418
8 Electric and Magnetic Phenomena
followed by replacement of the nonphysical partial derivative of E 0 with respect to
T using the (T , D, E 0 ) permutation rule to obtain
∂U
∂D
T ,V
= −
T
∂D
∂T
V ,E 0
∂E 0
∂D
T ,V
+ E 0
as the electric field thermodynamic analogue of Eq. (2.4.10).
We have seen from the expression for the work done on a dielectric system upon
inserting it into an electric field of magnitude E 0 that the macroscopic electric dipole
moment D of the system plays a role analogous to that of the system volume, while
E 0 plays a role analogous to that played by the pressure exerted on the system.
We have also seen in Chap. 2 that changes in the internal energy and the enthalpy
of a thermodynamic system associated with temperature changes arising from heat
(energy) transferred to or from its surroundings are manifested, respectively, through
the system heat capacities at constant volume and at constant pressure. Of course,
the effects of temperature changes are still partly manifested through C V and C P
for dielectric materials, as expression (2.5.3) for the heat capacity difference also
applies to them. Indeed, it is likely that these heat capacity contributions still play
important roles for gas phase dielectrics. For most liquid and essentially all solid
dielectric materials, however, field-dipole work makes the dominant contribution to
changes in the internal energy (largely because volume changes are very small and
pressures are not commensurately high). Thus, the analogous heat capacities C E
and C D may be expected to play significant roles in internal energy and enthalpy
changes associated with energy exchange between the dielectric system and its
surroundings.
Example 8.2 Heat capacity difference C E − C D for a dielectric system.
We shall examine the difference between the heat capacities determined for
temperature changes made while holding the applied electric field, E 0 , constant and
those made while maintaining the macroscopic electric dipole moment, D, at a fixed
value. For convenience, we shall consider only constant-volume thermodynamic
systems and we shall suppress the subscript ‘0’ on E 0 when referring to the heat
capacity obtained under conditions of constant electric field strength E = E 0 .
If we express the internal energy U as a function of T , and D, the heat capacity
C D is simply given as
C D ≡
∂U
∂T
D
,
while C E can be obtained from the enthalpy H (T , E 0 ) defined in terms of the
Legendre transform
H
(T , E 0 ) = U(T , D) − DE 0
8 Electric and Magnetic Phenomena
followed by replacement of the nonphysical partial derivative of E 0 with respect to
T using the (T , D, E 0 ) permutation rule to obtain
∂U
∂D
T ,V
= −
T
∂D
∂T
V ,E 0
∂E 0
∂D
T ,V
+ E 0
as the electric field thermodynamic analogue of Eq. (2.4.10).
We have seen from the expression for the work done on a dielectric system upon
inserting it into an electric field of magnitude E 0 that the macroscopic electric dipole
moment D of the system plays a role analogous to that of the system volume, while
E 0 plays a role analogous to that played by the pressure exerted on the system.
We have also seen in Chap. 2 that changes in the internal energy and the enthalpy
of a thermodynamic system associated with temperature changes arising from heat
(energy) transferred to or from its surroundings are manifested, respectively, through
the system heat capacities at constant volume and at constant pressure. Of course,
the effects of temperature changes are still partly manifested through C V and C P
for dielectric materials, as expression (2.5.3) for the heat capacity difference also
applies to them. Indeed, it is likely that these heat capacity contributions still play
important roles for gas phase dielectrics. For most liquid and essentially all solid
dielectric materials, however, field-dipole work makes the dominant contribution to
changes in the internal energy (largely because volume changes are very small and
pressures are not commensurately high). Thus, the analogous heat capacities C E
and C D may be expected to play significant roles in internal energy and enthalpy
changes associated with energy exchange between the dielectric system and its
surroundings.
Example 8.2 Heat capacity difference C E − C D for a dielectric system.
We shall examine the difference between the heat capacities determined for
temperature changes made while holding the applied electric field, E 0 , constant and
those made while maintaining the macroscopic electric dipole moment, D, at a fixed
value. For convenience, we shall consider only constant-volume thermodynamic
systems and we shall suppress the subscript ‘0’ on E 0 when referring to the heat
capacity obtained under conditions of constant electric field strength E = E 0 .
If we express the internal energy U as a function of T , and D, the heat capacity
C D is simply given as
C D ≡
∂U
∂T
D
,
while C E can be obtained from the enthalpy H (T , E 0 ) defined in terms of the
Legendre transform
H
(T , E 0 ) = U(T , D) − DE 0