Thermodynamics of the total system

We choose the total system to be the condenser and the entire dielectric medium. The condenser is immersed in the medium which, for purposes of this discussion, is taken to be a single-phase, multicomponent system. The pressure on the system is the pressure exerted by the surroundings on a surface of the dielectric. In setting up the thermodynamic equations we omit the properties of the metal plates, because these remain constant except for a change of temperature. The differential change of energy of the system is expressed as a function of the entropy, volume, and mole numbers, but with the addition of the new work term. Thus, 

It is evident that nt represents the chemical potential of the ith component when E = 0. However, we must determine the expression for the chemical potential of the components that are contained in the volume of the condenser. We use the symbol /if for this chemical potential. With the use of Equation (14.51) we extend the definition of the chemical potential, so 

We see from Equations (14.41) and (14.44) that D is actually the charge density, and it is the quantity that is held constant. However, D = eE and it is this product that is held constant while both e and E depend upon the mole numbers. Thus 

There are several relations, similar to the Maxwell relations, that can be obtained from Equations (14.51) and (14.52). Upon application of the conditions of exactness to each of the Equations (14.51) and (14.52) we obtain 

The dielectric constant of most substances decreases with increasing temperature, so the entropy of the system generally decreases with an increase of the displacement according to Equations (14.59) and (14.62). The volume 

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