8 Sensing Elements
8.5 Thermoelectric sensing elements
Thermoelectric or thermocouple sensing elements are commonly used for measuring temperature. If two different metals A and B are joined together, there is a difference in electrical potential across the junction called the junction potential. This junction potential depends on the metals A and B and the temperature T °C of the junction, and is given by a power series of the form:
The values of constants a1, a2, etc., depend on the metals A and B. For example, the first four terms in the power series for the e.m.f. of an iron v. constantan (Type J ) junction are as follows,[9]expressed in µV:
ETJ= 5.037 × 10+1T+ 3.043 × 10−2T2− 8.567 × 10−5T3
+ 1.335 × 10−7T4+ higher-order terms up to T7 [8.44]
A thermocouple is a closed circuit consisting of two junctions (Figure 8.16), at different temperatures T1and T2°C. If a high-impedance voltmeter is introduced into the circuit, so that current flow is negligible, then the measured e.m.f. is, to a close approximation, the difference of the junction potentials, i.e.
Thus the measured e.m.f. depends on the temperatures T1, T2of both junctions. In the following discussion T1will be the temperature to be measured, i.e. the tem-perature of the measurement junction, and T2will be the temperature of the reference
ETAB1,T2= ET1 AB− ET2
AB
= a1(T1− T2) + a2(T21− T22) + a3(T31− T23) + . . . [8.45]
ETAB= a1T+ a2T2+ a3T3+ a4T4+ . . . [8.43]
E= bmωrsin mωrt [8.42]
8.5 THERMOELECTRIC SENSING ELEMENTS 173
junction. In order to accurately infer T1 from the measured e.m.f., the reference junction temperature T2must be known.
Figure 8.16 summarises five ‘laws’ of thermocouple behaviour which are vital in temperature measurement.[10]Law 1 states that the e.m.f. of a given thermocouple depends only on the temperatures of the junctions and is independent of the temper-atures of the wires connecting the junctions. This is important in industrial installa-tions, where the leads connecting measurement and reference junctions may be exposed to large changes in ambient temperature.
Law 2 states that if a third metal C is introduced into A (or B) then, provided the two new junctions are at the same temperature (T3), the e.m.f. is unchanged. This means that a voltmeter can be introduced into the circuit without affecting the voltage produced.
If a third metal C is inserted between A and B at either junction, then Law 3 states that, provided the two new junctions AC and CB are both at the same temperature (T1or T2), then the e.m.f. is unchanged. This means that at the measurement junction, wires A and B can be soldered or brazed together with a third metal without affecting the e.m.f. A voltage measuring device can be introduced at the reference junction again without affecting the measurement.
Law 4 (law of intermediate metals) can be used, for example, to deduce the e.m.f.
of a copper–iron (AB) thermocouple, given the e.m.f. values for copper–constantan (AC) and constantan–iron (CB) thermocouples.
The fifth law (law of intermediate temperatures) is used in interpreting e.m.f.
measurements. For a given pair of metals we have:
Figure 8.16
Thermocouple principles.
Law of intermediate temperatures
where T3is the intermediate temperature. If T2= 0 °C, then
Suppose that we wish to measure the temperature T1°C of a liquid inside a vessel with a chromel v. alumel thermocouple. The measurement junction is inserted in the vessel and the reference junction is outside the vessel, where the temperature is measured to be 20 °C, i.e. T3= 20 °C. The measured e.m.f. is 5.3 mV using a volt-meter inserted at the reference junction, i.e. ET1,T3= ET1,20 = 5.3 mV. The value of ET3,0= E20,0is found to be 0.8 mV using thermocouple tables.[9]These tables give the e.m.f. ET,0for a particular thermocouple, with measured junction at T °C and refer-ence junction at 0 °C. From eqn [8.47], we have ET1,0= 5.3 + 0.8 = 6.1 mV; T1is then found to be 149 °C by looking up the temperature corresponding to 6.1 mV.
The importance of correct installation of thermocouples can be illustrated by the problem shown in Figure 8.17. Here we wish to measure the temperature of high-pressure steam in a pipe, at around 200 °C, with a chromel v. alumel thermocouple, for which E200,0= 8.1 mV.
ET1,0= ET1,T3+ ET3,0 [8.47]
ET1,T2= ET1,T3+ ET3,T2 [8.46]
Figure 8.17 Thermocouple installations.
8.5 THERMOELECTRIC SENSING ELEMENTS 175
Installation (a) with the meter located just outside the pipe is completely useless.
The reference junction temperature T2can vary widely from sub-zero temperatures in cold weather to possibly +50 °C if a steam leak occurs; the measured e.m.f. is there-fore meaningless. Installation (b) with the meter located in the control room and connected to the thermocouple with copper leads is equally useless – the reference junction is still located outside the pipe.
In installation (c), the thermocouple is extended to the control room using exten-sion or compensation leads made of chromel and alumel. This is an improve-ment because the reference junction is now in the control room where the variation in ambient temperature is smaller, possibly 10 °C at most. However, this is still not satisfactory for most applications, and one obvious solution is to place the reference in a temperature-controlled environment, e.g. a refrigerator at 0 °C.
An alternative solution which utilises the law of intermediate temperatures is shown in installation (d). The thermocouple e.m.f. is ET1, T2for a measured junction temperature of T1°C and a reference junction temperature of T2°C (T2around 20 °C).
If we introduce a second source of e.m.f. of magnitude ET2,0into the circuit in series with ET1,T2, then the voltmeter measures ET1,T2+ ET2,0which is equal to ET1,0. Thus the voltmeter measures an e.m.f. relative to an apparent fixed reference temperature of 0 °C, even though the actual reference temperature is varying about a mean of 20 °C.
The e.m.f. source producing ET2,0is known as an automatic reference junction compensation circuit (ARJCC). From eqn [8.45] we have:
ET2,0= a1T2+ a2T22+ a3T32+ . . . [8.48]
but since T2is small, we can approximate by ET2,0≈ a1T2. Thus we require a circuit giving a millivolt output signal proportional to reference temperature T2. This can be obtained with a metal resistance temperature sensor incorporated into a deflection bridge circuit, with a large value of R3/R2(Section 9.1). The output voltage of the bridge must be equal to ET2,0, so that using eqn [9.15] we require:
Thus any change in T2which causes the thermocouple e.m.f. to alter is sensed by the metal resistive sensor, producing a compensating change in bridge output voltage.
The thermocouple signal ET1,0 is at a low level, typically a few millivolts, and often requires amplification prior to processing and presentation. The open-loop temperature transmitter described in Section 9.4.2 is often used to convert a thermocouple e.m.f. to a current signal in a standard range, e.g. 4 to 20 mA.
In order to find an accurate estimate of T1from ET1,0an inverse equation of the form
T1= a′1ET1,0+ a′2E2T1,0+ a′3E3T1,0+ a ′4ET41,0+ . . . [8.50]
should be solved using a microcontroller (Section 3.3 and Chapter 10).
Table 8.2 summarises the measurement range, e.m.f. values, tolerances and characteristics of four thermocouples in common industrial use. The table can be used to quantify non-linearity: for example, a copper v. constantan thermocouple, used between 0 and +400 °C, has an e.m.f. of 9288 µV at 200 °C compared with an ideal straight line value of 10 436µV. Thus the non-linearity at 200 °C is −1148 µV or −5.5% of f.s.d. Typical tolerances are of the order of ±1%, i.e. about 10 times greater than for platinum resistance thermometers. For base metal thermocouples (types J, T and K), the extension or compensation leads are made of the same metals as the thermocouple itself. For rare metal thermocouples (e.g. type R), the metals in the extension leads are copper and copper–nickel, which have similar thermoelectric properties to platinum and platinum–rhodium but are far cheaper. In order to give mechanical and chemical protection, the thermocouple is often enclosed in a thermowell or sheath (Figure 14.1). An alternative is the mineral insulated thermo-couple (Figure 8.18). This is a complete package, where the space between the thermocouple wires and metal case is filled with material which is both a good heat conductor and an electrical insulator. The dynamic characteristics of both types of installation are discussed in Section 14.3.
Table 8.2 Thermocouple data and characteristics.
Type
ae.m.f. values are after International Standard IEC 584.1: 1995[9]. Temperature have little effect. Should be protected from moisture,