## Thermodynamic Potentials

13 Based on the assumed existence of a caloric equation of state, four thermodynamic potentials are introduced, Table 7.1. Those potentials are derived through the Legendre-Fenchel transformation

 Potential Relation to u Independent Variables Internal energy u u s,Vj Helmholtz free energy ^ = u - se e, Vj ^ Enthalpy h h = u — Tj Vj s,Tj Free enthalpy g g = u — se — Tj Vj e,Tj

Table 7.1: Thermodynamic Potentials on the basis of selected state variables best suited for a given problem.

Table 7.1: Thermodynamic Potentials on the basis of selected state variables best suited for a given problem.

14 By means of the preceding equations, any one of the potentials can be expressed in terms of any of the four choices of state variables listed in Table 7.1.

15 In any actual or hypothetical change obeying the equations of state, we have du d^ = —sdd + Tj dvj ^ dh = dds — Vj dTj dg = —sdd — Vj dTj and from these differentials we obtain the following partial derivative expressions e =< dU

j where the free energy ^ is the portion of the internal energy available for doing work at constant temperature, the enthalpy h (as defined here) is the portion of the internal energy that can be released as heat when the thermodynamic tensions are held constant.

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