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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 definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...
Four eutectic structures: A) lamellar B) rod-like C) globular D) acicular. The eutectic solidification is defined as follows: [5] + This type of reaction is an invariant reaction, because it is in thermal equilibrium; another way to define this is the change in Gibbs free energy equals zero.
When pressure and temperature are variable, only of components have independent values for chemical potential and Gibbs' phase rule follows. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena. [2] The equation is named after Josiah Willard Gibbs and ...
This equal area rule can also be derived by making use of the Helmholtz free energy. [24] In any event the Maxwell construction derives from the Gibbs condition of material equilibrium. However, even though g f = g g {\displaystyle g_{f}=g_{g}} is more fundamental it is more abstract than the equal area rule, which is understood geometrically.
Experimentally, phase lines are relatively easy to map due to the interdependence of temperature and pressure that develops when multiple phases form. Gibbs' phase rule suggests that different phases are completely determined by these variables. Consider a test apparatus consisting of a closed and well-insulated cylinder equipped with a piston.
The locus of these points (the inflection point within a G-x or G-c curve, Gibbs free energy as a function of composition) is known as the spinodal curve. [ 1 ] [ 2 ] [ 3 ] For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via spinodal decomposition .
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. [1] [2] Most modern equations of state are formulated in the Helmholtz free energy.