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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 ...
where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant.This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium.
The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy F at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (internal energy).
Only one equation of state will not be sufficient to reconstitute the fundamental equation. All equations of state will be needed to fully characterize the thermodynamic system. Note that what is commonly called "the equation of state" is just the "mechanical" equation of state involving the Helmholtz potential and the volume:
In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant pressure. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure ...
Hence, the main functional application of Gibbs energy from a thermodynamic database is its change in value during the formation of a compound from the standard-state elements, or for any standard chemical reaction (ΔG° form or ΔG° rx). The SI units of Gibbs energy are the same as for enthalpy (J/mol).
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field, assuming some simplifying assumptions (such as the sample system being ellipsoidal), one can derive a few compact thermodynamic relations. [4]
Another method to determine the coexistence points is based on the Helmholtz potential minimum principle, which states that in a system in diathermal contact with a heat reservoir =, = and >, namely at equilibrium the Helmholtz potential is a minimum. [25]