Thermodynamics of the dielectric medium

It is of interest to obtain thermodynamic relations that pertain to the dielectric medium alone. The system is identical to that described in Section 14.11. However, in developing the equations we exclude the electric moment of the condenser in empty space. We are concerned, then, with the work done on the system in polarizing the medium. Instead of D we use (D — e0E), which is equal to the polarization per unit volume of the medium, p. Finally, we define P, the total polarization, to be equal to Fcp. Now the equation for the differential of the energy is 

The differentials of the Helmholtz and Gibbs energies could be written in the usual manner. However, it is convenient to use the functions (A — EP) and (G — EP) in order to change the independent variable from P to E. When this is done we obtain 

The dependence of the total polarization on the field can be expressed in either of two ways. From Equation (14.44) we have 

The chemical potential for the material within the condenser is obtained from 

Partial molar quantities can be defined as the change of an extensive variable with respect to the mole number of one component at constant temperature, pressure, electric field, and mole numbers of all other components. Then, with Equations (14.73) and (14.74), the change of the partial molar entropy and partial molar volume with the electric field is given by 

---