Thermocouple measurements

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PRACTICAL

THERMOCOUPLE

THERMOMETRY

Second Edition Second Edition

Thomas W. Kerlin

Mitchell Johnson

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Notice

The information presented in this publication is for the general education of the reader. Because neither the author nor the publisher has any control over the use of the information by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of such use. The reader is expected to exercise sound professional judgment in using any of the information pre-sented in a particular application.

Additionally, neither the author nor the publisher has investigated or considered the effect of any patents on the ability of the reader to use any of the information in a particular application. The reader is responsible for reviewing any possible patents that may affect any particular use of the information presented.Any references to commercial products in the work are cited as examples only. Neither the author nor the publisher endorses any referenced commercial product. Any trademarks or trade-names referenced belong to the respective owner of the mark or name. Neither the author nor the publisher makes any representation regarding the availability of any referenced commercial prod-uct at any time. The manufacturer’s instrprod-uctions on use of any commercial prodprod-uct must be fol-lowed at all times, even if in conflict with the information in this publication.

Printed in the United States of America. 10 9 8 7 6 5 4 3 2

ISBN: 978-1-937560-27-0

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior

writ-ten permission of the publisher.

ISA

67 Alexander Drive P.O. Box 12277

Research Triangle Park, NC 27709

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xi xi

Preface to the Second

Edition

Mitchell Johnson, President of JMS-Southeast, joined Dr. Kerlin in preparing this second edition. He brings a wealth of knowledge about real-world applications of thermocouples.

The descriptions of thermocouple principles, the tools needed to analyze thermocouple performance, the causes of thermocouple errors, and the characteristics of the commonly-used thermocouples in the 1999 edition of this book are still as pertinent and correct as they were in 1999.

The second edition updates the book with increased coverage of topics related to thermocouple applications. It provides new solved sample problems that include illustrations of the use of the thermocouple loop analysis method. It includes new or revised sections to discuss new developments and to expand treatments of important technologies. It includes case studies of real-world problems and their solutions.

Part of the motivation for preparing this second edition is the apparent lack of widespread use of thermocouple loop analysis to characterize thermocouple performance and problems. We contend that this method is an essential tool for those who are responsible for measuring temperature with thermocouples. One might argue that internet information now makes a book on

thermocouples unnecessary. Certainly, almost everything found in this book can be found on the internet. However, the book eliminates the need to search through, evaluate, and digest a huge information resource. The book is intended as an easy-to-use reference that organizes and explains the subject in a concise fashion and is convenient to access.

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vii vii

1

1 Introduction

Introduction

1.

1.1 1 TThe he TTheherrmomococoupuplele

The thermocouple must surely be one of the simplest measuring devices ever conceived. What could be simpler than two different wires joined at one end? With this arrangement, a voltage is produced along the wires that increases in magnitude as the temperature difference between the joined end and the open end increases. All that is needed to determine the temperature at the junction of the wires is to measure the voltage at the open end, make adjustments to compensate for differences between the end temperature and the open-end temperature used in calibration, and convert this compensated voltage into temperature using the calibration for the wire types.

This approach is a proven technology for temperature measurement in industry. Thermocouples account for more temperature measurements in U.S. industry than any other sensor type. Thermocouples are rugged, inexpensive, and easy to use. However, they have significant inherent inaccuracies and a tendency to degrade with use. Users should understand these phenomena so they can properly assess the accuracy of their measurements, select the proper thermocouple for a given application, and install and operate the

thermocouple in the most advantageous way.

This short book focuses on the practical aspects of thermocouple

thermometry: how thermocouples work; how they go bad; how to assess measurement accuracy; and how to select, install, and operate them. In this book, a thermocouple will usually be shown schematically, as in Figure 1-1. In

practical applications, however, the arrangement is often as shown in Figure 1-2. In the case illustrated in Figure 1-2, the wires are contained in a metallic sheath where the junction is formed. The wires come in three categories: base metal (such as copper, nickel, and iron and are cheapest and most common), refractory metal (such as tungsten and rhenium and used for very high temperatures) and noble metals (such as platinum and rhodium and used for high accuracy and high temperature). The open end is connected to a readout that automatically measures the voltage, corrects for effects caused by the temperature at the open end, and then computes and displays the

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2 PPrraaccttiiccaal l TThheerrmmooccoouupplle e TThheerrmmoommeettrryy

temperature. This simplicity of implementation is both a blessing and a curse. On the one hand, it is very easy to obtain a measurement: just turn the system on and the result appears. On the other hand, this ease of use often

discourages users from expending enough time to understand what is happening, and the unfortunate result may be undetected and unnecessary measurement errors.

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1..2 2 TThhe e CCoommppeettiittiioonn

Thermocouples are used routinely for temperature measurements ranging from –270°C to 2320°C. Other sensor types are available for use over portions of this range.1-3 Specifically, the sensors that are alternatives to thermocouples (and their range of application) are as follows:

Fig

Figure 1ure 1-1.-1. SchemaSchematic tic VieView of a w of a TheThermormocoucoupleple

Figu

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IInnttrroodduuccttiioon n 33

S

Seennssoor r UUsseeffuul l TTeemmppeerraattuurre e RRaannggee Typical resistance temperature –196°C to 661°C

detectors (RTDs)1

Thermistors –55°C to 100°C

Integrated circuit sensors –55 °C to 150°C

Resistance temperature detectorsandthermistors(the latter for a narrow range of

temperatures near ambient) are the only serious competitors for use as immersion sensors in process environments that require a sheath or protection tube to isolate the sensor from the process.

Integrated circuit sensorsare used in benign environments such as for heating,

ventilating, and air conditioning systems or as components of electronic instrumentation systems.

The competitors to thermocouples for process measurements have different relative advantages, mainly with respect to measures of suitability for a given application. These measures are allowable temperature range, accuracy, and measurement system affordability (the measurement system consists of the three components needed to make a measurement: the sensor, wiring and instrumentation).

For a number of years, thermocouples have been losing market share to RTDs in total temperature sensor sales. This trend is likely to continue. RTDs have evolved from fragile, expensive laboratory sensors to quite rugged and inexpensive industrial sensors—largely due to improvements in the quality of thin film RTD elements—though they are still not as rugged as

thermocouples. RTDs have lower decalibration tendencies and lower costs for wiring between the sensor and its transmitter or readout. Greater achievable accuracy is an advantage for RTDs over any type of thermocouple up to around 460oC. Beyond this temperature, RTDs still have lower limits of error than base-metal thermocouples, but larger limits of error than noble-metal thermocouples.

Thermocouples remain the least expensive sensor for many applications, their accuracy and decalibration tendency are improving as the subtleties of the underlying principles of thermocouple thermometry are understood better and improvements arise in composition control and sensor fabrication procedures. They are suitable for use in unusual configurations, they are rugged, and they are able to operate at high temperatures. These advantages guarantee that thermocouples will continue to be very important sensors for industry.

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Table 1-1 summarizes the relative advantages and disadvantages of thermocouples and RTDs.

T

Tabable 1le 1-1-1.. ComCompaparirisoson of Tn of Thehermrmococououpleples ans and RTd RTDsDs

Noncontact temperature sensors are also available. They provide

measurement capability that includes situations where measurements with thermocouples are not possible. Infrared temperature sensors and optical pyrometers can measure temperatures that far exceed those possible by means of any contact temperature sensors. These sensors work by measuring the electromagnetic radiation emitted from an object. They are useful for monitoring surface temperatures. Disadvantages of non-contact sensors include high cost, error caused by emissivity uncertainties, the inability to take an internal temperature and the fragility of the measuring device itself.

T

Thheerrmmooccoouuppllee RRTTDD Accuracy

Accuracy Limits of error wider than for RTDs (except for noble metal thermocouples above roughly 460°C)

Limits of error smaller than base-metal thermocouples at all temperatures and noble metal thermocouples below roughly 460°C

Ruggedness

Ruggedness Excellent Relatively sensitive to

temperature-induced strain, thermal or mechanical shock and pressure

Range

Range –270°C to 2320°C –196°C to 661°C (typical)

(somewhat lower and higher limits in special designs) Size

Size Can be as small as .01" and may be tip sensitive

Limited to 1/16", temperature sensitive for length of bulb Drift

Drift Should be checked periodically

for drift

Less drift than thermocouples (typically 0.01 to 0.1°C / year) Resolution

Resolution

Must resolve fractions of millivolts per degree, lower signal-to-noise ratio

Must resolve fractions of ohms per degree, higher signal-to-noise ratio

Cold Junction

Cold Junction Required Not Required

Lead Wire

Lead Wire Must match lead wire calibration to thermocouple calibration

Can use copper wire for extension wire Response

Response Can be made small enough for

millisecond response time

Thermal mass restricts time to seconds in most cases Cost

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1

1..3 3 SSttaannddaarrddss

Standards serve to define the acceptable performance levels of products such as thermocouples. In the United States, consensus standards are prepared by professional societies and are then approved and promulgated by the American National Standards Institute (ANSI). The American Society for Testing and Materials (ASTM) maintains Committee E.20 to address the needs of thermometry standards in the United States. The Instrument Society of America (now renamed the International Society of Automation) previously developed and maintained a thermocouple standard (labeled MC 96.1), but this standard was abandoned in 1982 in favor of the ASTM standard. The ASTM standard has not received ANSI approval, but it is the pertinent and universally used standard for thermocouples in the U.S.

International commerce involves the movement of products across national boundaries, and its growth has created a need for international standards to

ensure compatibility and consistency of thermocouple performance. The International Electrotechnical Commission (IEC) serves this function by coordinating standards activities, publishing international standards, and maintaining its Committee WG65B to deal with thermometry. However, different standards still exist in different industrialized countries. These differences, especially differences in color coding, often cause confusion in selecting appropriate thermocouples for use in systems built in countries where standards differ from local standards. Chapter 5 provides information about U.S. and international standards.

Thermocouple standards define the nominal performance and tolerances for the thermocouples used in most industrial applications. The tolerances are chosen by defining products that are adequate in most applications but do not require unrealistically costly manufacturing processes. In their purchase specifications, purchasers of thermocouples often cite standards as minimum performance requirements.

Standards serve a crucial role in industrial temperature measurement. They greatly facilitate sensor replacement and interchangeability and the

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1..4 4 KKeey y RReeffeerreenncceess

Many useful books are available that provide information on thermocouples, their principle of operation, their construction, their degradation in use, and their selection.4-25

References References

1. Ball, K. E., “Thermocouples and RTD’s: The Controversy Continues,”

InTech, Vol. 33, August 1986, pp. 43–45.

2. Smith, J., “Matching Temperature Sensors with Process Tasks,”

Instrumentation and Control Systems, Vol. 67, April 1994, pp. 77–82.

3. Waterbury, R. C., “Hot Issue: RTDs vs. Thermocouples,”InTech,Vol. 41, March 1994, pp. 44–47.

4. The Theory and Properties of Thermocouple Elements, American Society

for Testing and Materials publication STP 492.

5. The Use of Thermocouples in Temperature Measurement, American Society

for Testing and Materials, ASTM 470B Fourth Edition, 1993. 6. Benedict, R. P.,Fundamentals of Temperature, Pressure, and Flow

Measurements, John Wiley & Sons, New York, 1969.

7. Burns, G. W. and Scroger, M. G., The Calibration of Thermocouples and

Thermocouple Materials, NIST Special Publication 250-35, April 1989.

8. Burns, G. W.,Temperature-Electromotive Force Reference Functions and

Tables for the Letter-Designated Thermocouple Types Based on the ITS-90,

National Institute of Standards and Technology publication NIST Monograph 175, Superintendent of Documents, U. S. Government Printing Office, Washington, DC, 1993.

9. Ripple, D.C. and Burns, G.W.,Standard Reference Material 1749: Au/Pt

Thermocouple Thermometer, NIST Special Publication 260-134, March

2002.

10. Garrity, K., Ripple, D. C. et al., A Regional Comparison of Calibration

Results for Type K Wire from 100 C to 1100 C, TEMPMEKO, Vol. 29, Issue

5, pp.1828–1837, 5 June 2008.

11. Kinzie, P. A.,Thermocouple Temperature Measurement, John Wiley & Sons, New York, 1973.

12. Kerlin, T. W., and Shepard, R. L.,Industrial Temperature Measurement,

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13. Magison, E. C.,Temperature Measurement in Industry, ISA, Research Triangle Park, NC, 1990.

14. McGee, T. D.,Principles and Methods of Temperature Measurement, John Wiley & Sons, New York, 1988.

15. Michalski, L., Eckersdorf, K., and McGhee, J.,Temperature

Measurement, John Wiley & Sons, New York, 1991.

16. Nicholas, J. V., and White, D. R.,Traceable Temperatures, John Wiley & Sons, New York, 1994.

17. Nicholas, J. V., and White, D. R.,Traceable Temperatures, New Zealand Department of Scientific and Industrial Research, DS.R Bulletin 234, 1982.

18. Pollock, D. D.,Thermoelectricity: Theory, Thermometry, Tool, American Society for Testing and Materials Special Technical Publication 852, 1985.

19. Pollock, D. D.,Thermocouples: Theory and Properties,CRC Press, Boca Raton, FL, 1991.

20. Quinn, T. J.,Temperature, Academic Press, New York, 1983. 21. Schooley, James F.,Thermometry,CRC Press, Boca Raton, FL, 1986. 22. Bentley, R. E., Handbook of Temperature Measurement, Vol. 3 Springer,

1998.

23. Liptak, B. G.,Temperature Measurement, CRC Press, 1993.

24. McMillan, G. K. Advanced Temperature Measurement & Control, ISA, 2nd Ed., 2010.

25. Kerlin, T. W., and Johnson, M. P., “Thermocouples: What One Needs To Know,”InTech, Vol. 58, Sept/Oct. 2011, pp. 52–53.

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2

Fundamentals

The Main Points The Main Points

• Voltage is not produced at the junction of the thermocouple wires. • Voltage is produced along the portions of the thermocouple wires

that experience temperature differences.

• Voltage for an ideal thermocouple is related to the temperature dif-ference between the junction end and the open end.

• Thermocouple loop analysis is simple and can explain all the important phenomena in thermocouples related to temperature measurement. Even casual users of thermocouples will benefit by understanding and using this simple analysis method.

• For temperature measurement, the quantity of interest is the open-circuit voltage (OCV), that is, the voltage that occurs when there is no current flowing.

• It does not matter how thermocouple wires are joined (twisted, welded, soldered, bolted, clamped, etc.) insofar as the thermocou-ple’s temperature measuring capability is concerned.

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2..11 TTeemmppeerraattuurre e SSccaalleess

It will be assumed that the reader knows what temperature is and why he or she wants to measure it. Precise definitions of temperature may be based on thermodynamics or on quantum physics.1-5These have tremendous practical importance to people working on defining the temperature scale or

performing high-accuracy sensor calibration, but they are usually not of much importance in industrial temperature measurements. The user wants his or

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1100 PPrraaccttiiccaal TThl heerrmmooccoouupplle e TThheerrmmoommeettrryy

her measurements to conform to a temperature scale that is universally consistent.

The most common scale for scientific use is the Celsius scale, and for

industrial use both the Celsius and Fahrenheit scales are commonly used. The Celsius and Fahrenheit scales are related to the Kelvin and Rankine absolute scales, respectively.

The relationships between the scales are as follows: °F = 1.8 × °C + 32

°C = (°F - 32)/1.8

°K =°C + 273.15 °R =°F + 459.67

It is customary to refer to the temperatures as “degrees C,” “degrees F,” “degrees R,” and “kelvins.” This special treatment of the terminology for the Kelvin scale honors Lord Kelvin’s contributions to thermometry.

The temperature scales are revised periodically because scientists are continually striving to improve the numbers used for the temperatures that define reference thermal states. Here, a reference thermal state is defined as a reproducible thermal condition such as a melting point for a pure material. Scientists also strive to develop interpolations that define temperatures at thermal states other than those that can be reproduced readily. This suggests that there are “correct temperatures,” not just values that are arbitrarily assigned (as in the creation of the Celsius and Fahrenheit scales). This conclusion is certainly true. Temperature appears as a variable in many laws of physics, and these variables cannot have arbitrary values. These values, which are the object of the scientific efforts to define “correct temperatures,” might be called “physical temperatures” but are commonly called

“thermodynamic temperatures.” One feature of a thermodynamic temperature scale is that it has a zero value at some lowest possible temperature. The Kelvin and Rankine scales have this feature.

Scientific experts meet regularly to evaluate new results in their effort to establish “correct temperatures” and to prescribe procedures for conforming to these values in industrial practice. During the twentieth century, this has led to revised specifications about every twenty years. Through 1968, these specifications were called the International Practical Temperature Scale and were designated by the abbreviation IPTS followed by the last two digits of the year of adoption. This led to IPTS-28, IPTS-48, and IPTS-68. The

terminology changed in 1990 when a new scale, called the International Temperature Scale and designated ITS-90, was adopted.5The difference

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Fuunnddaammeennttaallss 1111

between IPTS-68 and ITS-90 temperature scales is small (less than 0.4°C for temperatures below 1000°C and about 0.05 percent of the Celsius temperature above 1000°C).

The obvious question is, “How do these changes affect the industrial practitioner?” The answer is “Very little.” Thermocouples still provide the same output when they experience the same thermal state. The small differences in defining the scale result in small differences in the tables, graphs, and equations used to provide thermocouple calibration information. These differences are smaller than the uncertainties on industrial

measurements using thermocouples but are still a possible source of confusion. In this book, the values used in all tables, graphs, and equations will be based on ITS-90.

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2..22 WWhhaat t CCaauussees s tthhe e TThheerrmmooccoouuppllee Voltage?

Voltage?

It is not necessary to undertake a detailed analysis of the physics behind the thermoelectric voltage produced by a conductor in a temperature gradient. It is, however, useful to have a qualitative feel for the underlying physics so the behavior of thermocouples becomes understandable.6-7

Consider first a single conductor in a temperature gradient. The conductor experiences an electrical potential that can be viewed as being caused by variations in the density of free electrons in the conductor. The electrons in the high-temperature region have a higher kinetic energy than those in the low-temperature region. This electron diffusion causes production of a potential difference along a wire that experiences a temperature gradient. The magnitude of the effect depends on the composition of the conductor, its metallurgical state, and the absolute temperature of the conductor.

One might be tempted to conclude that the existence of a potential difference in a conductor that experiences a temperature gradient would permit the temperature to be measured by measuring the voltage on a single wire. Not so! The measurement of potential must be made by an instrument to which the wire is connected. Therefore, the potential increases along one leg of the loop and decreases by an equal amount in the other, giving a net potential of zero at the measuring instrument.

If one wire will not work, then how about two? Consider a situation involving two different conductors, as shown in Figure 2-1. Because of the different tendencies of the two conductors to generate variations in free electron densities (and therefore different tendencies to generate electrical potentials),

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the two wires produce different electrical potentials. The net result is a potential difference at the open end (where the measuring instrument is connected). This is the basis for thermocouple thermometry. The open end is also called the reference end of the thermocouple.

It should be noted that the voltage at the open end is the open-circuit voltage (OCV). That is, it is the voltage produced in the absence of electrical current in the thermocouple loop. If a current existed, it would reduce the differences in free electron density that are responsible for the thermoelectric electromotive force (emf). Consequently, the measurement of the thermoelectric emf must be

done in a way that ensures insignificantly small current flows. In a practical sense, this means that the input impedance of the voltage-measuring instrument must be large.

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2..33 TThhe e SSeeeebbeecck k CCooeeffffiicciieennt t aanndd Thermocouple Loop Analysis Thermocouple Loop Analysis

A homogeneous section of a conductor that experiences a temperature T ₀ at one end and a temperature T ₁ at the other end experiences a voltage difference, V , between the two ends. The voltage is given by the following equation:7-9

Figure

Figure 2-1.2-1. VVoltage oltage ProdProduced buced by Ty Two wo DissimDissimilar Coilar Conductonductorsrs



          MEASURED VOLTAGE EMF CONDUCTOR A CONDUCTOR B

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V = S (T ₁ – T ₀) (2-1)

where

S = the Seebeck coefficient (μV /°C)

The Seebeck coefficient (also called the “thermoelectric power”) is the fundamental thermoelectric property related to thermocouple thermometry. It is a physical property of a material, like its density, thermal conductivity, or electrical resistivity. It is independent of the size and shape of the conductor but does vary with temperature. Because of this temperature dependence, the

relation shown in Equation 2-1 is an approximation. This approximation is adequate for the qualitative analysis of thermocouple circuits but is inadequate for predicting the voltage that would be observed for a specific thermocouple in a specific temperature gradient. However, for the uses to which it is put in this book—understanding how various thermocouple configurations work—it is quite satisfactory.

The simple relation between voltage and temperature difference along the conductor may be used to predict thermocouple performance, analyze thermocouple configurations, and troubleshoot problems with thermocouple thermometry. This procedure is called thermocouple loop analysis.7-9 The procedure may be illustrated for the basic thermocouple shown in Figure 2-2. The approach is simply to sum up the voltage contributions for each

homogeneous portion of the conductor. For example, if we choose to start the summing process at the open end of conductor A, the voltage is as follows:

V = S_A(T ₁ – T ₀) + S_B(T ₀ – T ₁) (2-2) contribution contribution

from from

conductor A conductor B This is algebraically the same as

V = S A(T 1 – T 0) – SB(T 1 – T 0) (2-3) or

V = (S_A – S_B)(T ₁ – T ₀) (2-4) Note that the difference in the Seebeck coefficients for the two conductors appears in Equation 2-4. This always happens in thermocouple loop analysis, and it is the property that is of practical interest in thermocouple

thermometry. It is called the relative Seebeck coefficient (between material A and material B) and is written “S_AB.” That is,

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S_AB = S_A – S_B (2-5)

Consequently, Equation 2-4 may be written as follows:

V = S AB(T 1 – T 0) (2-6) This is the fundamental relation in thermocouple thermometry.

This is the fundamental relation in thermocouple thermometry. Thermocouple loop analysis provides the ability to characterize all

thermocouple configurations and the consequences of damage to any part of a thermocouple circuit, which often accompanies typical applications.

Appendix A contains hypothetical problems and their solutions that illustrate the use of thermocouple loop analysis for characterizing both normal and abnormal thermocouple configurations. These examples illustrate the power of loop analysis for understanding how thermocouples work, both as-installed and after degradation experienced in use. Readers are encouraged to study these examples in order to become proficient in using the loop analysis method.

An important use of thermocouple loop analysis is prediction of the voltage contribution of segments along a thermocouple circuit. Consider again the thermocouple circuit shown in Figure 2-2. The thermocouple consists of two homogeneous wires operating with a temperature difference of T ₁ – T ₀. At some point along the wires, there is a location where wires experience some other temperature, T 2. Thermocouple loop analysis gives

V = S_A(T ₂ – T ₀) + S_A(T ₁ – T ₂) + S_B(T ₂ – T ₁) + S_B(T ₀ – T ₂) (2-7) Fig

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or

V= (S A- SB )(T 2 – T 0) + (S A- SB )(T 1 – T 2) (2-8) or

V = S_AB(T ₂ – T ₀) + S_AB(T ₁ – T ₂) (2-9) That is, the voltage for a thermocouple operating between T 0 and T 1 is equal to the sum of voltages from a thermocouple operating between T 2 and T 0 and a thermocouple operating between T 1 and T 2. Stated differently

V(T 3 – T 1) = V(T 2 – T 0) + V(T 1 – T 2) (2-10) This result is often called the Law of Intermediate Temperatures in statements of the Laws of Thermoelectricity (see Section 2.10.1).

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2..44 TThheerrmmooccoouupplle e TTyyppeess

In principle, any two different conductors may be used to make a

thermocouple. In practice, however, only a few combinations of conductor materials are used. Materials are chosen on the basis of the magnitude of their relative Seebeck coefficient, chemical stability, metallurgical stability,

ductility, strength, and cost.

The data processing for converting measured voltage to temperature is different for every different pair of conductors, so it is necessary to have a reasonably small number of standard types to avoid complexity, cost, and confusion.

There are nine standard types of thermocouples used in the United States. The designations are based on the emf vs. temperature relation for the

thermocouples, not on their compositions. These types, which are given letter designations by the American Society for Testing and Materials (ASTM), are shown in Table 2-1 along with a specification of their main constituents. Different thermocouple wire manufacturers use slightly different concentrations of main constituents and may include trace materials to achieve desired thermoelectric properties or to improve durability and resistance to decalibration. The various manufacturers have their own trade names for their products.

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T

Tabable 2le 2-1-1.. ASASTM TTM Thehermrmococououplple Te Typypeses

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2..55 LLeeaad d WWiirre e EEffffeeccttss

The thermocouples used in industry are often located far from the readout instrumentation to which they are connected. If wires made of the

thermocouple wire materials are used all the way from the junction to the instrument, the system is as shown in Figure 2-2 and the electrical potential is as given by Equation 2-6. But what if different kinds of wire are used? Why would anyone do that, and what is the consequence?

Let us first consider the situation shown in Figure 2-3. Here, identical conductors are connected to each side of the thermocouple. Loop analysis gives the following:

V = S_C(T ₁ – T ₀) + S_A(T ₂ – T ₁) + S_B(T ₁ – T ₂) + S_C(T ₀ – T ₁) (2-11) or

V = S_AB(T ₂ – T ₁) (2-12) Note that the potential depends on the difference in temperature at the junction and at the temperature where the thermocouple is connected to the lead

wire. The lead wire may be any conductor so long as it is the same in both branches. It has no effect other than to move the reference temperature

location from the instrument to the connection point of the wires. Does this have any real significance? Yes, but mainly historical (insofar as industrial applications are concerned).

Consider the case in which the transition to identical lead wires in each branch is submerged in an ice bath (see Figure 2-4). In this case, T 1 is 0°C, and the emf

T

Tyyppee PPrriinncciipplle e WWiirre e CCoonnssttiittuueennttss J Iron vs. nickel-copper alloy T Copper vs. nickel-copper alloy

K Nickel-chromium alloy vs. nickel-manganese-silicon-aluminum alloy E Nickel-chromium alloy vs. nickel-copper alloy

N Nickel-chromium-silicon alloy vs. nickel-silicon-magnesium alloy C Tungsten-rhenium alloy vs. tungsten-rhenium alloy

S Platinum-rhodium alloy vs. platinum R Platinum-rhodium alloy vs. platinum

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is the result of the temperature difference between the junction temperature and 0°C. This is the way thermocouples were actually used before modern readout instrumentation was developed.

Another setup for dealing with the reference junction temperature is shown in Figure 2-5. Thermocouple loop analysis gives the following:

V = S A(T 2 – T 0) + SB(T 1 – T 2) + S A(T 0 – T 1) (2-13) or

Fig

Figure 2-ure 2-3.3. A ThermocA Thermocoupouple witle with Identh Identicaical Extel Extensinsion Wireon Wiress

Figu

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V = S A(T 2 – T 1) + SB(T 1 – T 2) (2-14) or

V = S_AB(T ₂ – T ₁) (2-15) This result shows that if the junction between A and B in the lower leg is placed in ice water, then the result is again referenced to 0°C. This analysis not only shows an alternate way to use an ice bath to establish the reference temperature; it also shows how the simple thermocouple loop analysis procedure can be used to understand how a configuration will work.

Now, let us consider the configuration shown in Figure 2-6. In this case, wires with Seebeck coefficients A‘ and B‘ are used to connect the thermocouple wires to the readout. Thermocouple loop analysis gives the following:

V = S_A‘(T ₁ – T ₀) + S_A(T ₂ – T ₁) + S_B(T ₁ – T ₂) + S_B‘(T ₀ – T ₁) (2-16) or

V = S A’B’(T 1 – T 0) + S AB(T 2 – T 1) (2-17) Now, if the wire pair A‘B‘ is chosen so as to have approximately the same relative Seebeck coefficient as AB, we obtain the following:

Figu

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F

S A’B’ ~ S AB (2-18)

and

V ~ S_AB(T ₂ – T ₀) (2-19) This causes the reference junction to move to the point where the wires connect to the readout instrument (just as if wires A and B are used throughout).

Wires that have a relative Seebeck coefficient that is approximately the same as the relative Seebeck coefficient of the wires to which they are attached are called thermocouple extension grade wiresthermocouple extension grade wires. They are cheaper than

thermocouple wire, and they introduce little error.

2

2..66 JJuunnccttiioon n CCoonnssttrruuccttiioon n EEffffeecctts os onn Thermoelectric Performance Thermoelectric Performance

All of the depictions of thermocouples in previous sections have showed the two thermocouple wires joined at the junction, but there was no mention of how they were joined. Were they twisted together, welded, soldered, bolted, clamped—or what? Thermoelectrically, it does not matter! Let us turn to thermocouple loop analysis to understand why this is so. Consider the configuration shown in Figure 2-7. Material C represents any material present because of the joining operation. Loop analysis gives the following:

V = S_A(T ₁ – T ₀) + S_C(T ₁ – T ₁) + S_B(T ₀ – T ₁) (2-20) Figu

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or

V = S_AB(T ₁ – T ₀) (2-21) That is, the material at the junction has no effect on temperature measurement if the temperature is the same at both of the points where it meets the

thermocouple material. The main issue in junction construction is obtaining a junction that is rugged and durable. The procedures for constructing junctions

are discussed in Section 4.2.

2

2..77 TThhe De Diiffffeerreennttiiaal Tl Thheerrmmooccoouuppllee

In some applications, it is more useful to know the temperature difference between two points than to know the temperature at each of these points. For

example, in some material processing operations, uniformity of temperature in a batch of material is important. Also, in performing energy balances, temperature differences between different points in the process are important. The differential thermocouple may be useful for applications such as these. The basic differential thermocouple is shown schematically in Figure 2-8. Note that two identical leads are bridged by another conductor (material B) operating between temperatures T ₁and T ₂. The loop analysis for this arrangement gives the following:

Figure

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F

V = S_A(T ₁ – T ₀) + S_B(T ₂ – T ₁) + S_A(T ₀ – T ₂) = S A(T 1 – T 2) + SB(T 1 – T 2)

= S_AB(T ₁ – T ₂) (2-22) This shows that the voltage is a function of the temperature difference between the two points where different conductors connect.

Two thermocouples can be configured for differential measurements as shown in Figure 2-9. A standard thermocouple readout cannot be used to obtain the temperature difference directly. Also, since the relative Seebeck coefficient is temperature dependent, one cannot simply use a tabulated value of the Seebeck coefficient to obtain the temperature difference. One possible approach is as follows:

1. Measure T 1 and T 2 individually.

2. Measure the emf, V , for the sensors connected in the differential configuration.

3. Estimate an “effective” Seebeck coefficient using

(2-23) 4. Use this Seebeck coefficient in subsequent measurements of T1 – T2

with the sensors connected in the differential configuration. This procedure may seem to violate the basic premise of a differential measurement: a direct measurement of temperature differences is preferable to subtracting temperatures from two separate measurements. However, if we use the procedure, small changes in the temperature difference are detectable Figu

Figure 2-re 2-8.8. BasBasic Diic Diffffereerentintial Thal Thermermocoocoupleuple

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with good accuracy so long as the temperatures remain close to their values when S AB was evaluated.

The differential thermocouple can also be configured with the monitored object as the bridging component of the thermocouple circuit (see Figure 2-10). In this case, there may be little or no information on the relative Seebeck coefficient between the wire and the monitored object. However, the approach just outlined may still be used.

Figure

Figure 2-9.2-9. TTwo Thwo Thermocoermocouples Cuples Configuonfigured fred for Diffor Differentierential Meaal Measuremsurementsents

Figure 2-1

Figure 2-10.0. ThermoThermocouple Bridgecouple Bridged by Monitored Objed by Monitored Obje ctct





 

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F

2

2..88 MMuullttiipplle e TThheerrmmooccoouupplle e CCiirrccuuiittss

Two or more thermocouples may be incorporated in a thermocouple circuit. They may be arranged in a series or in a parallel configuration. The

consequences of these arrangements are described in the following sections. 2.

2.88.1.1 SSererieies Ths Therermomoccououplple Cie Circrcuiuitsts

Thermocouples may be wired in a series as shown in Figure 2-11. The usual thermocouple loop analysis procedure may be used to determine the output of this arrangement. For N thermocouples arranged in a series, the output is N times the output that would be obtained with a single thermocouple

operating over the same temperature difference. This configuration, called a thermopile, may be used to obtain a larger signal than would be obtained with the normal single thermocouple arrangement.

2.

2.8.8.22 PaPararallllel el ThTherermomococoupuple le CiCircrcuiuitsts

Thermocouples may be wired in parallel as shown in Figure 2-12. Because electrical currents can flow around the loops, the standard thermocouple loop analysis is not applicable. It can be shown (see Appendix B) that the net output is a weighted average of the individual thermocouple outputs. The result for N parallel thermocouples is as follows:

Figure

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(2-24) where

ET = total emf from the circuit

Σ _i = 1/R_i = electrical conductance of thermocouple I Ei = emf from thermcouple I

Parallel thermocouples can be used to measure the average of the

temperatures at each of the parallel junctions; however, the equation above shows that the total output is the simple arithmetic average of all the thermocouple outputs only if all of the thermocouples have equal

conductances. Consequently, the parallel arrangement is potentially useful for measuring average temperatures, but caution must be exercised to ensure that there are equal conductances in each loop.

The equation also shows the consequence of shorting a thermocouple at some point between the junction and the open end. Shorting creates two parallel thermocouples, but the conductance in the loop created by the short is much higher than the conductance in the other loop. Therefore, a measurement gives the temperature at the location of the short. This is potentially very important. Consider a case in which the insulation on thermocouple wires is lost and the wires touch at some point behind the junction. If the

thermocouple feeds a controller, the invalid measurement would lead to an incorrect, possibly catastrophic, control section.

Figure

2-Figure 2-12.12. ThermoThermocouplecouples Wired in Pars Wired in Parallelallel

E_T



1



₁



+ ₂ +…

_

_n ---E₁



12



₁



+ ₂ +…

_

_n ---E₂ … + + =

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F

2

2..99 TThheerrmmooeelleeccttrriic c HHeeaatteerrss, , CCoooolleerrs s aanndd Generators

Generators

The focus of this book is temperature measurement with thermocouples, but there are other important applications of thermoelectricity. Temperature measurements with thermocouples must be made with insignificant current flowing in the circuit. Thermoelectric circuits can also achieve heating, cooling and electricity generation and all of these applications involve electric current in the circuit.

Consider a circuit of dissimilar conductors containing a source of direct current electricity as shown in Figure 2-13. This arrangement causes one junction to heat and the other to cool. Thermoelectric coolers find application

in devices such as beverage coolers.

Now consider a circuit of dissimilar conductors that is heated at one junction and cooled at the other junction as shown in Figure 2-14. This arrangement causes current to flow in the circuit, thereby providing a source of electric power. Thermoelectric generators find application in powering low-power devices and are being considered for large-scale applications such as using ocean temperature gradients to produce electricity.

Figure

2-Figure 2-13.13. A ThermoeA Thermoelectrilectric Heaterc Heater/Cooler/Cooler

WIRE B HOT COLD WIRE A DC POWER SUPPLY

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2.

2.1010 ThThe Le Lawaws os of Tf Thehermrmoeoelelectctriric Cc Cirircucuititss

2.1

2.10.10.1 The UThe Uselseless Less Laws oaws of Thef Thermormoeleelectrctricic Circuits

Circuits

Three laws of thermoelectric circuits were formulated long ago and they came to be considered essential knowledge required for proper use of

thermocouples. They became well known largely because of an important book published by Robert Benedict in 1969.2 The laws (as stated by Benedict)

along with comments are as follows: 1.

1. Law Law of Hoof Homogemogeneouneous Mets Metals: “als: “A theA thermoermoelectrlectric curic currenrent cant cannot bnot bee sustained in a circuit of a single homogeneous material, however sustained in a circuit of a single homogeneous material, however varying in cross section, by application of heat alone.”

varying in cross section, by application of heat alone.” Recall that measuring temperature with a thermocouple requires measurement of the open circuit voltage, the voltage that exists when no current is flowing. (Electrical current does flow in thermoelectric heaters, coolers and generators.) Referring to a current when

discussing thermocouple behavior clouds the issue and could lead to incorrect notions about how they work. Therefore, for temperature measurement, the law might be restated as follows:

Revised Law of Homogeneous Metals: A thermoelectric emf cannot be Revised Law of Homogeneous Metals: A thermoelectric emf cannot be created in a circuit of a single

created in a circuit of a single homogeneous material, howeverhomogeneous material, however

varying in cross section, by application of a temperature difference. varying in cross section, by application of a temperature difference.

As shown in Section 2.3 the thermoelectric voltage produced by two wires, A and B, with a junction at temperature T₂, and the open end at temperature T_1, is given by (S_A-S_B) (T₂-T₁) where S_A and S_B are the absolute Seebeck coefficients for wire A and B. If wires A and B are Figure 2

Figure 2-14.-14. A ThermoeA Thermoelectric lectric GeneraGeneratortor

ELECTRIC CURRENT HEATED JUNCTION COOLED JUNCTION WIRE B WIRE A

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F

identical, the factor containing the Seebeck coefficients is zero and there is no voltage produced, regardless of the temperatures. This law is trivial since it is doubtful that anyone would think that temperature could be measured by placing a loop of homogeneous wire into an environment whose temperature is to be determined. 2.

2. Law Law of Iof Intentermedrmediate iate MateMaterialrials: “Ts: “The ahe algeblgebraic raic sum sum of thof thee

thermoelectromotive forces in a circuit comprised of any number of thermoelectromotive forces in a circuit comprised of any number of dissimilar materials is zero if all of the circuit is at a constant dissimilar materials is zero if all of the circuit is at a constant temperature.”

temperature.”

This statement is correct, but a slightly less ponderous statement is as follows:

Revised Law of Intermediate Materials: The algebraic sum of the emfs Revised Law of Intermediate Materials: The algebraic sum of the emfs in a circuit comprised of any number of dissimilar materials is zero, if in a circuit comprised of any number of dissimilar materials is zero, if all of the circuit is at a

all of the circuit is at a constant temperature.constant temperature.

Loop analysis shows that the emf for each segment of a thermocouple composed of two wires, A and B, produces an emf that is proportional to the temperature difference across the segment. Consequently, the total emf is zero if there is no temperature difference across any of the segments

This law is also essentially trivial. 3.

3. Law oLaw of Sucf Successcessive or Iive or Interntermedimediate Teate Tempermperaturatures: “Ies: “If two dif two dissimissimilarlar homogeneous metals produce a thermal emf of E

homogeneous metals produce a thermal emf of E11 when the when the junctions are at temperatures T

junctions are at temperatures T₁₁ and T and T₂₂ and a thermal emf of E and a thermal emf of E₂₂ when the junctions are at T

when the junctions are at T₂₂ and T and T₃₃ , the emf , the emf generategenerated when d when thethe junctions are at T

junctions are at T₁₁ and T and T₃₃ will be E will be E₁₁ + E + E_2._2.””

This statement is correct, but a more general statement applies for the configuration that is important in practical applications. That

configuration is a series of two parallel wire segments, each composed of dissimilar metals with the final segment terminated at a junction. The following statement applies for that configuration:

Revised Law of Intermediate Temperatures: If a segment of two Revised Law of Intermediate Temperatures: If a segment of two parallel dissimilar h

parallel dissimilar homogeneous metals produces omogeneous metals produces a thermal emf of Ea thermal emf of E₁₁

when the temperatures at the ends of the segments are T

when the temperatures at the ends of the segments are T ₁₁ and T and T ₂₂ and a and a

thermal emf of E

thermal emf of E₂₂ when the temperatures at the ends of the segment when the temperatures at the ends of the segment

are at T

are at T ₂₂ and T and T ₃₃ , the , the emf generateemf generated when d when the end the end of the of the segments are segments are atat

T

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This result follows from loop analysis as proved in Section 2.3. Thermocouple loop analysis, as presented in this book, eliminates the need for the three laws that served practitioners in the past. The traditional laws provide little help to the practitioner who strives to make accurate

temperature measurements with thermocouples. The loop analysis method is simpler, more comprehensive and easier to remember for occasional users. Loop analysis, unlike the Laws, explains how thermocouples work when they are used properly and it explains the consequences of using damaged or improperly installed thermocouples. The traditional Laws of

Thermoelectricity, even as revised above, are essentially useless and should be forgotten and replaced by widespread reliance on loop analysis.

2.1

2.10.20.2 The The UseUseful ful Law Law of Tof Therhermocmocoupouplele Thermometry

Thermometry

Thermocouple loop analysis provides the following concise and useful law that replaces the traditional three Laws of Thermoelectricity in applications of thermocouples for temperature measurement.

The Law of Thermocouple Thermometry: The emf produced by

The Law of Thermocouple Thermometry: The emf produced by aa

segment of parallel dissimilar wires that experiences a temperature segment of parallel dissimilar wires that experiences a temperature difference across the segment is proportional to the temperature difference across the segment is proportional to the temperature difference. The total emf produced by the total circuit is

difference. The total emf produced by the total circuit is the algebraicthe algebraic

sum of the emfs produced by each segment between the open end and sum of the emfs produced by each segment between the open end and the junction of the wires.

the junction of the wires.

The constant of proportionality is called the relative Seebeck coefficient. The relative Seebeck coefficient has the following properties:

• It depends on the composition of the two wires in the segment, but is independent of the dimension or shape of the conductors. • It may be positive or negative.

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F

References References

1. The Theory and Properties of Thermocouple Elements, American Society for Testing and Materials publication STP 492.

2. Benedict, R. P., Fundamentals of Temperature, Pressure, and Flow Measurements, John Wiley & Sons, New York, 1969.

3. Schooley, James F., Thermometry, CRC Press, Boca Raton, FL, 1986. 4. Burns, G. W., Temperature-Electromotive Force Reference Functions and

Tables for the Letter-Designated Thermocouple Types Based on the ITS-90, National Institute of Standards and Technology publication NIST Monograph 175, Superintendent of Documents, U. S. Government Printing Office, Washington, DC, 1993.

5. The Use of Thermocouples in Temperature Measurement, American Society for Testing and Materials, ASTM 470B Fourth Edition 1993.

6. Reed, R. P., “Thermoelectric Thermometry: A Functional Model,” Temperature: Its Measurement and Control in Science and Industry, Vol. 5, Part 2, James F. Schooley, editor, American Institute of Physics, New York, 1982.

7. Kerlin, T. W., and Shepard, R. L., Industrial Temperature Measurement, ISA, Research Triangle Park, NC, 1982.

8. Nicholas, J. V., and White, D. R., Traceable Temperatures, John Wiley & Sons, New York, 1994.

9. Moffat, R. J., “The Gradient Approach to Thermocouple Circuitry,” Experimental Technique, April 1984, pp. 23-25.

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31

3

3 Measuring Temperature with

Measuring Temperature with

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.

3

3..11 CCoonnvveerrttiinng Eg EMMF tF to To Teemmppeerraattuurree

We have seen previously that the open-circuit voltage (OCV) of a

thermocouple depends on the temperature difference between the 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.

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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 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

                                                             

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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?

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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

3

3..22 EEqquuaattiioonns s ffoor r EEMMF F vveerrssuuss Temperature

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:

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or

V = b₀ + b₁T (3-3)

where

T = temperature

V = thermocouple voltage (corrected for a 0°C reference temperature)

a₀, a_1, 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 + … + b_nT 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

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the general equation. Equation 3-4 can be rewritten to accomplish this. Taking the fifth order case as an example, we obtain

(3-6)

3

3..33 MMooddeerrn n TThheerrmmooccoouuppllee Instrumentation

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 +     +     +     +     +     =

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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

Thermocouple measurements

PRACTICAL

PRACTICAL

THERMOCOUPLE

THERMOCOUPLE

THERMOMETRY

THERMOMETRY

Thomas W. Kerlin

Thomas W. Kerlin

Mitchell Johnson

Mitchell Johnson

Preface to the Second

Preface to the Second

Edition

Edition

Table of Contents

Table of Contents

1

1

Introduction

Introduction

2

2

Fundamentals

Fundamentals

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3

3

Measuring Temperature with

Measuring Temperature with

a Thermocouple

a Thermocouple