Modern Engineering Thermodynamics

774 CHAPTER 19: Introduction to Coupled Phenomena
EXAMPLE 19.2 (Continued )
Solution
a. From Eq. (19.15), we have that
Thus,
α fe-cu = − dϕ fe
dT
cu
I=0
where T is in °C not K. At T = 100.°C, this becomes
α fe-cu = −ð−13:4 + 0:028 T + 0:00039 T 2 Þ × 10 −6 V/K
α fe-cuð100:°CÞ = 6:70 × 10 −6 V/K
b. From Eq. (19.33) we have 11 π fe-cu = Tα fe-cu = ð100: + 273:15 KÞð6:70 × 10 −6 V/KÞ = 2:50 × 10 −3 V
11 Note that, even though most of the temperature to voltage correlations published for thermocouples are written in terms of relative temperature units
(°C or°F), the multiplying temperature factor T in the Peltier and Kelvin coefficient equations is always in absolute units (K or R).
The following example illustrates the thermoelectric effect used in a temperature measurement circuit. Note particularly
the result obtained in part c, where the effect of connecting the thermocouple wires to a remote instrument
using standard copper lead wires is investigated.
EXAMPLE 19.3
The chromel-alumel thermocouple circuit shown below has its cold junction at 0°C and its hot junction at 100.°C. Assuming
that the absolute Seebeck coefficients α ch = 23.0 × 10 −6 V/K and α al = −18.0 × 10 −6 V/K are constant over this temperature
range, determine
a. The open circuit thermoelectric (Seebeck) voltage for the chromel-alumel portion of the circuit.
b. The absolute and relative Peltier coefficients for each chromel-alumel junction.
c. The influence of the copper lead wires on the potentiometer voltage reading for the lead wire junction temperatures
shown in Figure 19.8.
Alumel
20°C
Potentiometer
a f
Copper
b e
25°C 25°C
20°C
Alumel
c
0°C
Chromel
d
100°C
FIGURE 19.8
Example 19.3.
Solution
a. The relative Seebeck coefficient for the chromel-alumel circuit is
α ch-al = α ch − α al = ½23:0 − ð−18:0ÞŠ × 10 −6 V/K = 41:0 × 10 −6 V/K
and for a constant α ch-al , Eq. (19.15) can be integrated to give
−ϕ ch-al = α ch-alðT H − T C Þ = ð41:0 × 10 −6 V/KÞð100: − 0KÞ = 4:1 × 10 −3 V = ϕ al-ch
(note that ϕ al-ch = −ϕ ch-al ).