Environmental Engineering Reference
In-Depth Information
s
T
o
c
T
¼
ð
10
:
3
Þ
o
E
T
Taking into account the Maxwell relation
ð
o
P
=
o
T
Þ
E
¼
o
s
=
o
E
ð
Þ
T
, the speci
c
heat at constant temperature can be written as:
P
o
T
T
o
c
T
¼
ð
10
:
4
Þ
E
where P is the polarization of the electrocaloric material. This expression is then
inserted into Eq. (
10.1
) to obtain:
c
E
T
dT
P
o
ds
ð
T
;
E
Þ¼
þ
dE
ð
10
:
5
Þ
o
T
E
Let us rst consider the case where the change of the electric eld occurs under
adiabatic conditions. In this case, the total entropy of the electrocaloric material
remains constant, and therefore:
c
E
T
dT
P
o
0
¼
þ
dE
ð
10
:
6
Þ
T
o
E
From Eq. (
10.6
), the adiabatic temperature change of the material can be expressed
as:
Z
E
2
T
c
E
P
o
D
T
ad
¼
dE
ð
10
:
7
Þ
o
T
E
E
1
If we now consider the isothermal case (dT = 0), the total entropy change of the
material can be written as:
P
Þ¼
o
ds
ð
T
;
E
dE
ð
10
:
8
Þ
T
o
E
After the integration of Eq. (
10.8
), the expression for the isothermal entropy
change of the material is obtained:
Z
E
2
P
o
D
s
ist
¼
dE
ð
10
:
9
Þ
T
o
E
E
1
It is clear from Eqs. (
10.7
) and (
10.9
) that in order to achieve a large electro-
caloric effect, the rate of change of the polarization of the electrocaloric material
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