en>KylieTastic: Reverted 1 edit by 91.106.87.29 (talk) to last revision by Omnipaedista. (TW)

2013-12-15T12:59:24Z

Reverted 1 edit by 91.106.87.29 (talk) to last revision by Omnipaedista. (TW)

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			[[File:vanderwaals2.jpg\|thumb\|400px\| The black curve is an ''isotherm'' in the pressure-volume phase diagram of a model for a real gas that can undergo a phase transition to a liquid. The oscillating middle part of it is in reality replaced by a horizontal line. The two monotonically decreasing parts that are removed describe ''metastable'' states (overheated liquid, undercooled gas), while the rising part in the middle is absolutely unstable. The height of the horizontal line is such that the two shaded areas are equal.]]
			In thermodynamic equilibrium, a necessary condition for stability is that pressure <math>P</math> does not increase with volume <math>V</math>. This basic consistency requirement—and similar ones for other ''conjugate'' pairs of variables—are sometimes violated in analytic models for first order phase transitions. The most famous case is the ''Van der Waals equation'' for real gases, see Fig.~1 where a typical ''isotherm'' is drawn (black curve). The '''Maxwell construction''' is a way of correcting this deficiency. The decreasing right hand part of the curve in Fig. 1 describes a diluted gas, while its left part describes a liquid. The intermediate (rising) part of the curve in Fig. 1 would be correct, if these two parts were to be joined smoothly—meaning in particular that the system would remain also in this region spatially uniform with a well defined density. But this is not what happens. If the volume of a vessel containing a fixed amount of liquid is expanded at constant temperature, there comes a point where some of the liquid boils and the system consists of two well separated phases. While this two-phase coexistence holds as the volume continues to increase, the pressure remains constant. It decreases again, after all liquid is evaporated and the gas expands. Thus the sinusoidal part of the isotherm is replaced by a horizontal line (red line in Fig.~1). According to the Maxwell construction (or "equal area rule"), the height of the horizontal line is such that the two green areas in Fig.~1 are equal. The Maxwell construction is derived from the condition that the [[Gibbs free energy\|Gibbs free energies]] of the gas and the liquid must be equal when they coexist. Essentially the same applies to any other thermodynamic system, where <math>P</math> and <math>V</math> are replaced by a different pair of ''conjugate variables'', e.g. magnetic field and magnetization or
			chemical potential and number of particles.

			== See also ==
			*[[Van der Waals equation]]
			*[[Phase transition]]
			*[[Conjugate variables (thermodynamics)]]


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			{{reflist}}
			* {{cite journal
			\| author=Maxwell, J. C.
			\| title = On the Dynamical Evidence of the Molecular Constitution of Bodies.
			\| journal=Nature
			\| volume=11
			\| year=1875 \| pages=357–359
			\| doi = 10.1038/011357a0
			\|bibcode = 1875Natur..11..357C }}

			* {{cite book
			\| author=Reichl, L. E.
			\| title=A Modern Course in Statistical Physics
			\| publisher= Wiley-VCH
			\| location = New York, NY USA
			\| edition=3rd
			\| year=2009
			\| isbn =9783527407828
			}}

			[[Category:Statistical mechanics]]

en>Omnipaedista at 02:37, 26 July 2012

2012-07-26T02:37:15Z

New page

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Wright Omega function - Revision history

en>KylieTastic: Reverted 1 edit by 91.106.87.29 (talk) to last revision by Omnipaedista. (TW)

en>Omnipaedista at 02:37, 26 July 2012