Page 147 - Mechanical Engineers' Handbook (Volume 2)

136 Temperature and Flow Transducers

Figure 1 The emf vs. temperature calibrations for several
materials. (Reproduced from Ref. 2, with permission.)

the contributions from each length of material in the circuit—the junctions are merely elec-
trical connections between the wires. Formally,
L dT 0 dT

E dx dx (1)
net 1 2
0 dx L dx
where total thermoelectric power of material; equal to sum of Thomson coefficient and
temperature derivative of Peltier coefficient
T temperature
x distance along the wire
L length of the wire
When the wire is uniform in composition, so that is not a function of position,
E T L d d (2)
T 0

net
T 0 1 T L 2
Commercial wire is homogeneous within close limits, but used thermocouples may be far
from uniform.
When only two wires are used in a circuit, it is customary to further simplify the
problem. If both wires begin at one temperature (say T ) and end at another (say T ), the
L
0
two integrals above can be collected:
T L

E ( ) d (3)
1
2
net
T 0
Three simplifications are built into this reduced equation:
1. is not a function of position (i.e., the wires are homogeneous).
2. There are only two wires.
3. Each wire begins at T and ends at T .
0
L
These are the conditions for which the emf–temperature tables are intended. If any of the
three conditions is not met, the tables cannot be used to interpret the output.