The Thermodynamics of Magnetocaloric Energy Conversion - Magnetocaloric Energy Conversion: From Theory to Applications - page 5

dw ¼l 0 H dM ð 1 : 2 Þ

Now, the rst law of thermodynamics can be rewritten as:

du ¼ dq þ l 0 H dM ð 1 : 3 Þ

And for a reversible process, where

dq ¼ Tds ð 1 : 4 Þ

Equation ( 1.3 ) takes the following form:

du ¼ T ds þ l 0 H dM ð 1 : 5 Þ

The derivative of the speci c total entropy (for isobaric and isochoric conditions)

can be de ned in our particular case as:

s s

Þ¼ o

o

dsT ð H dT þ dH ð 1 : 6 Þ

;

o T o H

H T

Applying Eqs. ( 1.4 ) and ( 1.6 ), we can dene the derivative of the specic heat
and the speci c heat capacities as:

dq ¼ c H T ð H Þ dT þ c T ð T H Þ dH ð 1 : 7 Þ

; ;

with:

H ¼

q s

o

T o

c H ¼ ð 1 : 8 Þ

o T o T

H

T ¼

q s

o

T o

c T ¼ ð 1 : 9 Þ

o H o H

T

The following Maxwell relation can be applied as well:

T ¼ l 0 o M H ð 1 : 10 Þ

o s
o

H T

o

In an open system (Fig. 1.2 ) related to the control volume, the magnetocaloric
material ows or moves out from the system boundaries. In this particular case, we

consider the magnetocaloric

fl

fl uid or the magnetocaloric solid regenerator to move

in such a way (Fig. 1.2 ).