8.2 Thermodynamics of Polarizable Media
415
dielectric upon inserting it into an externally-maintained constant electric field E 0
is thus given by the sum of the first two terms as
δW
elec = −
0 E 0 · dE 0 dV +
V
P dV
· dE 0
= −
d(
1
2 0 E
2
0 ) dV +
V
P dV
· dE 0 .
As the first term in this expression is disconnected from the dielectric system, we
see that the incremental work δW elec required to create the polarization P of the
dielectric system is thus given simply by
δW elec =
V
P dV
· dE 0 .
(8.2.4)
That P appears in the expression δW elec for incremental work only in the form of
an integral over the volume occupied by the thermodynamic system is suggestive
that a simplification can be achieved by working with the incremental work density
δw elec related to δW elec by
δW elec =
V
δw elec dV .
(8.2.5a)
Thus δw elec , given by
δw elec = P · dE 0 ,
(8.2.5b)
represents the incremental work density pertinent to the thermodynamic description
of a dielectric medium.
For the remainder of this section we shall consider only a thermodynamic system
that is both spatially and electrically isotropic, so that the polarization P induced
by the (externally maintained) applied electric field, and thus also D, is parallel to
E 0 . This allows us to replace the vectors P, D, and E 0 everywhere by the scalars
P, D, and E 0 , respectively. Moreover, we shall restrict our discussion to uniform
dielectric systems, for which
V
P dV ≡ D
(8.2.6a)
more generally, with D the dipole moment of the macroscopic thermodynamic
system, or
V
P dV = PV ,
(8.2.6b)
more specifically for fixed-volume systems.