Biomedical Engineering Reference
In-Depth Information
circuit is proportional to the temperature difference between the two junctions over a
reasonable wide range of temperatures.
The relationship between the EMF across a junction of two dissimilar metals,
,and
E
the temperature of the measurement junction,
, assuming the cold reference junction is
maintained at 0
C, can be approximated using the following truncated power series
expansion:
T
2
E
¼
c
o
þ
c
T
þ
c
T
þ
ð
10
:
17
Þ
1
2
where
c
i
are empirically derived calibration coefficients,
T
is given in degrees Centigrade,
and
, which describes the temperature sensitivity of
the thermocouple, can be derived by differentiating Eq. (10.17) with respect to
E
is in mV. The Seebeck coefficient
a
T
:
¼
dE
a
dT
¼
c
1
þ
2
c
2
T
þ
ð
10
:
18
Þ
Note that
is a function of temperature. The properties of commonly used thermocouple
materials are given in Table 10.3.
The small size, fast response, and rugged design of thermocouple probes make them
very attractive for in vivo applications. They can be inserted into the body through a hypo-
dermic needle or a catheter. Examples of medical applications of thermocouples include
medical equipment, deep-tissue hyperthermia, and cryogenic therapy.
a
EXAMPLE PROBLEM 10.12
A Chromel/Alumel thermocouple has the following empirical coefficients:
10
2
C
0
¼
1
:
76004
10
2
C
1
¼
3
:
89212
10
5
C
2
¼
1
:
85587
Find the EMF generated by this thermocouple at a temperature of 500
C.
Solution
Substituting the calibration coefficients just given into Eq. (10.17) yields E
24.1 mV.
TABLE 10.3
Properties of Selected Thermocouple Materials
V/
C (@25
C)
Operating Range (
C)
Thermocouple
Sensitivity
m
Chromel/Alumel
40.6
270 to 1,300
Copper/Constantan
40.9
270 to 600
Iron/Constantan
51.7
270 to 1,000
Chromel/Constantan
60.9
200 to 1,000
