Page 486 - Advanced thermodynamics for engineers

478 CHAPTER 20 IRREVERSIBLE THERMODYNAMICS

The voltage representing temperature T H is obtained due to the thermoelectric effect in the leads
when zero current flows, i.e. the potentiometer is balanced and J I ¼ 0. At zero current, as previously
discussed, the electromotive force (emf) at the potentiometer (or DVM) equals the thermal emf
generated by the thermocouple.
From Eqn (20.48), the potential difference between each end of a wire of material M is related to
the temperature difference between the points by the following equation.

dεÞ J I ¼0 ¼ S dT J I ¼0 (20.50)
M
where S M is the value of S* for material M.
Equation (20.50) can be applied to each wire in the system shown above, to give the following
T
Z C

Wire ec ε c ε e ¼ S dT
Z
T R
T
Z H

Wire ca ε a ε c ¼ S dT
Y
T C
T
Z C

Wire ab ε b ε a ¼ S dT
X
T H
T
Z R

Wire bd ε d ε b ¼ S dT
Z
T C
Adding these equations to obtain the potential difference between points e and d gives the potential
difference measured by the potentiometer or DVM
T
T
T
T
Z C Z H Z C Z R

ε d ε e ¼ S dT S dT S dT S dT
X
Z
Y
Z
T R T C T H T C
(20.51)
T
Z H

¼ S S X dT
Y
T C
This can be written as
T
Z H

ε X;Y ¼ ε d ε e ¼ S S Y dT (20.52)
X
T C
Thus the emf of a thermocouple between any particular temperature T H and the cold junction at
T C ¼ 0 C is dependent only on the materials between the hot and cold junctions if the leads bd and ce