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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 ...
ML 2 T −2 Θ −1: Planck potential, Gibbs free entropy: ... Derivation of heat capacity (constant volume) ... Gibbs–Helmholtz equation; Phase rule;
He wrote the phase rule n + 2 - r, where r is the number of phases. Because n is now used otherwise, I call C, the components, the number of independent constituents (Gibbs's 'n'). The phase rule is thus C + 2 - P, where C is your 'number of "chemically independent" components'.
which is known as the Gibbs-Duhem relationship. The Gibbs-Duhem is a relationship among the intensive parameters of the system. It follows that for a simple system with r components, there will be r+1 independent parameters, or degrees of freedom. For example, a simple system with a single component will have two degrees of freedom, and may be ...
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 ...
Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. The Clausius–Clapeyron relation does not make sense for second-order phase transitions, [ 1 ] as both specific entropy and specific volume do not change in second ...
[2] Calculating the number of components in a system is necessary when applying Gibbs' phase rule in determination of the number of degrees of freedom of a system. The number of components is equal to the number of distinct chemical species (constituents), minus the number of chemical reactions between them, minus the number of any constraints ...