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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
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 ...
There is a large number of perturbation theory based equations of state available today, [23] [24] e.g. for the classical Lennard-Jones fluid. [ 11 ] [ 25 ] The two most important theories used for these types of equations of state are the Barker-Henderson perturbation theory [ 26 ] and the Weeks–Chandler–Andersen perturbation theory.
The theorem is Gibbs's phase rule, not Gibbs' phase rule. (In English, one leaves off the final s only when it's difficult to pronounce.) Gibb's phase rule first appeared in the Transactions of the Connecticut Academy of Sciences in the paper 'On the Equilibrium of . Heterogeneous Substances', published in parts between 1875 & 1878.
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 ...
By changing the spacing of the secondary phase, the fraction of contact between the two phases through shared phase boundaries is also changed. By decreasing the spacing of the eutectic phase, creating a fine eutectic structure, more surface area is shared between the two constituent phases resulting in more effective load transfer. [16]
Oklahoma City's program began as a pilot study in the spring of 2023, and as officials were encouraged by the results, it was formally launched late this past summer.
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.