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In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
The Lennard-Jones potential is a simple model that still manages to describe the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and eventually stop interacting at infinite distance, as shown in the Figure.
Phase reduction is a method used to reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. [1] [2] Many phenomena in our world such as chemical reactions, electric circuits, mechanical vibrations, cardiac cells, and spiking neurons are examples of rhythmic phenomena, and can be considered as nonlinear limit cycle ...
There are many correct collections of "Schreinemaker's rules" and the choice to use a given set of rules depends on the nature of the phase diagrams being created. Due to the phrasing of the Morey–Schreinemaker coincidence theorem, only one rule is essential to the Schreinemaker's rules. This is the so-called metastable extensions rule: [1]
If multiple phases of matter are present, the chemical potentials across a phase boundary are equal. [6] Combining expressions for the Gibbs–Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule.
In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor , provide the basis for the simplest form of the theorem of corresponding states .
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .
There are two ways that the vectors can be dependent. One is that some pairs of elements always appear in the same ratio in each species. An example is a series of polymers that are composed of different numbers of identical units. The number of such constraints is given by Z. In addition, some combinations of elements may be forbidden by ...