Page 491 - Advanced thermodynamics for engineers

20.6 THERMOELECTRICITY – THE APPLICATION OF IRREVERSIBLE 483

Substituting the above relations into Eqn (20.61) gives

TdS J I
0
J ¼ J I TS þ DT þ S DT J I TS þ J I D‘ S DT
Q
dT l
dS 2 D‘
¼ J I T DT þ J I (20.67)
dT l
|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |ffl{zffl}
Thomson heat extracted Ohmic heat generated
to maintain temperature
Now the Thomson heat was defined in Eqn (20.60) as
J Q ¼ sJ I DT (20.60a)
Thus
dS
s ¼ T (20.68)
dT
For the thermocouple shown in Fig. 20.3, the difference in Thomson coefficients for the two
wires is

d

s X s Y ¼ T S S Y (20.69)
X
dT
20.6.6 SUMMARY
The equations for thermocouple phenomena for materials X and Y acting between temperature limits
of T H and T C are as follows:
Seebeck Effect

T
Z H

Seebeck coefficient ε X;Y ¼ S S Y dT (20.52a)

X
T C
Peltier Effect
Peltier coefficient p X;Y ¼ T S S Y (20.59a)

X
Thomson Effect

Thomson coefficient s X s Y ¼ T d S S Y (20.68)
X
dT