Environmental Engineering Reference
In-Depth Information
s
s
M
o
o
¼
o
¼l
0
o
dT
dH
dH
ð
1
:
17
Þ
o
T
o
H
T
H
T
H
By using Eq. (
1.17
) and the de
nition of the speci
c heat at a constant magnetic
eld from Eq. (
1.7
), it follows:
l
0
c
H
M
o
T
o
dT
¼
T
dH
ð
1
:
18
Þ
H
ne the adiabatic temperature change. However,
since the measurement of c
H
has a much longer characteristic time than the mea-
surement of the magnetization M [
46
], this kind of calculation is rather problematic.
Therefore, the adiabatic temperature change can simply be derived or by using the
following equation and knowledge on two temperatures at constant total entropy.
From Eq. (
1.14
), we can de
Z
T
2
T
¼
dT
¼
T
2
s
ð
H
2
Þ
T
1
s
ð
H
1
Þ
ð
1
:
19
Þ
D
;
;
T
1
The derivative of the enthalpy in the adiabatic
isentropic case equals:
-
dh
¼l
0
M dH
ð
1
:
20
Þ
We will further denote the process of heat transfer during a constant magnetic
eld process of cooling or heating. Such a process is analogous to
isobaric heating and cooling and similar to condensation and evaporation, respec-
tively. However, the temperature of the solid magnetocaloric material is not held
constant in such a process.
The derivative of the heat and enthalpy in this case equals (Eqs.
1.8
and
1.12
):
eld as the iso
s
T
o
dq
¼
dh
¼
c
H
dT
¼
dT
ð
1
:
21
Þ
o
T
H
c entropy
diagram for a reference magnetocaloric material, i.e. gadolinium. The diagram was
constructed using the mean-
Figure
1.3
shows the magnetic
eld
enthalpy
temperature-speci
-
-
eld approximation [
47
49
]. This led to information
-
about the speci
c total entropy as a function of the temperature and the internal
magnetic
eld. With the use of Eq. (
1.12
), the enthalpy values can be de
ned. It
should be pointed out that the speci
c enthalpy and entropy presented in Fig.
1.3
are given per unit of mass and not per unit of volume. Note, also, that in analogy
with conventional vapour compression this diagram is analogous to a p
h (log
-
p
h diagram), which is usually applied for conventional refrigerants.
-
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