Editing Phase diagram (section)

== Types ==

=== 2-dimensional diagrams ===
====Pressure vs temperature====
[[Image:Phase-diag2.svg|class=skin-invert-image|thumb|310x310px|A typical phase diagram. The solid green line shows the behaviour of the [[melting point]] for most substances; the dotted green line shows [[Water (molecule)#Density of water and ice|the anomalous behavior of water]].  The red lines show the [[Sublimation (phase transition)|sublimation temperature]] and the blue line the [[boiling point]], showing how they vary with pressure.]] The simplest phase diagrams are pressure–temperature diagrams of a single simple substance, such as [[water (molecule)|water]]. The [[Cartesian coordinate system|axes]] correspond to the [[pressure]] and [[temperature]]. The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of [[solid]], [[liquid]], and [[gas]].

The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and pressure in this example) change discontinuously (abruptly). For example, the heat capacity of a container filled with ice will change abruptly as the container is heated past the melting point.  The open spaces, where the [[Thermodynamic free energy|free energy]] is [[analytic function|analytic]], correspond to single phase regions. Single phase regions are separated by lines of non-analytical behavior, where [[phase transition]]s occur, which are called '''phase boundaries'''.

In the diagram on the right, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the [[critical point (thermodynamics)|critical point]]. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable,<ref>{{cite book |first1=P. |last1=Papon |first2=J. |last2=Leblond |first3=P. H. E. |last3=Meijer |title=The Physics of Phase Transition : Concepts and Applications |location=Berlin |publisher=Springer |year=2002 |isbn=978-3-540-43236-4 }}</ref> in what is known as a [[supercritical fluid]]. In water, the critical point occurs at around ''T''<sub>c</sub> = {{convert|647.096|K|C}}, ''p''<sub>c</sub> = {{convert|22.064|MPa|atm|abbr=on}} and ''ρ''<sub>c</sub> = 356&nbsp;kg/m<sup>3</sup>.<ref>The International Association for the Properties of Water and Steam [http://www.iapws.org/relguide/fundam.pdf "Guideline on the Use of Fundamental Physical Constants and Basic Constants of Water"], 2001, p. 5</ref>

The existence of the liquid–gas critical point reveals a slight ambiguity in labelling the single phase regions. When going from the liquid to the gaseous phase, one usually crosses the phase boundary, but it is possible to choose a path that never crosses the boundary by going to the right of the critical point. Thus, the liquid and gaseous phases can blend continuously into each other. The solid–liquid phase boundary can only end in a critical point if the solid and liquid phases have the same [[symmetry group]].<ref>{{cite book
 |author-first1=Lev D. |author-last1=Landau |author-link1=Lev Landau
 |author-first2=Evgeny M. |author-last2=Lifshitz |author-link2=Evgeny Lifshitz
 |date=1980
 |title=Statistical Physics
 |edition=3rd |volume=5
 |publisher=[[Butterworth-Heinemann]]
 |isbn=978-0-7506-3372-7
}}</ref>

For most substances, the solid–liquid phase boundary (or fusion curve) in the phase diagram has a positive [[slope]] so that the melting point increases with pressure. This is true whenever the solid phase is [[Density|denser]] than the liquid phase.<ref name=Whitten>{{cite book |last1=Whitten |first1=Kenneth W. |last2=Galley |first2=Kenneth D.  |last3=Davis |first3=Raymond E. |date=1992 |title=General Chemistry. |url=https://archive.org/details/generalchemistry00whit_0 |url-access=registration |edition=4th |page=[https://archive.org/details/generalchemistry00whit_0/page/477 477] |publisher=Saunders College Publishing|isbn=9780030751561 }}</ref> The greater the pressure on a given substance, the closer together the molecules of the substance are brought to each other, which increases the effect of the substance's [[intermolecular forces]]. Thus, the substance requires a higher temperature for its molecules to have enough energy to break out of the fixed pattern of the solid phase and enter the liquid phase. A similar concept applies to liquid–gas phase changes.<ref name=Dorin>{{cite book |title=Chemistry : The Study of Matter Prentice |last1=Dorin |first1=Henry |last2=Demmin |first2=Peter E. |last3=Gabel |first3=Dorothy L. |edition=Fourth |pages=[https://archive.org/details/prenticehallchem00henr/page/266 266–273] |isbn=978-0-13-127333-7 |publisher=[[Prentice Hall]] |url-access=registration |url=https://archive.org/details/prenticehallchem00henr/page/266 |year=1992 }}</ref>

Water is an exception which has a solid-liquid boundary with negative slope so that the melting point decreases with pressure. This occurs because ice (solid water) is less dense than liquid water, as shown by the fact that ice floats on water. At a molecular level, ice is less dense because it has a more extensive network of [[hydrogen bond]]ing which requires a greater separation of water molecules.<ref name=Whitten/> Other exceptions include [[antimony]] and [[bismuth]].<ref>{{cite book |last1=Averill |first1=Bruce A. |last2=Eldredge |first2=Patricia |date=2012 |title=Principles of General Chemistry |chapter=11.7 Phase Diagrams |chapter-url=https://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s15-07-phase-diagrams.html |publisher=Creative Commons}}</ref><ref>{{cite book |last1=Petrucci |first1=Ralph H. |last2=Harwood |first2=William S.  |last3=Herring |first3=F. Geoffrey |date=2002 |title=General Chemistry. Principles and Modern Applications |edition=8th |page=495 |publisher=Prentice Hall |isbn=0-13-014329-4}}</ref> 

At very high pressures above 50 GPa (500 000 atm), [[liquid nitrogen]] undergoes a liquid-liquid phase transition to a polymeric form and becomes denser than [[solid nitrogen]] at the same pressure. Under these conditions therefore, solid nitrogen also floats in its liquid.<ref name=Muk007>{{cite journal|last1=Mukherjee|first1=Goutam Dev|last2=Boehler|first2=Reinhard|title=High-Pressure Melting Curve of Nitrogen and the Liquid-Liquid Phase Transition|journal=Physical Review Letters|date=30 November 2007|volume=99|issue=22|pages=225701|doi=10.1103/PhysRevLett.99.225701|pmid=18233298|bibcode=2007PhRvL..99v5701M}}</ref>

The value of the slope d''P''/d''T'' is given by the [[Clausius–Clapeyron relation|Clausius–Clapeyron equation]] for fusion (melting)<ref>{{cite book |last1=Laidler |first1=Keith J. |last2=Meiser |first2=John H. |date=1982 |title=Physical Chemistry |pages=173–74 |publisher=Benjamin/Cummings}}</ref>

:<math>\frac{\mathrm{d}P}{\mathrm{d}T} = \frac{\Delta H_\text{fus}}{T\,\Delta V_\text{fus}}, </math>

where Δ''H''<sub>fus</sub> is the heat of fusion which is always positive, and Δ''V''<sub>fus</sub> is the volume change for fusion. For most substances Δ''V''<sub>fus</sub> is positive so that the slope is positive. However for water and other exceptions, Δ''V''<sub>fus</sub> is negative so that the slope is negative.

====Other thermodynamic properties====
In addition to temperature and pressure, other thermodynamic properties may be graphed in phase diagrams.  Examples of such thermodynamic properties include [[specific volume]], [[specific enthalpy]], or specific [[entropy]].  For example, single-component graphs of temperature vs. specific entropy (''T'' vs. ''s'') for water/[[steam]] or for a [[refrigerant]] are commonly used to illustrate [[thermodynamic cycle]]s such as a [[Carnot cycle]], [[Rankine cycle]], or [[vapor-compression refrigeration]] cycle.

Any two thermodynamic quantities may be shown on the horizontal and vertical axes of a two-dimensional diagram. Additional thermodynamic quantities may each be illustrated in increments as a series of lines—curved, straight, or a combination of curved and straight. Each of these '''iso-'''lines represents the thermodynamic quantity at a certain constant value.

<gallery mode="packed" heights="250" caption="Chart in U.S. units" class="skin-invert-image">
File:Mollier enthalpy entropy chart for steam - US units.svg|enthalpy–entropy (''h''–''s'') diagram for steam
File:Pressure-enthalpy chart for steam, in US units.svg|pressure–enthalpy (''p''–''h'') diagram for steam
File:Temperature-entropy chart for steam, imperial units.svg|temperature–entropy (''T''–''s'') diagram for steam 
</gallery>