652 atm (66,100 kPa)
1,476.9 °C (1,750.1 K) 1,720 atm (174,000 kPa)
1,040.85 °C (1,314.00 K) 207 atm (21,000 kPa)
8,227 °C (8,500 K)
6,977 °C (7,250 K) 5,000 atm (510,000 kPa)
7,577 °C (7,850 K)

参见

• 共形场论 Conformal field theory
• 临界指数 Critical exponents
• 临界现象 Critical phenomena
• 要素临界点 Critical points of the elements (data page)
• 居里点 Curie point
• 液体-液体临界点 Liquid–liquid critical point
• Néel点 Néel point
• 过滤阈值 Percolation thresholds]]
• 相变
• Rushbrooke不等式 Rushbrooke inequality
• 比例不变性 Scale invariance
• 自组织临界性
• Widom缩放 Widom scaling

参考文献

1. Wagner, W.; Pruß, A. (June 2002). "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use". Journal of Physical and Chemical Reference Data. 31 (2): 398. doi:10.1063/1.1461829.
2. 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.
3. P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.
4. K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.
5. P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.
6. Fisher, Widom: Decay of Correlations in Linear Systems, J. Chem. Phys. 50, 3756 (1969).
7. Das, Tamoghna; Ganguly, Saswati; Sengupta, Surajit; Rao, Madan (3 June 2015). "Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals". Scientific Reports. 5 (1): 10644. Bibcode:2015NatSR...510644D. doi:10.1038/srep10644. PMC 4454149. PMID 26039380.
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". Annales de Chimie et de Physique (in français). 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. Mendeleev called the critical point the "absolute temperature of boiling".
11. Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].
12. 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. doi:10.1098/rstl.1869.0021. The term "critical point" appears on page 588.
13. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93. ISBN 978-0-07-121688-3.
14. 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.
15. Emsley, John (1991). The Elements (Second ed.). Oxford University Press. ISBN 978-0-19-855818-7.
16. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: An Engineering Approach (Fourth ed.). McGraw-Hill. pp. 824. ISBN 978-0-07-238332-4.
17. "Ammonia - NH3 - Thermodynamic Properties". www.engineeringtoolbox.com. Retrieved 2017-04-07.
18. "Critical Temperature and Pressure". Purdue University. Retrieved 2006-12-19.

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集智课程

• 复杂系统与复杂性简介
• 统计系统理论
• 平衡态系统临界现象
• 非平衡与复杂系统临界现象

平衡态系统相变临界现象

• 平衡态临界现象的根本特征是长程关联
• 系统的宏观性质具有标度性和普适性
• 描述系统宏观性质的临界指数只依赖系统维数和序参量的维数
• 在平均场近似下，不同空间维数系统的临界指数相同

临界现象的标度性与超标度关系

• 由自由能奇异部分的齐次性，可将所有临界指数用关联长度的临界指数表示
• 关联长度有对温度和外场两个临界指数
• 各热力学量的临界指数并不独立，满足超标度（hyperscaling）关系
• 临界现象理论得到了微重力、高精度实验的证实