Measuring Temperature with
a Thermocouple
a Thermocouple
The Main Points The Main Points
• Thermocouples measure temperature differences. To obtain the temperature at the closed end, we must know the temperature at the open end and account for it.
• Ice was used to establish the open-end temperature in early tem- perature measurements using thermocouples.
• Temperature versus thermocouple emf tables or formulas must be based on some fixed open-end temperature. The ice point (0°C) is by far the most common.
• Modern readout devices handle the open-end temperature com- pensation automatically.
• Installation effects can influence the accuracy of temperature mea- surements.
• Temperature measurements always lag behind changing process temperatures. The speed of response of a temperature sensor depends strongly on the conditions (especially flow rate) in the monitored medium.
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We have seen previously that the open-circuit voltage (OCV) of a
thermocouple depends on the temperature difference between the measuring- junction end and the open end. To find the temperature at the measuring junction, one must know the temperature at the open end and account for it.
32 Practical Thermocouple Thermometry
The most convenient and reproducible reference temperature available is 0°C. A mixture of ice chips and water is all that is needed to hold the open end at 0°C.
In early temperature measurements with thermocouples, an ice bath was used for the reference end. (This approach is still used in calibration laboratories.) It became standard practice to develop thermocouple calibration data for a
reference temperature of 0°C. Figure 3-1 shows the emf versus measuring- junction temperature for the standard thermocouple types for the reference
temperature of 0°C. If the reference end were placed in an ice bath, this calibration could be used to obtain the temperature of the measuring junction. Condensed tables for all common U.S. thermocouple types are given in Appendix C. The internet provides easy access to tables with greater resolution. A web search for “thermocouple tables” provides numerous options for obtaining high-resolution tables.
Now, let us consider the situation in which the reference-end temperature is not 0°C but is known. If the known temperature is T 1, then we can write Figure
Figure 3-1.3-1. ThermoThermoelectrelectric ic EMFs EMFs for for StandStandard ard ThermoThermocouplecoupless
Measuring Temperature with a Thermocouple 33
(3-1) where
V(0°C→T 2)= voltage produced by the thermocouple with the refer- ence end at 0°C and the measuring junction at tempera- ture T 2
V(0°C→T 1
)= voltage produced by the thermocouple with the refer- ence end at 0°C and the measuring junction at tempera- ture T 1
V(T 1→T 2) = voltage produced by the thermocouple with the refer- ence end at temperature T 1and the measuring junction at temperature T 2
The emf V(T 1→T 2) is what is measured. The emf V(0°C→T 1) is what must be added to the measured emf to obtain the emf that would have been measured if the reference end had been at 0°C. After this addition is done, standard calibrations based on a 0°C reference temperature can be used.
Let us use an example to clarify this procedure.
EXAMPLE EXAMPLE
A Type N thermocouple produces an emf of 10.610 mV when the open-end temperature is 20°C. What is the measuring-junction temperature?
SOLUTION SOLUTION
According to Appendix C, V(0°C→20°C) is 0.525 mV. Therefore,
V(0°C→T 2) = 0.525 + 10.610 = 11.135 mV
This is the emf that would have been measured if the reference temperature had been 0°C. Again, using Appendix C, we find that T 2= 350°C.
Another example further illustrates the use of Equation 3-1.
EXAMPLE EXAMPLE
A Type J thermocouple is connected to copper wires that connect to a readout instrument. What voltage is produced if the junction is at 400oC and the connection to copper is at 100oC?
34 Practical Thermocouple Thermometry
SOLUTION SOLUTION
The copper section contributes no voltage because both conductors are identical. The Type J segment contributes the following voltage:
V = V(400oC – 100oC) Using Equation 2-10 gives
V(400oC – 100oC) = V(400oC – 0oC) – V(100oC – 0oC)
That is, we can use the thermocouple tables (referenced to 0oC). Using the table in Appendix C for Type J thermocouple gives
V(400oC – 100oC) = 21.848 – 5.269= 16.579 mv
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Temperature
There are three ways to present the nominal calibration data for standard thermocouple types: tabular, graphical, and analytical. Neither the graphical nor tabular approach is well suited for use in instruments that measure thermocouple emf and convert to temperature. For this application, it is necessary to have an equation (or a set of equations for different temperature ranges) to represent the relationship between emf and temperature.
In practical thermocouple measurements, it is useful to have equations for temperature as a function of voltage and for voltage as a function of
temperature. Consider the first example in the previous section. The first step is an evaluation of the voltage that would have occurred if the open end were at 0°C and the measuring junction were at 20°C. This step requires a relation for voltage as a function of temperature. (We used a table in the example, but an equation would be needed for automatic readout systems.) The next step is to evaluate the temperature that corresponds to the voltage obtained by adding the measured voltage and the voltage from the previous step. This requires a relation that gives temperature as a function of voltage.
If the relationship were linear (the curve representing voltage versus temperature is assumed to be a straight line), the equations would be as follows:
Measuring Temperature with a Thermocouple 35
or
V = b0 + b1T (3-3)
where
T = temperature
V = thermocouple voltage (corrected for a 0°C reference temperature)
a0, a1, b0, b1 = constants
Unfortunately, the emf versus temperature relationships for thermocouples are not linear. The linear approximation is useful only for making rough estimates or for portions of the whole range of the thermocouple over which the relationship is nearly linear.
If the nonlinearity is to be handled explicitly by an equation, the usual form is as follows:
T = a0 + a1V + a2V 2 + … + anV n (3-4)
or
V + b0 + b1T + b2T 2 + … + bnT n (3-5) The terms raised to the second and higher powers account for the curvature of the relations. The highest power, n, is called the order of the equation. It has been found that the equation order must be high (n = 5 to 14, depending on
thermocouple type) to accomplish adequately the conversion from emf to temperature or temperature to emf in standard thermocouples for a wide range of temperatures.1-3Polynomials for the standard U.S. thermocouples are shown in Appendix D.
Lower-order (even linear) polynomials are adequate over a narrow range. Since open-end compensation usually involves ambient temperatures of 0°C to 40°C, linear equations for emf as a function of temperature are often used, and this causes little error for this application.
The form of Equation 3-4 results in some very small coefficients being multiplied by factors (powers of V or T ) that are very large numbers. Therefore, it is necessary to process some very large numbers and some very small numbers. This is handled adequately with the precision available in modern computers, but numerical errors are possible in calculations with lower precision. A way to improve the situation is to use the nested form of
36 Practical Thermocouple Thermometry
the general equation. Equation 3-4 can be rewritten to accomplish this. Taking the fifth order case as an example, we obtain
(3-6)
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Instrumentation
Modern thermocouple instrumentation operates as follows:2, 4-8 • Measure the thermocouple emf, V(T 1→ T 2).
• Measure the temperature of the reference end, T 1. (This must be done with an auxiliary temperature sensor.)
• Calculate the emf, V(0°C→ T 1), that is, the emf that would be pro- duced by the thermocouple if the measuring junction were at T 1 and the reference end were at 0°C. An emf-versus-temperature equation may be used for this.
• Add V(0°C→ T 1) and V(T 1→ T 2). This gives the emf, V(0°C→ T 2), which would have been measured if the measuring junction was at T 2and the open end was at 0°C.
• Calculate the temperatures corresponding to V(0°C→ T 2). A tem- perature-versus-emf equation may be used for this.
The reader may ask, “Why use a thermocouple at all if it is necessary to use a totally different temperature sensor in the instrumentation?” The answer is that the thermocouple and the reference temperature sensor have different requirements. The thermocouple must operate over a wide temperature range (possibly at quite a high temperature) and be rugged enough to tolerate harsh industrial environments. The reference temperature sensor must operate only over a narrow range near ambient, and it operates in a much more benign environment. The sensors used for reference temperature measurements are resistance thermometers, thermistors, and integrated circuit sensors. The open-end compensation may be done electronically or computationally. In the electronic approach, the auxiliary sensor is configured so as to add a voltage to the thermoelectric emf of the thermocouple. The circuit is designed so that the added voltage is the same as would have been produced by a
T a0 1 a1 a0 ---V 1 a2 a1 ---V 1 a3 a2 ---V 1 a4 a3 ---V 1 a5 a4 ---V + + + + + =
Measuring Temperature with a Thermocouple 37
thermocouple operating between 0°C and the actual temperature at the point where the thermocouple emf is measured. Figure 3-2 shows an arrangement that involves a resistance thermometer or a thermistor in a Wheatstone bridge. The fixed resistors in the bridge are chosen to give the appropriate
voltage-versus-temperature relation for the thermocouple type that is to be connected to the readout. Figure 3-3 shows an arrangement for computational compensation for the open-end temperature. It uses a resistance thermometer, thermistor, or integrated circuit sensor to provide a signal that is sampled by an analog-to-digital converter. The thermocouple emf is likewise sampled by an analog-to-digital converter. In the logic processor, the reference
temperature is determined, the emf (V(0°C→ T 1)) is calculated and added to the thermocouple emf, and the temperature corresponding to this emf is calculated and output to a display or other device.
It has been argued that the open-circuit voltage (OCV) is the output of interest for a thermocouple. That is, there should be no current flow in a thermocouple circuit. However, voltage measurements in thermocouple instrumentation involve measuring the voltage drop across a fixed resistor in the instrument. This means that a nonzero current must flow through the resistor. To
approximate open-circuit conditions adequately, the input resistance must be large, which results in a very small current.
In industrial applications, the cold junction compensation and the associated signal processing is handled by indicators (usually with digital displays), transmitters, loggers, controllers, recorders or Universal Serial Bus devices that send the temperature measurement result to a computer.
Figu
38 Practical Thermocouple Thermometry
A typical indicator is shown in Figure 3-4. They may be designed for bench- top use or for rack mounting. Some are designed for one specific
thermocouple type, but most modern instruments will accommodate all ASTM approved thermocouple types. Many instruments will accommodate either thermocouples or resistance thermometers. Typical achievable accuracies (in measuring the OCV of the thermocouple, performing the reference junction compensation, and converting to temperature) are a fraction of a degree at low temperature to several degrees at high temperature. Users should consult manufacturers’ specifications if the instrumentation accuracy is needed.
Typical transmitter designs are shown in Figure 3-5. A transmitter measures the thermocouple voltage, applies the open-end compensation, and provides an analog or digital output. An analog output is usually a 4-to-20-mA or 10-to- 50-mA current signal that is proportional to the temperature. A digital output is usually a binary-coded decimal (BCD) output that corresponds to the temperature. Transmitters are available for a single thermocouple type or for multiple types (with software for selecting the appropriate type).
Communication protocols also exist to assist with device management as add- ons to the 4–20mA signal (e.g., HART) or as digital substitutes for the 4–20 mA signal (e.g., FOUNDATION Fieldbus, Profibus).
Isolated transmitters are recommended for thermocouple applications as they provide a safeguard against common mode noise. Common mode noise results from ground-to-ground potential differences between a ground in the thermocouple circuit and a ground at some other point or points in the plant. If a grounded thermocouple is not properly isolated and is installed into a Figure
Measuring Temperature with a Thermocouple 39
system which has a different ground potential, then voltage which is
unrelated to the thermocouple’s emf can be introduced into the thermocouple loop, thereby overwhelming the thermocouple’s signal. In many cases, common mode noise can also be avoided in the thermocouple circuit by using shielded thermocouple wire with the shield grounded at the thermocouple so that the shield maintains the same ground potential as the thermocouple, thus avoiding common mode noise.
In recent years, wireless means of transmitting data have emerged, permitting operators to monitor process variables remotely without the need for
extension wire or conduit. A typical wireless transmitter is shown in Fig
40 Practical Thermocouple Thermometry
Figure 3-6. These systems either operate as a point to point communication between the receiver and the sensor-transmitter or in a “mesh” fashion with a
sensor’s transmitter acting as both a transmitter and repeater. Both styles of wireless transmitter are extremely well suited for monitoring in applications where line-of-sight clearances permit effective communication. Because of the possibility of signal interruption, they are less well suited for applications in which a given measurement will be used to control a process.
A typical temperature logger is shown in Figure 3-7. Loggers monitor the thermocouple, determine the temperature and save the result for subsequent transfer to another device.
A typical recorder is shown in Figure 3-8. Recorders provide graphical records of temperature data.
A typical temperature controller is shown in Figure 3-9. Controllers operate like an indicator, but they have the added capability of providing a control signal output that is a function of the difference between the measured temperature and a desired temperature (a set point) that is dialed or punched Figu
Measuring Temperature with a Thermocouple 41
into the controller. Controllers may have proportional, integral, and/or derivative control action.
A typical USB device is shown in Figure 3-10. It measures the temperature and transmits the result to a computer. It may have the capability to handle multiple thermocouples. It operates like a transmitter, with digital signals transmitted to the computer. Depending on the computer software that is employed, the computer may operate as an indicator, logger, or controller. Figure 3-11 shows a typical hand-held calibrator and a typical sensor calibrator with heat block.
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42 Practical Thermocouple Thermometry
It is important to check the accuracy of thermocouple instrumentation and, if an adjustment capability is included in their design, to recalibrate them when necessary. Special calibrators are manufactured for this purpose. The hand held calibrator provides the voltage that would be provided by a
thermocouple (of a specific type) that operated between a specified temperature and the temperature of the calibrator.
A sensor calibrator allows the user to compare the signal provided by the probe under test to a standard probe of known accuracy (often NIST traceable). However, thermocouple calibration should only be performed on new thermocouples. Attempts to recalibrate thermocouples that have been used in a process are inadvisable. Decalibration in use usually is caused by development of inhomogeneities residing in a temperature gradient. The process conditions that cause measurement errors are not duplicated in a calibration facility.
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Measuring Temperature with a Thermocouple 43
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44 Practical Thermocouple Thermometry
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It is sometimes desirable to minimize the wiring from a group of
thermocouples installed in a process. A zone box may be used for this purpose (though they are not common in U.S. industrial practice).1The configuration is shown in Figure 3-12. All of the thermocouples are terminated in an insulated box. The transition is to copper wire. Switches are used in the copper portion within the zone box to select specific thermocouples for Figure 3
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Measuring Temperature with a Thermocouple 45
measurement. The insulation ensures that the temperature in the zone box is uniform and slowly varying, but the temperature of the zone box is not meant to remain isothermal. Instead, the temperature of the zone box is monitored with a separate thermocouple. As seen in Figure 3-10, four wires must be used between the zone box and the reference temperature region. Two wires are
copper, and two are thermocouple material. Of course, additional wiring will be required to provide the signals that are needed to actuate the switches.
Thermocouple loop analysis may be used to determine the OCV measured in this configuration:
(3-7)
That is, the voltage is the same as a thermocouple (consisting of wires A and B) operating between T 0and T 2.
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Figure 3-ure 3-12.12. Zone BZone Boxox
A B A B A B A B C C C C C C C C C C C A B V T2 T2 T2 T2 T1 T0 ZONE BOX V = Sc( T 1–T 0)+S A( T 2–T 1)+SB( T 1–T 2)+Sc( T 0–T 1) S A( T 1–T 0)+SB( T 0–T 1) + S A( T 2–T 0)+SB( T 0–T 2) = S AB( T 2–T 0) =
46 Practical Thermocouple Thermometry
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In considering the accuracy of temperature measurement, the usual focus is on the accuracy of the transduction from the measurable output to
temperature. However, the measurement can never be more accurate than the difference between the temperature of the monitored process or object and the temperature of the sensing element itself. Such differences arise if heat transfer effects cause the sensor temperature to differ from the temperature being monitored. The five main effects that merit consideration in
thermocouple thermometry are discussed in the following five sections.5 3
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The casing in a metal-sheathed sensor is a good conductor of heat.
Furthermore, the thermocouple wires can carry heat axially along the sensor, and, if metallic thermowells or protection tubes are used, they also provide a good path for axial heat conduction. This can affect temperature measurement if the back end of the sensor is hotter or colder than the tip (the usual case). For example, if the monitored temperature in a container is high and the back end of the sensor is located in a cool region outside the container, heat will flow from the tip to the back end. This will cool the tip and make the
temperature lower than the monitored temperature. Heat transfer will always occur to some extent in this common situation where the tip and the back end are at different temperatures.
The question is, does heat transfer along the sensor alter the temperature measurement significantly? The answer can be found by comparing the radial heat transfer between the sensor and the process with the axial heat transfer between the sensor tip and its back end. The radial heat transfer is the
mechanism by which the sensor and the monitored medium achieve the same temperature, and the axial heat transfer is the mechanism by which the sensor assumes a different temperature than the monitored temperature.
Consequently, this problem, called the stem loss effect, can be reduced by the following actions:
• Reduce axial heat transfer
1. Use a longer sensor (longer heat transfer path) 2. Insulate the back end
• Increase radial heat transfer