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Another type of binary phase diagram is a boiling-point diagram for a mixture of two components, i. e. chemical compounds. For two particular volatile components at a certain pressure such as atmospheric pressure , a boiling-point diagram shows what vapor (gas) compositions are in equilibrium with given liquid compositions depending on temperature.
The phase space can also refer to the space that is parameterized by the macroscopic states of the system, such as pressure, temperature, etc. For instance, one may view the pressure–volume diagram or temperature–entropy diagram as describing part of this phase space. A point in this phase space is correspondingly called a macrostate.
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space.
A generic phase diagram with unspecified axes; the invariant point is marked in red, metastable extensions labeled in blue, relevant reactions noted on stable ends of univariant lines. This rule is geometrically sound in the construction of phase diagrams since for every metastable reaction, there must be a phase that is relatively stable. This ...
In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa. An unusual feature of the water phase diagram is that the solid–liquid phase line (illustrated by the dotted green line) has a negative slope. For most substances, the slope is positive as exemplified by the dark green line.
At this point the phase space changes qualitatively and the dynamical system is said to have gone through a bifurcation. Bifurcation theory considers a structure in phase space (typically a fixed point, a periodic orbit, or an invariant torus) and studies its behavior as a function of the parameter μ. At the bifurcation point the structure may ...
A typical phase diagram.The solid green line applies to most substances; the dashed green line gives the anomalous behavior of water. In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. [1]
For tricritical points to be observed, one needs a mixture with more components. It can be shown [5] that three is the minimum number of components for which these points can appear. In this case, one may have a two-dimensional region of three-phase coexistence (F = 2-3+3 =2) (thus, each point in this region corresponds to a triple point). This ...