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Pourbaix diagram of iron. [1] The Y axis corresponds to voltage potential. In electrochemistry, and more generally in solution chemistry, a Pourbaix diagram, also known as a potential/pH diagram, E H –pH diagram or a pE/pH diagram, is a plot of possible thermodynamically stable phases (i.e., at chemical equilibrium) of an aqueous electrochemical system.
The solid–liquid phase boundary can only end in a critical point if the solid and liquid phases have the same symmetry group. [5] 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.
= , where k B is the Boltzmann constant, and Ω denotes the volume of macrostate in the phase space or otherwise called thermodynamic probability. d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}} , for reversible processes only
To use potentiometric (e.m.f.) measurements in monitoring the + concentration in place of readings, one can trivially set [+] = and apply the same equations as above, where is the offset correction /, and is a slope correction / (1/59.2 pH units/mV at 25°C), such that replaces .
A volume is a measurement of a region in three-dimensional space. [11] The volume of a polyhedron may be ascertained in different ways: either through its base and height (like for pyramids and prisms), by slicing it off into pieces and summing their individual volumes, or by finding the root of a polynomial representing the polyhedron. [12]
The data of the liquids given from the table above is then graphed on the Zisman Plot (Figure 2) with the independent variable as the surface tension of the liquid in dynes/cm and the dependent variable as 1-cos(θ SL). There also are different variations of the Zisman plot since the Y-axis is unitless as seen in Table 1 and as mentioned above.
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. This unusual feature of water is related to ice having a lower density than liquid water.
In hydrodynamics, the free surface is defined mathematically by the free-surface condition, [11] that is, the material derivative on the pressure is zero: = In fluid dynamics , a free-surface vortex , also known as a potential vortex or whirlpool, forms in an irrotational flow, [ 12 ] for example when a bathtub is drained.