8.3 Dielectric Constant of a Polar Gas
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of the internal energy U (T , D) as
C E ≡
∂H
∂T
E 0
=
∂U
∂T
E 0
− E 0
∂D
∂T
E 0
or as
C E =
∂U
∂T
D
+
∂U
∂D
T
− E 0
∂D
∂T
E 0
.
The difference C E − C D is then given by
C E − C P =
∂U
∂D
T
− E 0
∂D
∂T
E 0
which, upon utilizing the expression obtained for the partial derivative of the internal
energy with respect to the electric dipole moment in Example 8.1, gives
C E − C D = −T
∂D
∂T
2
E 0
∂E 0
∂D
T
.
This result is more commonly expressed as
C E − C D = −T
∂D
∂T
2
E 0
∂D
∂E 0
T
,
as D is, in principle, a function of E 0 and T . This expression is analogous to C P −
C V for non-dielectric systems.
8.3 Dielectric Constant of a Polar Gas
8.3.1 Setting the Stage
For simplicity, we shall consider a gas of N heteronuclear diatomic molecules, such
as HF, HCl, or HBr in a container of volume V , and subject to an applied electric
field E. In the absence of an applied electric field, molecules of this type behave in
exactly the same way as do homonuclear diatomic molecules like H 2 , N 2 , or O 2 .
However, because heteronuclear diatomic molecules do not have equivalent nuclei,
there is no longer an inversion centre midway between the nuclei, and consequently
it is possible for heteronuclear diatomic molecules to develop noncentrosymmetric
charge distributions. For the HCl molecule, for example, we might indicate this by
writing a formula of the type H δ+ Cl
δ− to indicate the greater localization of charge