Direct Energy, 2018a

8 THERMOELECTRICS 177
per unit volume for a given strength of external electric eld, in units of
F
m . It is the ratio of the displacement ux density −→ D to the electric eld
intensity −→ E .
ɛ = |−→ D|
| −→ (8.8)
E|
If we take a material and apply an external pressure, the material compresses
and energy is stored in this compressed volume. The inverse of the
bulk modulus per unit volume is a measure of the change in volume for a
given external pressure
1
( B
) = − ∂V
(8.9)
∂P
V
in units of m 3
Pa
. Both Eqs. 8.8 and 8.9 can be called constitutive relationships
because they describe how a material changes when an external
inuence is applied.
Multiple other measures describe the variation of a gas, liquid, or solid,
with respect to variation of a thermodynamic property. The specic heat
describes the ability of a material to store thermal energy, and it has units
J
g·K
[109, p. 98]. More specically, the specic heat over temperature is
equal to the change in entropy with respect to change in temperature [108].
It may be given either assuming a constant volume or assuming a constant
pressure.
Specic heat at constant volume = C v = T ∂S
∂T ∣ (8.10)
V
Specic heat at constant pressure = T ∂S
∂T ∣ (8.11)
P
The Joule-Thomson coecient is dened as the ratio of change in temperature
to change in pressure for a given total energy of the system
Joule-Thomson coecient = ∂T
∂P , (8.12)
and it has units
Pa K [102, p. 685]. When a pressure is applied and overall
energy is held xed but entropy is allowed to vary, some materials cool and
others heat. So, this coecient may be positive, negative, or even zero at
an inversion point. Additionally, the volume expansivity is dened as
Volume expansivity = 1 ∂V
V ∂T ∣ (8.13)
P
[108].