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Module M08

Measurement of temperature

Paul Regtien, Eva Kureková, Martin Halaj

8.1 Introduction

Temperature is a thermodynamic state quantity defined by the efficiency of the reversible Carnot cy-cle. When considering a reversible Carnot cycle, working between the same baths with certain tem-

peratures, its efficiency depends only on those temperatures and does not depend on the thermometricmaterial used. This enables it possible to define a thermometric scale based only on thermodynamiclaws and therefore independent of the thermometric material being used. Based on this definition, the

gas thermometer is realised, utilising a gas (e.g. hydrogen or helium) whose properties are close to the properties of an ideal gas.

Lord Kelvin defined a thermodynamic scale based on the triple point of water, i.e. based on theequilibrum between three states of water (ice, water and saturated vapor). The triple point of water hasthe following value on a thermodynamic scale:

T = 273.16 K

The basic unit of the thermodynamic temperature is the kelvin (K) defined as the 273.16 part of thethermodynamic temperature of the triple point of water.

Due to the historical definition of temperature scales, the degree Celsius (symbol ( °C) is used as atemperature unit also, The Celsius temperature (symbol t ) is defined as the difference between thethermodynamic temperature T and the temperature T 0 = 273.15 K:

t (°C) = T (K) – 273.15 (8.1)

According to this definition, the degree Celsius is equal to the kelvin (1K = 1 °C). Temperatures can beexpressed either in kelvin or in degree Celsius. Indeed, ∆t = ∆T .

The Fahrenheit temperature scale is primarily used in the USA. The ice melting point is set at 32 °Fand the water boiling point reaches 212 °F. The scale is divided into 180 °F between those two points.Conversion from Fahrenheit to Celsius temperature and vice versa is performed by the following equa-tions

υ (°F) = (9/5) t + 32 (8.2)

t (°C) = (5/9)( υ - 32) (8.3)

where

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υ is temperature expressed in Fahrenheit,t is temperature expressed in Celsius.

Although gas thermometry is the most accurate method for temperature measurements, it requires expensive laboratory equipment and is very time consuming. Therefore, the General Conference forweights and measures (CGPM) introduced an International practical temperature scale in 1927. Thattemperature scale has been gradually updated and corrected. Its latest version (1990) is called ITS-90(The International Temperature Scale of 1990).

The ITS-90 defines the ‘so called’ International Kelvin temperature , symbol T 90 and an Interna-tional Celsius temperature , symbol t 90. The relation between T 90 and t 90 is the same as between T and t ,i.e.

t 90(°C) = T 90(K) – 273.15 (8.4)

The thermodynamic temperature T,as well as the temperature T 90, have the same value kelvin. Simi-larly, Celsius temperature t and temperature t 90 have the same unit degree Celsius, The ITS-90 is de-signed in such a way that for any temperature within its whole range, the numerical value of T 90, is aclose approximation of the numerical value of T . That approximation is performed according to the

best estimations known at the time of the ITS-90 establishment. Compared to the direct measurementof the thermodynamic temperature T , measuring the temperature T 90 is easier.

The ITS-90 covers the temperature range from 0.65 K to the highest temperature that can be practi-cally measured by Planck’s radiation law for monochromatic radiation. The whole scale is divided intoseveral ranges and sub-ranges. Some of these ranges are overlapping. Several definitions of the tem-

perature T 90 exist in overlapping areas, having an equal status. Deviations in the numerical values ob-tained by different definitions at the same temperature can be determined by very precise measure-ments. In most situations these deviations can be neglected.

Four major ranges are considered in the ITS-90:

1) in the range 0.65 K to 5.0 K T 90 is defined by the pressure of3He and 4He vapours,

2) in the range 3.0 K to 24.5561 K (triple point of neon) T 90 is defined by the helium gas thermometer,calibrated in three defined fixed points,

3) in the range 13.8033 K (triple point of hydrogen equilibrium) to 961.78 °C (freezing point of sil-ver) T 90 is defined by the platinum resistance thermometer, calibrated in specified fixed points,

4) above 961.78 °C (freezing point of silver) T 90 is defined by specific fixed points and Planck’s ra-diation law.

Specified fixed points of the International Temperature Scale ITS-90 are shown in table 8.1.According to the ITS-90, triple points have defined fixed points. A triple point is a temperature at

which three states (solid, liquid and gas phase) of a particular material or mixture are in equilibrium.The triple point of water is used most often for defining the temperature unit.

A glass cell is used for the realization of the triple point of water. The water properties are precisely

specified, and the water is hermetically sealed in a cell. The space above the water level is a vacuum.Borum silicate glass or siliceous glass is most often used for the container.

Preparation for the triple point of water consists of two phases and is performed minimally 48hours before the actual measurement. The first phase consists of creating an ice sheath that covers thethermometric bushing used for thermometer immersion. The ice sheath can be prepared in differentways, for example by adding dry ice, liquid nitrogen, by special instrumentation, etc. The water triple

point cell should be placed into an environment with temperature closely above 0 °C for 24 hours as aminimum. A suitable environment is a mixture of water and ice.

The second phase consists of releasing the ice sheath from the cell. It starts by inserting a siliceoustube or rod at room temperature into the thermometric bushing. The next step is slowly heating by barehands, slowly rotating the cell. When properly released, the ice sheath should freely rotate within thecell.

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After having thus prepared the water triple point cell it is again inserted into a thermostat. Beforestarting the actual temperature measurement, one must cool the thermometer close to the temperatureof the triple point of water. Only after cooling can the thermometer can be inserted into the preparedcell. Temperature measurement can start about 20 minutes after thermometer insertion.

Realisation of the triple point of argon is even more complicated. A vacuum must be created in thevessel during the first phase, later the argon is cooled by liquid nitrogen. To create a homogenous dis-tribution of all three phases (the solid, liquid and gaseous); solid argon must be heated by a spiralheater.

Table 8.1 Defined fixed points according to the International Temperature Scale ITS-90

Number Temperature Material Status W r (T 90)

T 90 (K) t 90 (°C)1 3 to 5 -270.15 to

-268.15He saturated steam

2 13.8033 -259.3467 e-He 2 triple point 0.001 190 07

3 ≈17 ≈-256.15 e-He 2 or He saturated steam or gas4 ≈20.3 -252.85 e-He 2 or He saturated steam or gas5 24.5561 -248.5939 Ne triple point 0.008 449 74

6 54.3584 -218.7916 O 2 triple point 0.091 718 04

7 83.8058 -189.3442 Ar triple point 0.215 859 75

8 234.3156 -38.8344 Hg triple point 0.844 142 11

9 273.16 0.01 H 2O triple point 1.000 000 00

10 302.9146 29.7646 Ga melting point 1.118 138 89

11 429.7485 156.5985 In freezing point 1.609 801 85

12 505.078 231.928 Sn freezing point 1.892 797 68

13 692.677 419.527 Zn freezing point 2.568 917 30

14 933.473 660.323 Al freezing point 3.376 008 60

15 1234.93 961.78 Ag freezing point 4.286 420 53

16 1337.33 1064.18 Au freezing point

17 1357.77 1084.62 Cu freezing point

8.2 Principles of temperature measurement

Two categories of temperature measurement are distinguished: contact thermometry and radiationthermometry . In the first category the object, of which the temperature is being measured, should make

proper contact with the temperature sensor. This has the immediate consequence of (thermally) load-ing the measurement object. Furthermore, it takes time to heat up the sensor, according to a first order

response. The time constant is determined by the heat capacity of the sensor and the heat resistance be-

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tween the sensor and the object. The second category is based on the measurement of (thermal) radia-tion of the body whose temperature has to be measured. The radiation is directed to the temperaturesensitive device whose temperature rises accordingly. The thermal load in this method is considered to

be negligible.In general, thermometers utilise several basic principles:

1) the thermal expansion of solid, liquid or gaseous thermometric materials. The temperature is de-rived either from the volume change of the thermometric material at constant pressure (dilatationthermometers) or determined from the pressure change of the thermometric material at constantvolume (pressure thermometers),

2) change of the electrical properties are related to the temperature change. The following phenom-ena are applied:

a) the dependency of the electrical resistance of conductors or semiconductors on temperature.Such sensors are called resistance thermometers or thermistors,

b) the generation of a thermoelectric voltage in a circuit created by junctions of two different metalconductors and the junctions being subjected to two different temperatures (so called Seebeck

effect). Such sensors are called thermocouples,3) sensing of the total radiation energy . Solid and liquid materials emit thermal radiation at each tem-

perature above absolute zero,4) utilisation of the spectral radiance of the measured object. When the temperature of the measured

object increases, its spectral radiance increases.

8.3 Dilatation thermometers

Dilatation thermometers utilise the principle of volumetric (or linear) expansion of gaseous, liquid orsolid thermometric materials at constant pressure. When the temperature of the thermometric materialchanges, its volume changes accordingly. This change is characterised by the coefficient of volumetric(respectively linear) expansion.

The following equation describes the temperature dependence of the sensor’s active length over alimited temperature range:

l = l 0(1 + α ls ∆t ) (8.5)

where

α ls is the average coefficient of the linear expansion,l is the final length,l 0 is the original length,∆t is the temperature change.

Over a limited temperature range the volumetric change can be expressed as

V = V 0(1 + α vs ∆t ) (8.6)

where

α vs is the average coefficient of the volumetric expansion,V is the final volume,V 0 is the original volume,

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end. An excessive volume of thermometric liquid can fill that space when the measuring range is ex-ceeded. Thermometric liquid is normally only present in bulb 1 and capillary 2 during a measurement.Scale 5 is usually marked at the outer surface of the tube. An immersion line 4 is shown on the scale ofthermometers that are intended for partial immersion.

Enclosed scale thermometers (see Fig. 8.2a) have a thermometric scale on a separate glass or por-celain plate. This plate is usually firmly attached to the capillary and they are sealed together in glass.

A stem thermometer (see Fig. 8.2b) contains a stem instead of a vessel at the lower end. The fulllength of the stem should be immersed in the substance to be measured, ensuring that the scale is al-ways outside the vessel. Stem thermometers are manufactured in different shapes that include straight,rectangular, bent (under an angle of 120 °), and they may be either short or long.

Fig. 8.2 Mercury thermometersa) enclosed scale thermometer, b) stem

thermometer, c) thermometer with attenu-ated scale

When a larger measuring range and a finer scale divi-sion is required, the thermometer length could exceed therecommended value of 500 mm. Therefore, the use of athermometer with attenuated scale is preferred for precisereadout in a certain range (see Fig. 8.2c). The thermome-ter capillary is widened in certain places so that this space

contains a larger amount of thermometric liquid corre-sponding to the attenuated range. The scale can be at-tenuated at several places within the range except at thecalibration positions (e.g. water triple point, water boiling

point, etc.). A set of Alinh’s thermometers is recom-mended, in which the respective measuring range is di-vided into three to seven separate thermometers, each of them having a widened capillary set in different posi-tions.

The function of the maximum and minimum (Six’s)thermometer is to register the maximum and minimumtemperature during a certain period (see Fig. 8.3a). Thethermometric liquid (alcohol in most cases) is located in amain bulb. The bulb end is a U-shaped stem. Part of thestem capillary is filled with alcohol, the U-bend is usuallyfilled with mercury. When the temperature increases, thealcohol expands and moves the mercury column. A smallmetal float (index) with a friction hook floats on the mer-cury level (see Fig. 8.3b).

After reaching the maximum temperature, the mercurycolumn starts to drop. Due to the friction hook the metalfloat adheres to the capillary wall and does not drop withthe mercury level. The lowering mercury column at the

other side pushes the second float up to the level of minimum temperature. A new temperature rise moves themercury column again and the metal float adheres at the

position of the minimum temperature. Before conductinga new measurement both floats should be reset by a smallmagnet, otherwise the floats will only be pushed to a new

position when they exceed the previous maximum or minimum temperature.

Contact thermometers are used for temperature controlled electric switching; they use the electricalconductivity of mercury to realise an electrical switch. Two basic design types are available – withfixed contacts (see Fig. 8.4a) and with movable contacts (see Fig. 8.4b). Contact thermometers wereoften used for on-off temperature regulation or as a thermal fuse. Recently they have most often been

replaced by bimetal thermometers.

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A contact thermometer with movable contacts consists of a thermometric part and a contact part(see Fig. 8.4b). The solid contact 1 is located at the upper part of the stem. The mercury column 2 issupplied by energy through that contact. A platinum wire 3, fixed in a square nut 8, represents themovable contact. The platinum wire and the signal wire are electrically connected through connection4, friction contact 5, spindle 6 and square nut 8. When spinning the adjustment spindle, the square nutis forced to move in a vertical direction and accordingly adjusts the position of the end of the platinumwire. The selected switching temperature is adjusted as is indicated by the square nut at scale 7 . Whenthe thermometer is heated, the mercury column rises to a position corresponding to the adjustedswitching temperature and touches the end of the platinum wire, closing the electrical circuit. As thethermometer is hermetically sealed, the operator cannot rotate the adjustment spindle. Therefore amagnetic clutch 9 is used.

Fig. 8.3 Maximum and minimum thermometera) scheme, b) metal float (index) with friction hook

Fig. 8.4 Contact thermometersa) with fixed contacts, b) with fixed and movable

contacts

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Contact thermometers with movable contacts have circuits with a transistor relay switch. Accordingto the design and relay used, the reproducibility of the switching temperature is only 0.0018 °C at 50°C measuring range and 0.1 °C scale division. The operating life of this type of thermometer is about 6million switches. A mercury fill, enables temperature switching within a range of –38 to 600 °C.

8.3.2 Rod thermometers

Rod thermometers utilise the thermal expansion of the material according to formula (8.3). The ther-mal expansion coefficient is not constant but varies with temperature. Therefore, its average value α ls is used over a given temperature interval. The thermometer thus obtains a linear static characteristicover a restricted operational range. Metal rod thermometers and bimetal thermometers are described inmore detail in the following sections.

Metal rod thermometer

Metal rod thermometers are based on the different thermal expansion of two materials (see Fig. 8.5).The thermometer rod is made of a material with a large thermal expansion, e.g. brass, steel, zinc, alu-minum or nickel. The rod is located in a casing with the smallest possible thermal expansion, e.g. in-var, siliceous glass, porcelain or glass. The rod and casing are firmly connected at one end, whereasthe other end of the rod moves freely in the casing and moves the thermometer index. When the tem-

perature changes about ∆t , the rod expands about ∆ y1, whereas the casing expands only about ∆ y2 atthe same time (see Fig. 8.5a). Therefore, the total difference between the rod’s free end and casing isequal to:

∆ y = ∆ y1 - ∆ y2 = l (α l 1 - α l 2)∆t (8.7)where

∆ y is the resulting displacement of both the rod end and the casing end,l is the basic (nominal) length of the thermometer,∆t is the measured temperature difference,α l 1 is the thermal expansion coefficient of the rod,α l 2 is the thermal expansion coefficient of the casing.

Fig. 8.5b shows a design scheme of the metal rod thermometer with a system to transfer the expansionof the measuring rod to the index of the thermometer. Typical measuring range reaches -30 to 1000°C. A disadvantage of metal rod thermometers is a lower accuracy (permissible error up to 2% of themeasuring range) and a longer time constant.

Bimetal thermometer

Bimetal thermometers are based on the deformation of two firmly connected metal strips with differentthermal expansion coefficients (see Fig. 8.6a). Strips with the same length are fixed together over thewhole length by welding or pressing. Both connected strips have the same shape at the initial tempera-ture. When heated, they bend towards the side of the metal with the lower thermal expansion. Variousmaterial combinations are used in practice, e.g. invar (36% Ni, 64% Fe) – brass (62% Cu, 38% Zn),invar – nickel, invar – steel, etc. Increased bending is obtained by the appropriate shaping of the bi-

metal strip, for instance U-shape strips (see Fig. 8.6b), a flat spiral (see Fig. 8.6c) or a cylindrical spiral(see Fig. 8.6d) give increased bending.

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Fig. 8.5 Metal rod thermometera) expansion of both rod and casing due to temperature, b) one of the possible design schemes

Fig. 8.6 Bimetal stripa) flat strip, b) U-shaped, c) flat spiral, d) cylindrical spiral

Bimetal thermometers are often used for on-off temperature regulation. One possible connection isgiven in Fig. 8.7. A simple bimetal strip 1, fixed at one end, is used as sensitive element. When reach-

ing the desired temperature, the strip bends and touches contact 2, thereby closing the secondary cir-cuit of transformer 5. As a consequence electromagnet coil 3 is activated and opens the heavy-currentcontacts 4. When the temperature decreases again, the bimetal strip straightens and the contact 2 opens.

Fig. 8.8 shows a possible design of a bimetal thermometer. The temperature sensitive element is a bimetal cylindrical spiral 1. The strip is firmly welded to shaft 2 with index 5. The shaft is firmly con-nected to plug 3, inserted into a stem 4. When the temperature increases, the bimetal strip tries to un-fold and thereby rotates shaft 2 and pointer 5. The measured temperature is indicated on dial 6 . Thistype of thermometer can be used in the range from –40 °C to 500 °C, with a permissible error down to1% of the measuring range. This thermometer is resistant against overloading up to 50% of the meas-uring range. Its disadvantage is that it has a large time constant, up to 40 seconds. The thermometercan be used in many applications, e.g. in food industry, in gardening, in textile and rubber industry,etc.

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Fig. 8.7 On-off temperature regulation1 – bimetal strip, 2 – contact, 3 – electromagnet coil, 4 – heavy-current contacts, 5 – transformer

Fig. 8.8 Bimetal thermometer with cylindrical spiral strip

1 – bimetal strip, 2 – shaft, 3 – plug, 4 – stem, 5 – pointer, 6 – dial

8.3.3 Pressure thermometers

Pressure thermometers measure the temperature change of a thermometric liquid. This thermometricliquid is enclosed in a vessel with a constant volume. When the pressure of the thermometric liquidchanges, the thermometer element deforms. This deformation is transferred to a thermometric scale.Since the pressure in the thermometer is relatively high, the vessel with thermometric liquid is usuallya metal, for instance steel or bronze. The most popular pressure thermometer is the pressure liquidthermometer .

The thermometric filling must always remain in the liquid phase during operation of the thermome-ter. Therefore, one can only measure temperatures below the boiling point and above the melting pointof the thermometric liquid. Mercury or organic liquids (xylol, methyl alcohol, petrolum) are oftenused.

The thermometric liquid is located in a metal vessel 1 that is fully immersed in the substance ofwhich the temperature is measured (see Fig. 8.9a). The thermometric liquid passes capillary 2 connect-ing the metal vessel with the deformation manometer (Bourdon tube) 3. This manometer is connectedto an indicating mechanism. The thermometric liquid fully fills the vessel, capillary and manometer.When the temperature increases, the metal vessel and thereby the thermometric liquid is heated. Thisincreases pressure, causing deformation of the Bourdon tube. The deformation is transferred by sometransmission mechanism to the index.

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Fig. 8.9 Pressure liquid thermometera) without correction, b) with partial correction, c) with total correction

1 – metal vessel, 2 – connecting capillary, 3 – Bourdon tube, 4 – bimetal strip, 5 – common index, 6 – blind cap-illary, 7 –Bourdon tube

The measurement uncertainty of pressure liquid thermometers is relatively high, in particular thosewith long capillaries. It is affected by temperature changes of the surrounding medium in which thethermometer is placed as well as by the hydrostatic pressure of the thermometric liquid. Therefore,when the capillary length exceeds 6 meters, partial or total correction of the surrounding temperaturemust be undertaken.

With short capillaries partial temperature correction of the indication device (see Fig. 8.9b) is per-

formed, using a suitably shaped bimetal strip 4. It is designed in such a way that, when the temperaturechanges, it acts against the deformation of the Bourdon tube. This device compensates for possible in-dication errors caused by environmental temperature changes.

With long capillaries, having a length up to 50 m, it is necessary that a total temperature correc-tion (see Fig. 8.9c) is performed. This correction eliminates effects of both the environmental tempera-ture on the capillary and the sensitive element (Bourdon tube) as well as the influence of the hydro-static pressure of thermometric liquid. The whole sensor consists of two systems – a measurement sys-tem and a correction system. The correcting system is the same as the measuring one but it does notcontain the vessel with thermometric liquid, only a blind capillary 6 and its own Bourdon tube 7 . Theliquid filling is the same as in the measuring system. When the temperature in the proximity of thecapillary and the sensitive element changes, both tubes introduce the same deviation at the commonindex 5, but with opposite sense, so that their effects cancel.

A major advantage of the pressure liquid thermometer is the possibility of remote temperaturemeasurement. The measuring range is relatively high, from -39 °C up to 600 °C. Although the boilingtemperature of mercury is 357 °C, the measuring range can be extended to 600 °C by increasing the

pressure in the measuring system. Other advantages are the linear static characteristic, a robust designand a large conversion force, enabling the application of the pressure liquid thermometer in severeworking conditions.

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8.4 Temperature sensors with electric output

8.4.1 Introduction

In this part we present various temperature sensors - resistive sensors, thermocouples, band-gap sen-sors and special sensors with electronic output. In a separate section we discuss the principles of radia-tion thermometry. All of these temperature sensors are based on a change in the electrical parametersdue to a temperature change.

8.4.2 Resistive temperature sensors

The resistivity of a conductive material depends on the concentration of free charge carriers and theirmobility. The mobility is a parameter that accounts for the ability of charge carriers to move more orless freely throughout the atomic lattice; their movement is constantly hampered by collisions. Bothconcentration and mobility vary with temperature, at a rate that depends strongly on the material em-

ployed.In intrinsic (or pure) semiconductors, the electrons are bound quite strongly to their atoms; only a

very few have enough energy (at room temperature) to move freely. At increasing temperature moreelectrons will gain sufficient energy to be freed from their atom, so the concentration of free chargecarriers increases with increasing temperature. As the temperature has much less effect on the mobilityof the charge carriers, the resistivity of a semiconductor decreases with increasing temperature: its re-sistance has a negative temperature coefficient .

In metals, all available charge carriers can move freely throughout the lattice, even at room tem-

perature. Increasing the temperature will not affect the concentration. However, at elevated tempera-tures the lattice vibrations become stronger, increasing the chance of the electrons to collide and ham- per free movement throughout the material. Hence, the resistivity of a metal increases at higher temperature: their resistivity has a positive temperature coefficient .

The temperature coefficient of the resistivity is used to construct temperature sensors. Both metalsand semiconductors are used, They are called (metal) resistance thermometers and thermistors, respec-tively.

8.4.2.1 Resistance thermometer

The construction of a resistance thermometer of high quality requires a material (metal) with a resistiv-ity temperature coefficient that is stable and reproducible over a wide temperature range. By far the

best material is platinum , due to a number of favourable properties. Platinum has a high melting point(1769 °C), is chemically very stable, resistant against oxidation and available with high purity. Plati-num resistance thermometers are used as an international temperature standard for temperatures be-tween triple point of the hydrogen equilibrium (13.8033 K) and freezing point of silver (+961.78 °C),

but they can be used up to 1000 °C.A platinum thermometer has a high linearity. Its temperature characteristic is given by:

R(T ) = R(0) {1 + aT + bT 2 + cT 3 + dT 4 + … } (8.8)

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with R(0) the resistance at 0 °C. The values of the coefficients R(0), a , b, …are specified according tovarious standards and temperature ranges. As an example, the resistance of a Pt100 is characterized,according to the DIN-IEC 751 standard, as:

R(0) = 100.00 Ω a = 3.90802 ⋅10 -3 K -1 b = −5.8020 ⋅10 -7 K -2c = 4.2735 ⋅10 -10 K -3

for a temperature range −200 °C < T < 0 °C; for temperatures from 0 °C to 850 °C the parameters a and b are the same, and the value of c = 0. Also the tolerances are specified in the standard definition.For instance, the resistance value of a “class A” Pt100 temperature sensor at 0 °C is 0.06%, which cor-responds to a temperature tolerance of 0.15 K. At the upper end of the range (850 °C) the tolerance is0.14% or 1.85 K. Class B sensors have wider specified tolerances, for instance 0.3 K at 0 °C. Table 8.2shows more tolerance values for both accuracy classes.

Table 8.2 Permissible deviations of resistance and temperature for metal resistance thermometers

Accuracy class A Accuracy class B

Temperature Deviation Deviation

Ω °C Ω °C-200 ± 0,24 ± 0,55 ± 0,56 ± 1,3-100 ± 0,14 ± 0,35 ± 0,32 ± 0,8

0 ± 0,06 ± 0,15 ± 0,12 ± 0,3100 ± 0,13 ± 0 ,35 ± 0,30 ± 0,8

200 ± 0,20 ± 0,55 ± 0,48 ± 1,3300 ± 0,27 ± 0,75 ± 0,64 ± 1,8400 ± 0,33 ± 0,95 ± 0,79 ± 2,3500 ± 0,38 ± 1,15 ± 0,93 ± 2,8600 ± 0,43 ± 1,35 ± 1,06 ± 3,3650 ± 0,46 ± 1,45 ± 1,13 ± 3,6700 ± 1,17 ± 3,8800 ± 1,28 ± 4,3850 ± 1,34 ± 4,6

There also exists resistance temperature sensors having other values than, 100 Ω at 0 °C, for in-stance the Pt1000 with a resistance value of 1000 Ω at 0 °C. However, the Pt100 sensor is most popu-lar for industrial applications.

The sensitivity of a Pt100 is approximately 0.4%/K or 0.39 Ω/K. The parameters b and c accountfor the non-linear relationship between temperature and resistance. Within a limited temperature rangethe non-linearity might be neglected, when medium accuracy is required. The non-linearity error fol-lows from the parameters a and b as given above. For instance, compared to the straight line throughthe origin ( T = 0) the deviation is

NL(0, T ) = b⋅ R(0) ⋅T 2 (8.9)

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which is −0.58 Ω or –1.5 °C. When compared to the straight line between two end points ( T =0 and T =T e), the maximum non-linearity is just halfway along the range ( T = ½ T e) and amounts:

2)0(4

1),0( ee T RbT NL ⋅⋅= (8.10)

For instance, over the temperature range 0 to 100 °C, the non-linearity error is 0.145 Ω or +0.37 °C,occurring at T = 50 °C. For accurate temperature measurements, where these errors are too high to ne-glect them, the standardized expression should be used to calculate the temperature from the measuredresistance value.

Metal resistance thermometers are con-structed either with a wire wound resistor or a film resistor (Figure 8.10). To reduce theself-inductance of a wire wound resistor, thewire is bifilarly wound over an isolating

body (Figure 8.10a) - the two “coils” are inseries but oppositely wound. The design ac-cording to Figure 8.10b is used regularly.Several segments of resistive spirals are

placed in a protecting cover, enabling theuse of a relatively long resistive wire in asmall space. The special layout of a metalfilm resistor allows laser trimming of thevalue at 0 °C (Figure 8.10c). Some sensorsare protected against mechanical damage bya cover from a robust material with highthermal conductivity (see the measuring

probe in Fig. 8.10d).The tolerances and non-linearity errorsdiscussed so far relate to the sensor only.Additional errors may arise due to:

- self-heating,- errors within the interface circuit,- connecting cable resistance.

Self-heating should be minimized by reduc-ing the current through the sensor and ensur-ing a low thermal resistance to the environ-ment. A measurement current I introduces

heat dissipation of I 2

R(T ) in the sensor. Forexample, at 0 °C and 1 mA current the dissi-

pation is 0.1 mW. In order to limit the error due to self-heating to 0.1 °C, the sensor sho-uld be mounted in such a way that the ther-mal resistance is less than 10 3 K/W.

Fig. 8.10 Resistance thermometersa) thin wire bifilarily wounded on the core (1 - thin resistance wire, 2 - glass rod, 3 – protecting cover, 4 –

terminal),b) spiral in ceramic bushing,

c) thin foil (1 – resistance foil, 2 – base, 3 – protectingcover, 4 – terminals),

d) measuring probe (1 – sensing element, 2 – protect-ing cover, 3 – connecting wires, 4 – terminal)

A simple interface circuit for a resistance thermometer is shown in Figure 8.11.The output voltage of this circuit (assuming ideal properties of the operational amplifier) is:

( )

−

+=

13

4

43

30 R

T R R R

R R R

E U (8.11)

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Fig. 8.11 Interface circuit using an operational amplifier

With the resistors R3 and R4 the output can be adjusted to zero at an arbitrary temperature (for instance0°C). The resistor R1 sets the sensitivity of the circuit. The accuracy of this interface is set by the toler-ances of the voltage source E and the resistances R1, R3 and R4, which all should be chosen in accor-dance with the required performance of the measurement system.

Resistive sensors are often connected in a bridge configuration, in order to reduce non-linearity andunwanted, common mode interferences. The effect of cable resistance might be substantial, in particu-lar when the sensor is located at a distance from the measuring circuit. Its influence can be compen-sated for in various ways. Figure 8.12 shows three basic configurations: a two-wire, a three-wire and afour-wire configuration. The criterion is zero output at a particular reference temperature (for instance0 °C). In the two-wire case (see Fig. 8.12a) this is achieved by adjusting the bridge with a variable re-sistor Rn. In the three-wire situation (see Fig. 8.12b) an extra lead resistance is added to the resistor in

the other arm of the bridge ( R1). Full compensation is achieved when the wire resistances Rv1 and Rv2 are exactly equal. The four-wire solution (see Fig. 8.12c) is the most expensive, but there are no spe-cial conditions required for the elimination of the wire resistances: the bridge is current driven and theoutput voltage is measured using a measuring device with high input resistance, so no current flowsthrough these terminals.

8.4.2.2 Thermistor

A thermistor (contraction of the words therm ally sensitive res istor ) is a resistive temperature sensor

built up from ceramics. Commonly used materials are sintered oxides from the iron group (chromium,manganese, nickel, cobalt, iron); the most popular material is Mn 3O4. These oxides are doped withelements of different valence to obtain a lower resistivity giving them semiconductor properties(mainly of the p-type). Several other oxides are added to improve the reproducibility. To obtain a sta-

ble sensitivity; thermistors are aged by employing a special heat treatment process. A typical value ofthe drift in resistance after aging treatment is +0.1% per year.

Thermistors cover a temperature range from −100 °C to +350 °C, but particular types go down to 2K (ruthenium oxide). Their sensitivity is much larger than that of metal resistance thermometers. Fur-thermore, the size of thermistors can be very small, so that they are applicable for temperature meas-urements in or on small objects. Compared to metal resistance thermometers, a thermistor is less stablein time and shows a much larger non-linearity.

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Fig. 8.12 Connecting of the thermometer to the measuring circuit

a) two-wires wiring, b) three-wires wiring, c) four-wires wiring

The resistance of most semiconductors has a negative temperature coefficient. This also applies tothermistors. That is why a thermistor is also called an NTC-thermistor or just an NTC . Thermistorswith a positive temperature coefficient – PTC – also exist. The resistivity of the NTC-material is de-termined by the concentration of free charge carriers in the material, and this concentration is de-scribed by:

2 E kT n c e −= ⋅ (8.12)

where

c is a constant, E is the band-gap energy of the dopant,k is the Boltzmann’s constant,T is the temperature in K.

Since the resistivity is the reciprocal of the conductivity, and the latter is proportional to the concentra-tion, the resistivity (and hence resistance) of a thermistor varies with temperature according to:

( ) 21 c kT R T c e= (8.13)

For practical reasons, the expression for the temperature dependence of an NTC is given in a differentway:

( ) ( ) 01 1

0

BT T R T R T e − = (8.14)

where

R(T 0) is the resistance at a reference temperature T 0 (usually 25 °C), B is a constant that depends on the type of NTC.

From this equation it follows for the temperature coefficient (or sensitivity) of an NTC:

2

1 dR BS

R R T = = − [K -1] (8.15)

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Further, it should be realized that due to the non-linearity of the temperature characteristic, the sensi-tivity varies with temperature (as also appears from the expression given above). The parameter B is inthe order of 2000 to 5000 K. For instance, at B = 3600 K and room temperature ( T = 300 K) the sensi-tivity amounts − 4% per K. At 350 K the sensitivity has reduced to –3% per K. When improved linear-

ity is required; the temperature characteristic can be linearized by a parallel resistor, a series resistor oralternatively a combination of these. The resistance values can be chosen in accordance with the temperature range and the non-linearity that is required for the specific application. Note that the sensitiv-ity of the linearized NTC network is always lower than that of the NTC itself.

For high accuracy applications, it should be noted that the NTC parameter B is also slightly temperature dependent:

( ) ( ){ }20 1 B T B aT bT = + + (8.16)

The coefficients a and b in this expression are composition dependent; for their appropriate numericalvalues, the manufacturer should be consulted. An even more precise approximation of thermistor char-acteristics is the ‘so–called’ Steinhart-Hart equation:

3lnln1

)( RC R B AT

+⋅+= (8.17)

where

T is the measured temperature (in K), R is the thermistor resistivity (in Ω), A, B, C are constants.

The constants A, B, C can be determined from three equations, resulting from three measurements atdifferent temperatures: R1 = R(T 1), R2 = R(T 2) and R3 = R(T 3). Further, the following conditions must be

met:a) -40 °C ≤ T 1,

b) T 2, T 3 ≤ 150 °C andc) ( T 2 - T 1) ≤ 50 °C; ( T 3 - T 2) ≤ 50 °C,d) the temperatures T 1, T 2, T 3 should be evenly spaced.

Under these conditions, the accuracy of the data calculated by the Steinhart-Hart equation will be bet-ter than ±0.01 °C.

The resistance value of a thermistor at the reference temperature depends on the material, the dop-ing type and concentration, the device dimension and geometry. Values of R25 (the resistance at 25 °C)range from a few ohm to some 100 k Ω. The accuracy of thermistors is in the order of ±1 °C for stan-

dard types and ±0.2 °C for high precision types.Like metal resistive sensors, NTC’s also suffer from self-heating. The current through the sensorshould be kept low in order to avoid large errors due to self-heating. Generally, a current less than 0.1mA is acceptable in most cases (this is called zero power mode ). The effect of self-heating also de-

pends on the encapsulation material and on the dimensions and shape of the sensor. In particular thecondition of the environment (gas or liquid, still or flowing) determines the self-heating. A measurefor this effect is the thermal dissipation constant, a figure that is provided by the manufacturer forvarious sensor types and various environmental conditions. It ranges from about 0.5 mW/K to some 10mW/K.

The basic shape of a thermistor is a chip: a slice of ceramic material with metallised surfaces forthe electrical contacts. The device is encapsulated in a coating of thermally conductive epoxy to ensuremechanical protection and a low thermal resistance to the measurement object. There are various

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shapes available: disc, glass bead, probe, surface-mount (SMD). The smallest devices have a sizedown to 1 mm (Figure 8.13).

Fig. 8.13 Thermistorsa) stick thermistor (1 - sensitive stick, 2 – holder, 3 – protecting foil, 4 – protecting cover, 5 – insulating sub-

stance),b) flat thermistor,

c) bead-type thermistor (1 – core, 2 – connecting wires, 3 – protecting cover)

To measure the resistance value of an NTC, it can be connected in a single-element bridge (one NTC and three fixed resistances), or in a half or full bridge configuration (with two or four NTC’s).This type of interfacing is used when small temperature changes or temperature differences have to bemeasured. Another useful interface circuit is the one as shown in Figure 8.11, where R(T ) is the NTC.Here, the offset (temperature at zero output) and circuit sensitivity can be adjusted with the resistancevalues R1 to R4. When necessary, for R(T ) an NTC with linearising resistors can be used, to obtain amore linear temperature-to-output voltage characteristic. The reduction in sensitivity resulting fromlinearisation can be compensated by a higher gain of the interface circuit.

Thermistors are small-sized and low cost temperature sensors, and are useful in applications where

accuracy is not a critical design parameter. They can be found in all kinds of systems, for the purposeof temperature monitoring and control, for temperature compensation in electrical circuits (amplifiers,oscillators) and many others. Figure 8.14 shows some typical application examples.

Fig. 8.14 Examples of thermistors applicationsa) sequential temperature measurement at several places (Te – thermistor, P – switch, O – resistor, S – indica-

tor),b) compensation of the coil‘s self-heating (Te – thermistor, O – resistor, C – coil),

c) temperature control (Te – thermistor, O – resistor, VO – variable resistor, Z – amplifier, R – relay)

In addition to NTC thermistors there are PTC thermistors too. The base material is barium or stron-tium titanate, made semiconductive, by adding particular impurities. The temperature effect differs es-sentially from that of a thermistor. PTC's have a positive temperature coefficient over a rather re-

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stricted temperature range. Altogether they cover a temperature range from 60 – 180 °C. Within therange of a positive temperature coefficient, the characteristic is approximated by

( ) ( )0 1 2 BT R T R T e T T T = < < (8.18)

The sensitivity in that range is B (K -1) and can be as high as 60% per K. Figure 8.15 shows a typicaltemperature characteristic of a PTC, together with the characteristics of other resistance thermometers,for comparison. PTC’s are rarely used for temperature measurements, because of lack of reproducibil-ity and the restricted temperature range of the individual device. They are mainly applied as a safetycomponent to prevent overheating at short-circuits or overload.

Fig. 8.15 Characteristics of various resistance thermometers

NTC and PTC can be combined in a network (compound temperature sensor) to create a particularresistance-temperature characteristic. For instance it is possible to create a temperature characteristicwith a flat plateau over a specified temperature range and a sharp resistance change when the tempera-ture comes beyond that range.

8.4.3 Thermoelectric sensors

The (free) charge carriers in different materials have different energy levels. When two different mate-

rials are electrically connected to each other (a couple ), the charge carriers at the junction will rear-range due to diffusion, resulting in a voltage difference across this junction. The value of this junction

potential depends on the type of materials used and the temperature. Of course, neutrality is main-tained for the whole construction. This phenomenon of a spontaneously generated voltage is called theSeebeck effect , and the voltage is the Seebeck voltage .

When connecting a number of junctions in series (Figure 8.16), the voltage U s across the series isthe sum of the Seebeck voltages U i,j across each of the junctions:

( )∑= ji

ji ji s T U U ,

,, (8.19)

where T i,j is the absolute temperature of the junction i, j. Note that U i,j = −U j,i.

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Fig. 8.16 A series of thermo-voltages

The Seebeck voltage is a particular property of the materials that form the junction. The Seebeckvoltage of a single material is defined as the thermoelectric voltage when connected to a reference ma-terial, usually lead. So, the Seebeck voltage of a junction of two materials a and b can also be writtenas U ab = U ar + U rb = U ar - U br ; where r denotes the reference material.

Since the Seebeck voltage is temperature dependent, this property can be used as the basis for atemperature sensor: a thermocouple . The basic layout of a thermocouple is depicted in Fig. 8.17a. Thethermoelectric voltage across this series of junctions is U s = U ab(T 1) + U ba(T 2). Obviously, if the tem-

peratures T 1 and T 2 are equal, the voltages U ab, U ba are equal also, but have opposite sign, so U s = 0.

Fig. 8.17 Thermocouple layoutsa) basic layout, b) hot and cold junction

If, on the contrary, the two junctions have different temperatures, the thermal voltages do not can-cel, hence there is a net voltage across the end points of the couple U s = U ab(T 1) + U ba(T 2) = U ab(T 1) -U ab(T 2). Clearly, thermocouples measure only a temperature difference , not an absolute temperature.To measure the temperature at one junction, the temperature of the other junction must be known. That

junction is the reference junction or cold junction . It is kept at a constant, well known temperature (forinstance 0 °C). The other junction (the hot junction ) is connected to the object whose temperature hasto be measured.

Figure 8.17b shows this layout, where T 1 is the temperature of the hot junction. To measure theSeebeck voltage of this junction, the end points of the junction have to be connected to a voltagemeasuring device, by electric wires of material c (for instance copper). Now two new junctions arecreated, and also two new thermoelectric voltages. The total voltage equals

U s = U ca(T 3) + U ab(T 1) + U bc(T 4) =

= U ca(T 3) + U ab(T 1) + U ba(T 4) + U ac(T 4) =

= U ab(T 1) – U ab(T 4) + U ca(T 3) – U ca(T 4)

When both junctions a-c and b-c have the same temperature (that is: T 3 = T 4) the last two terms cancel,and the remaining voltage only depends on the materials a and b of the thermocouple. This voltage is ameasure for the temperature difference T 1 – T 4, with T 4 the temperature at the connection point withmaterial c.

When connecting thermocouples, three basic rules apply:

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1) rule of the inserted conductor – a third metal that is inserted between two different metals does notinfluence the resulting thermoelectric voltage, when their junctions have equal temperature,

2) rule of the circuit homogeneity – if a third conductor is inserted between two conductors having thesame material as the third conductor, this conductor does not affect the resulting thermoelectricvoltage even if the two junctions have different temperatures. This applies under the specific condi-tion that the inserted conductor is made of the same material and has the same internal structure asthe two adjacent conductors,

3) superposition rule – when the temperature of the reference junction changes, the whole transfercharacteristic (thermoelectric voltage versus temperature relationship) shifts over the same value.

Unequal temperatures at the nodes of the connecting wires introduce a measurement error. This mayoccur when the distance between the measurement junction and the measurement instrument is large,and as a consequence long connecting wires are needed. The best way to avoid such errors is the ex-tension of the thermocouple wires up to the reading instrument. In general, the wires are too thin andfragile to ascertain proper operation in an industrial application. Making them thicker will increase thecosts. An alternative is the insertion of what is called a “compensation wire”. These are wires with dif-ferent composition, diameter (and lower cost and quality), but having the same thermoelectrical char-acteristics as the couple itself. They only serve as an electrical connection between the open ends ofthe couple and the reference junctions (Figure 8.18).

Fig. 8.18 Compensating wires for remote temperature measurement

Obviously, the connecting cable does not introduce errors if:

- the junctions a-a’ and b-b’ have the same temperature, and- the junctions a-b and a’-b’ have the same Seebeck voltage.

This means that compensation wires should match the type of thermocouple used in the application.Accurate temperature measurements with thermocouples require careful design of the measurement

system, in particular with respect to the temperatures of the various junctions in the chain of wires, andwith respect to the “cold junction”. The latter should be kept at a fixed and known temperature, a pro-cedure called cold junction compensation . Various methods for this compensation are shown in Figure8.19. This figure reviews all the steps to be taken for correct temperature measurement with thermo-couples, and the development from systems without compensation to the most sophisticated software-

based compensation.The starting point is a T-type thermocouple (Cu-Co). Figures 8.19a and 8.19b show the equivalent

circuits. Suppose the connecting wires of the voltmeter are made of Cu. We like to measure only thevoltage U 1 generated in junction J 1 by the temperature t J1. However, the connection of the voltmetercreates two new junctions J 2 and J 3. Since J 3 is a Cu-Cu junction it does not generate any other ther-moelectric voltage. A spurious thermoelectric voltage U 2 is generated in the Cu-Co junction J 2. So thevoltmeter measures a resulting thermoelectric voltage U = U 1 – U 2 that is proportional to the tempera-ture difference between J 1 and J 2. This shows that we cannot determine the temperature at J 1 withoutknowing the temperature at J 2 (see Fig. 8.19c).

When we put the J 2 junction in a bath with melting ice, its temperature is just 0 °C. So J 2 acts as thereference (or cold) junction. The voltmeter indicates a voltage that corresponds to the temperature (in°C) at J 1 junction only (see Figure 8.19d). Note that the thermoelectric voltage U 2 generated at J 2 junc-tion at temperature 0 °C is not equal to zero. It is a function of the absolute temperature.

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Fig. 8.19 Thermocouple - from a single junction to software compensation(picture adapted from Newport Omega Co., www.omega.com)

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A thermocouple connection according to Figure 8.19d is a special case because the connectingwires are made of the same material as one of the thermocouple wires. In general, the practical situa-tion is more complicated. Figure 8.19e shows a J-type thermocouple (Fe – Co) connected to the volt-meter by iron conductors. This increases the number of metallic junctions (J 3 and J 4) and thereby alsothe number of additional spurious thermoelectric voltages. Further inaccuracy is introduced when bothconnecting junctions on the front panel have different temperatures. Therefore, the connecting wires ofthe voltmeter are extended and they are terminated in a so-called isothermal block (see Figure 8.19f).

The isothermal block is an electrical insulator but is chosen to be an excellent heat conductor, so both junctions J 3 and J 4 have the same temperature. The absolute temperature of the isothermal blockis not important as both junction temperatures are equal and have opposite signs. So, the voltage read-out is proportional to the temperature difference between J 1 and the reference point. If we replace theice bath by another isothermal block, we get the connection according to Figure 8.19g. The isothermal

block will be kept at the reference temperature T ref . As both junctions J 3 and J 4 have still the same temperature, the read-out voltage does not change.

The next step is the interconnection of junctions J 4 and J ref . First, both isothermal blocks are con-nected, which will not change the output voltage. When extending the iron wire between the junctions

J4 and J ref , the rule of the inserted conductor applies (see Fig. 8.19h). This means that both junctions J 3 and J 4 are located in the same isothermal block and have the same reference temperature T ref (see Fig-ure 8.19i). A further logical step is to remove the necessity to insert the isothermal block into an ice

bath, which simplifies installation and maintenance of the system. However, the need still arises tomeasure the isothermal block temperature (see Figure 8.19j), for instance with a thermistor, thermallyconnected to the block. The thermistor resistance is converted to the temperature T ref and afterwards tothe respective reference voltage U ref . From the obtained voltage U 1 the actual temperature T 1 can bereconstructed. This procedure is called software compensation .

For situations where the temperature has to be measured simultaneously at various locations, thecompensation hardware for the thermocouples can be shared; this approach is shown in Figure 8.20.

Fig. 8.20 Connection of more thermocouples to a single compensating box

(picture adapted from Newport Omega Co., www.omega.com)

Since a thermocouple consists basically of a junction of two metals (wires), the dimensions of sucha temperature sensor can be very small. The junction itself can be soldered or welded (see Figure8.21).

A general expression for the temperature dependence of the Seebeck voltage is

( ) ( ) ...21 2

212211ab +−+−= T T T T U β β (8.20)

So, a thermocouple is a non-linear temperature sensor. Its sensitivity is found by taking the derivativeof the Seebeck voltage to the variable T 1:

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( ) ab2121ab ...dd

α β β =+−+= T T t

U (8.21)

Fig. 8.21 Design of a thermocouple measuring junctiona) illustrative dimension, b) brazed junction, c) welded junction

Fig. 8.22 Overview of the temperature ranges for some common thermocouples

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This parameter is called the Seebeck coefficient , and is a measure for the sensitivity of the thermocouple. Its value depends on the materials a and b, as well as on the temperature. The Seebeck coefficientcan always be written as the difference between two other coefficients:

br ar ab α α α

−= (8.22)

with α ar and α br the Seebeck coefficients of the couples of materials a and r (a reference material) and b and r, respectively. Usually, as mentioned before, the reference material is lead.

Thermocouple materials should have a Seebeck coefficient that is high (to achieve high sensitivity),with a low temperature coefficient (to obtain high linearity) and be stable in time (for a good long-term stability of the sensor). Thermocouples cover a temperature range from almost 0 K to over 2900 K(however not in a single device). The various types are denoted by the characters K, E, J, N, B, R, S and T;a notation that refers to the temperature range of the particular device. Figure 8.22 shows a graphicaloverview of the individual temperature ranges for some common thermocouples.

More detailed properties of these thermocouples are given in table 8.3.The lower end of the temperature range is 3K (with a copper/gold-cobalt couple). The higher end is

2700 °C (with a tungsten-5% rhenium/tungsten-26% rhenium couple). The sensitivity of most couplesfrom Table 8.3 increases with temperature (see Figure 8.23). For instance, the sensitivity of the E-typecouple at 500 °C is about 80 µV/K. The sensitivity drops sharply at temperatures below 0 °C, for mosttypes.

Fig. 8.23 Static characteristics of the main thermocouples

Thermocouple characteristics are standardized over their working range. Usually, the voltage-temperature characteristic is approximated by a polynomial because the devices are rather non-linearover their full range:

U = a0⋅t 0 + a 1⋅t

1 + a 2⋅t 2 +, ... + a i⋅t

i +, ... + a n⋅t n (8.23)

where

U is the generated thermoelectric voltage (mV),t is the temperature of the measuring junction ( ° C),a 0, ... a n are polynomial coefficients (Table 8.4).

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Table 8.3 Thermocouples overview (table adapted from Newport Omega, Co., www.omega.com)

Alloy combination Temperaturerange ( C) 2

U te (mV) 4 Permissible error 5 Environment, comments of thermocoupleuse

Code Lead + Lead - Ther-mocou-

ple

Exten-sion

grade 3

Standard Special

J Fe(iron)

Cu-Ni(constantan)

0 to750

0 to200

0 to42.283

2.2 °C or0.75%

1.1 °C or0.4%

Reducing, vacuum, inert. Limited use in oxi-dizing at high temperatures. Not recom-mended for low temperatures.

K Ni-Cr(nickel-

chromium)

Ni-Al(nickel-

aluminium)

-200 to1250

0 to200

-5.973 to50.633

a)2.2 °C or0.75%

b)2.2 °C or 2.0%

1.1 °C or0.4%

Clean oxidizing and inert. Limited use invacuum or reducing.

TCu

(copper)Cu-Ni

(constantan)-200 to

350-60 to100

-5.602 to17.816

a)1.0 °C or0.75%

b)1.0 °C or1.5%

0.5 °C or0.4%

Mild oxidizing, reducing, vacuum or inert.Good for moisture environment. Low tem-

perature and cryogenics.

E Ni-Cr(nickel-

chromium)

Cu-Ni(constantan)

-200 to900

0 to200

-8.824 to68.783

a)1.7 °C or0.5%

b)

1.7 °C or1.0%

1.0°C or0.4%

Oxidizing or inert. Limited use in vacuum orreducing. Highest voltage change per degree.

N1

Ni-Cr-Si(nicrosil)

Ni-Si-Mg(nisil)

-270 to1300

0 to200

-4.345 to47.502

a)2.2°C or0.75%

b)2.2°C or2.0%

1.1 °C or0.4%

Alternative to the K type.

RPt-13%Rh(platinum-rhodium)

Pt(platinum)

0 to1450

0 to150

0 to16.741

1.5 °C or0.25%

0.6 °C or0.1%

Oxidizing or inert. Not for inserting intometal tubes. Beware of contamination. Hightemperature.

SPt-10%Rh(platinum-rhodium)

Pt(platinum)

0 to1450

0 to150

0 to14.973

1.5°C or0.25%

0.6 °C or0.1%

Oxidizing or inert. Not for inserting intometal tubes. Beware of contamination. Hightemperature.

BPt-30% Ř h(platinum-rhodium)

Pt-6%Rh(platinum-rhodium)

0 to1700

0 to100

0 to12.426

0.5% over800 °C

not estab-lished

Oxidizing or inert. Not for inserting intometal tubes. Beware of contamination. Hightemperature. Common use in glass industry.

G 1 W

(tungsten)W-26%Re(tungsten-rhenium)

0 to2320

0 to260

0 to38.564

4.5 °C to425 °C1.0% to2320 °C

not estab-lished

Vacuum, inert, hydrogen. Beware of embrit-tlement. Not for oxidizing atmosphere.

C 1 W-5%Re(tungsten-rhenium)

W-265Re(tungsten-rhenium)

0 to2320

0 to870

0 to37.066

4.5 °C to425 °C1.0% to2320 °C

not estab-lished


D1 W-3%Re(tungsten-rhenium)

W-25%Re(tungsten-rhenium)

0 to2320

0 to260

0 to39.506

4.5 °C to425 °C1.0% to2320 °C

not estab-lished


1 Not an official symbol or standard.2 Nominal temperature range. Thermocouples can be used also outside this range but the permissible

error is not guaranteed in this case.3 Extension grade.4 Range of the output voltage, generated within the nominal temperature range.5 Stated in °C or % of the measured value, whichever is greater.a) Over 0 °C.

b) Below 0 °C.

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Table 8.4 Coefficients a 0... a n of the polynomial that represents the relation between the thermoelectricvoltage and temperature (source NIST, http://srdata.nist.gov/its90/download/download.html) – part 1/4

Type B ETemperature range ( °C) 0.000 to 630.615 630.615 to1820.000 -270 to 0 0 to 1000

a0 0.000000000000 ⋅100 -0.389381686210 ⋅10 1 0.000000000000 ⋅10 0 0.000000000000 ⋅10 0 a1 -0.246508183460 ⋅10 -3 0.285717474700 ⋅10 -1 0.586655087080 ⋅10 -1 0.586655087100 ⋅10 -1 a2 0.590404211710 ⋅10 -5 -0.848851047850 ⋅10 -4 0.454109771240 ⋅10 -4 0.450322755820 ⋅10 -4 a3 -0.132579316360 ⋅10 -8 0.157852801640 ⋅10 -6 -0.779980486860 ⋅10 -6 0.289084072120 ⋅10 -7 a4 0.156682919010 ⋅10 -11 -0.168353448640 ⋅10 -9 -0.258001608430 ⋅10 -7 -0.330568966520 ⋅10 -9 a5 -0.169445292400 ⋅10 -14 0.111097940130 ⋅10 -12 -0.594525830570 ⋅10 -9 0.650244032700 ⋅10 -12 a6 0.629903470940 ⋅10 -18 -0.445154310330 ⋅10 -16 -0.932140586670 ⋅10 -11 -0.191974955040 ⋅10 -15 a7 0.989756408210 ⋅10 -20 -0.102876055340 ⋅10 -12 -0.125366004970 ⋅10 -17 a8 -0.937913302890 ⋅10 -24 -0.803701236210 ⋅10 -15 0.214892175690 ⋅10 -20 a9 -0.439794973910 ⋅10 -17 -0.143880417820 ⋅10 -23 a 10 -0.164147763550 ⋅10 -19 0.359608994810 ⋅10 -27 a 11 -0.396736195160 ⋅10 -22 a 12 -0.558273287210 ⋅10 -25 a 13 -0.346578420130 ⋅10 -28 a 14

Table 8.4 Coefficients a 0... a n of the polynomial that represents the relation between the thermoelectricvoltage and temperature (source NIST) – part 2/4

Type J KTemperature range ( °C) -210.000 to760.000 760.000 to 1200.000 -270.000 to 0.000 0.000 to 1372.000

a0 0.000000000000 ⋅100 0.296456256810 ⋅10+3 0.000000000000 ⋅10 0 -0.176004136860 ⋅10 -1 a1 0.503811878150 ⋅10 -1 -0.149761277860 ⋅10+1 0.394501280250 ⋅10 -1 0.389212049750 ⋅10 -1 a2 0.304758369300 ⋅10 -4 0.317871039240 ⋅10 -2 0.236223735980 ⋅10 -4 0.185587700320 ⋅10 -4 a3 -0.856810657200 ⋅10 -7 -0.318476867010 ⋅10 -5 -0.328589067840 ⋅10 -6 -0.994575928740 ⋅10 -7 a4 0.132281952950 ⋅10 -9 0.157208190040 ⋅10 -8 -0.499048287770 ⋅10 -8 0.318409457190 ⋅10 -9 a5 -0.170529583370 ⋅10 -12 -0.306913690560 ⋅10 -12 -0.675090591730 ⋅10 -10 -0.560728448890 ⋅10 -12 a6 0.209480906970 ⋅10 -15 -0.574103274280 ⋅10 -12 0.560750590590 ⋅10 -15 a7 -0.125383953360 ⋅10 -18 -0.310888728940 ⋅10 -14 -0.320207200030 ⋅10 -18 a8 0.156317256970 ⋅10 -22 -0.104516093650 ⋅10 -16 0.971511471520 ⋅10 -22 a9 -0.198892668780 ⋅10 -19 -0.121047212750 ⋅10 -25 a 10 -0.163226974860 ⋅10 -22 a 11 a 12 a 13 a 14


Type N RTemperature range ( °C) -270.000 to 0.000 0.000 to 1300.000 -50.000 to 1064.180 1064.180 to 1664.500 1664.500 to 1768.100

a0 0.000000000000 ⋅100 0.000000000000 ⋅100 0.000000000000 ⋅10 0 0.295157925316 ⋅10 1 0.152232118209 ⋅10 3 a1 0.261591059620 ⋅10 -1 0.259293946010 ⋅10 -1 0.528961729765 ⋅10 -2 -0.252061251332 ⋅10 -2 -0.268819888545 ⋅10 0 a2 0.109574842280 ⋅10 -4 0.157101418800 ⋅10 -4 0.139166589782 ⋅10 -4 0.159564501865 ⋅10 -4 0.171280280471 ⋅10 -3 a3 -0.938411115540 ⋅10 -7 0.438256272370 ⋅10 -7 -0.238855693017 ⋅10 -7 -0.764085947576 ⋅10 -8 -0.345895706453 ⋅10 -7

a4 -0.464120397590 ⋅10-10

-0.252611697940 ⋅10-9

0.356916001063 ⋅10-10

0.205305291024 ⋅10-11

-0.934633971046 ⋅10-14

a5 -0.263033577160 ⋅10 -11 0.643118193390 ⋅10 -12 -0.462347666298 ⋅10 -13 -0.293359668173 ⋅10 -15 a6 -0.226534380030 ⋅10 -13 -0.100634715190 ⋅10 -14 0.500777441034 ⋅10 -16 a7 -0.760893007910 ⋅10 -16 0.997453389920 ⋅10 -18 -0.373105886191 ⋅10 -19 a8 -0.934196678350 ⋅10 -19 -0.608632456070 ⋅10 -21 0.157716482367 ⋅10 -22 a9 0.208492293390 ⋅10 -24 -0.281038625251 ⋅10 -26 a 10 -0.306821961510 ⋅10 -28 a 11 a 12 a 13 a 14

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Type S TTemperature range ( °C) -50.000 to 1064.180 1064.180 to 1664.500 1664.500 to 1768.100 -270.000 to 0.000 0.000 °C to 400.000

a0 0.000000000000 ⋅100 0.132900444085 ⋅101 0.146628232636 ⋅103 0.000000000000 ⋅10 0 0.000000000000 ⋅10 0 a1 0.540313308631 ⋅10 -2 0.334509311344 ⋅10 -2 -0.258430516752 ⋅10 0 0.387481063640 ⋅10 -1 0.387481063640 ⋅10 -1 a2 0.125934289740 ⋅10 -4 0.654805192818 ⋅10 -5 0.163693574641 ⋅10 -3 0.441944343470 ⋅10 -4 0.332922278800 ⋅10 -4 a3 -0.232477968689 ⋅10 -7 -0.164856259209 ⋅10 -8 -0.330439046987 ⋅10 -7 0.118443231050 ⋅10 -6 0.206182434040 ⋅10 -6 a4 0.322028823036 ⋅10 -10 0.129989605174 ⋅10 -13 -0.943223690612 ⋅10 -14 0.200329735540 ⋅10 -7 -0.218822568460 ⋅10 -8 a5 -0.331465196389 ⋅10 -13 0.901380195590 ⋅10 -9 0.109968809280 ⋅10 -10 a6 0.255744251786 ⋅10 -16 0.226511565930 ⋅10 -10 -0.308157587720 ⋅10 -13

a7 -0.125068871393 ⋅10 -19 0.360711542050 ⋅10 -12 0.454791352900 ⋅10 -16 a8 0.271443176145 ⋅10 -23 0.384939398830 ⋅10 -14 -0.275129016730 ⋅10 -19

a9 0.282135219250 ⋅10 -16 a 10 0.142515947790 ⋅10 -18 a 11 0.487686622860 ⋅10 -21 a 12 0.107955392700 ⋅10 -23 a 13 0.139450270620 ⋅10 -26 a 14 0.797951539270 ⋅10 -30

To calculate the temperature from the measured output voltage, the inverse function applies, i.e. temperature as a function of the generated thermoelectric voltage:

t = b0⋅U 0 + b1⋅U

1 + b2⋅U 2 +,.. + bi⋅U

i +,.. + bn⋅U n (8.24)

where

b0, ..., bn are polynomial coefficients (see Table 8.5).

Table 8.5 Coefficients b0... bn of the polynomial that represents the relation between temperature andthe thermoelectric voltage (source NIST, http://srdata.nist.gov/its90/download/download.html) – part1/4

Type B ETemperat. range ( °C) 250 to 700 700 to 1820 -200 to 0 0 to 1000

b0 9.8423321 ⋅101 2.1315071 ⋅102 0.0000000 ⋅10 0 0.0000000 ⋅100 b1 6.9971500 ⋅102 2.8510504 ⋅102 1.6977288 ⋅10 1 1.7057035 ⋅101 b2 -8.4765304 ⋅10 2 -5.2742887 ⋅10 1 -4.3514970 ⋅10 -1 -2.3301759 ⋅10 -1 b3 1.0052644 ⋅103 9.9160804 ⋅100 -1.5859697 ⋅10 -1 6.5435585 ⋅10 -3 b4 -8.3345952 ⋅10 2 -1.2965303 ⋅10 0 -9.2502871 ⋅10 -2 -7.3562749 ⋅10 -5 b5 4.5508542 ⋅102 1.1195870 ⋅10 -1 -2.6084314 ⋅10 -2 -1.7896001 ⋅10 -6 b6 -1.5523037 ⋅10 2 -6.0625199 ⋅10 -3 -4.1360199 ⋅10 -3 8.4036165 ⋅10 -8 b7 2.9886750 ⋅101 1.8661696 ⋅10 -4 -3.4034030 ⋅10 -4 -1.3735879 ⋅10 -9 b8 -2.4742860 ⋅10 0 -2.4878585 ⋅10 -6 -1.1564890 ⋅10 -5 1.0629823 ⋅10 -11 b9 0.0000000 ⋅10 0 -3.2447087 ⋅10 -14 b10

Error ( °C) -0,02 do 0,03 -0,01 do 0,02 -0,01 do 0,03 -0,02 do 0,02

Table 8.5 Coefficients b0... bn of the polynomial that represents the relation between temperature andthe thermoelectric voltage (source NIST) – part 2/4

Type J KTemperat. range ( °C) -210 to 0 0 to 760 760 to 1200 -200 to 0 0 to 500 500 to 1372

b0 0.0000000 ⋅100 0.000000 ⋅10 0 -3.11358187 ⋅10 3 0.0000000 ⋅10 0 0.000000 ⋅10 0 -1.318058 ⋅102 b1 1.9528268 ⋅101 1.978425 ⋅10 1 3.00543684 ⋅10 2 2.5173462 ⋅10 1 2.508355 ⋅10 1 4.830222 ⋅10 1 b2 -1.2286185 ⋅10 0 -2.001204 ⋅10 -1 -9.94773230 ⋅10 0 -1.1662878 ⋅10 0 7.860106 ⋅10 -2 -1.646031 ⋅100 b3 -1.0752178 ⋅10 0 1.036969 ⋅10 -2 1.70276630 ⋅10 -1 -1.0833638 ⋅10 0 -2.503131 ⋅10 -1 5.464731 ⋅10 -2 b4 -5.9086933 ⋅10 -1 -2.549687 ⋅10 -4 -1.43033468 ⋅10 -3 -8.9773540 ⋅10 -01 8.315270 ⋅10 -2 -9.650715 ⋅10 -4 b5 -1.7256713 ⋅10 -1 3.585153 ⋅10 -6 4.73886084 ⋅10 -6 -3.7342377 ⋅10 -1 -1.228034 ⋅10 -2 8.802193 ⋅10 -6 b6 -2.8131513 ⋅10 -2 -5.344285 ⋅10 -8 0.00000000 ⋅10 0 -8.6632643 ⋅10 -2 9.804036 ⋅10 -4 -3.110810 ⋅10 -8 b7 -2.3963370 ⋅10 -3 5.099890 ⋅10 -10 0.00000000 ⋅10 0 -1.0450598 ⋅10 -2 -4.413030 ⋅10 -5 0.000000 ⋅10 0 b8 -8.3823321 ⋅10 -5 0.000000 ⋅10 0 0.00000000 ⋅10 0 -5.1920577 ⋅10 -4 1.057734 ⋅10 -6 0.000000 ⋅10 0 b9 0.0000000 ⋅10 0 -1.052755 ⋅10 -8 0.000000 ⋅10 0

b10 Error ( °C) -0,05 do 0,03 -0,04 do 0,04 -0,04 do 0,03 -0.02 do 0.04 -0.05 do 0.04 -0.05 do 0.06

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Type N RTemperat. range ( °C) -200 to 0 0 to 600 600 to 1300 -50 to 250. 250 to 1200 1064 to 1664.5 1664.5 to 1768.1

b0 0.0000000 ⋅10 0 0.00000 ⋅100 1.972485 ⋅10 1 0.0000000 ⋅10 0 1.334584505 ⋅101 -8.199599416 ⋅10 1 3.406177836 ⋅104 b1 3.8436847 ⋅10 1 3.86896 ⋅101 3.300943 ⋅10 1 1.8891380 ⋅10 2 1.472644573 ⋅102 1.553962042 ⋅10 2 -7.023729171 ⋅103 b2 1.1010485 ⋅10 0 -1.08267 ⋅10 0 -3.915159 ⋅10 -1 -9.3835290 ⋅10 1 -1.844024844 ⋅101 -8.342197663 ⋅10 0 5.582903813 ⋅102 b3 5.2229312 ⋅10 0 4.70205 ⋅10 -2 9.855391 ⋅10 -3 1.3068619 ⋅10 2 4.031129726 ⋅100 4.279433549 ⋅10 -1 -1.952394635 ⋅101 b4 7.2060525 ⋅10 0 -2.12169 ⋅10 -6 -1.274371 ⋅10 -4 -2.2703580 ⋅10 2 -6.249428360 ⋅10 -1 -1.191577910 ⋅10 -2 2.560740231 ⋅10 -1 b5 5.8488586 ⋅10 0 -1.17272 ⋅10 -4 7.767022 ⋅10 -7 3.5145659 ⋅10 2 6.468412046 ⋅10 -2 1.492290091 ⋅10 -4 0.000000000 ⋅100 b6 2.7754916 ⋅10 0 5.39280 ⋅10 -6 0.000000 ⋅10 0 -3.8953900 ⋅10 2 -4.458750426 ⋅10 -3 0.000000000 ⋅10 0 0.000000000 ⋅100 b7 7.7075166 ⋅10 -1 -7.98156 ⋅10 -8 0.000000 ⋅10 0 2.8239471 ⋅10 2 1.994710149 ⋅10 -4 0.000000000 ⋅10 0 0.000000000 ⋅100 b8 1.1582665 ⋅10 -1 0.00000 ⋅100 0.000000 ⋅10 0 -1.2607281 ⋅10 2 -5.313401790 ⋅10 -6 0.000000000 ⋅10 0 0.000000000 ⋅100 b9 7.3138868 ⋅10 -3 0.00000 ⋅100 0.000000 ⋅10 0 3.1353611 ⋅10 1 6.481976217 ⋅10 -8 0.000000000 ⋅10 0 0.000000000 ⋅100 b10 -3.3187769 ⋅10 0 0.000000000 ⋅100 0.000000000 ⋅10 0 0.000000000 ⋅100

Error ( °C) -0.02 to 0.03 -0.02 to 0.03 -0.04 to 0.02 -0.02 to 0.02 -0.005 to 0.005 -0.0005 to 0.001 -0.001 to 0.002


Type S TTemperat. range ( °C) -50 to 250 250 to 1200 1064 to 1664.5 1664.5 to 1768.1 -200 to 0 0 to 400

b0 0.00000000 ⋅10 0 1.291507177 ⋅10 1 -8.087801117 ⋅101 5.333875126 ⋅104 0.0000000 ⋅10 0 0.000000 ⋅10 0 b1 1.84949460 ⋅10 2 1.466298863 ⋅10 2 1.621573104 ⋅10 2 -1.235892298 ⋅10 4 2.5949192 ⋅10 1 2.592800 ⋅10 1 b2 -8.00504062 ⋅10 1 -1.534713402 ⋅10 1 -8.536869453 ⋅100 1.092657613 ⋅103 -2.1316967 ⋅10 -1 -7.602961 ⋅10 -1 b3 1.02237430 ⋅10 2 3.145945973 ⋅10 0 4.719686976 ⋅10 -1 -4.265693686 ⋅10 1 7.9018692 ⋅10 -1 4.637791 ⋅10 -2 b4 -1.52248592 ⋅10 2 -4.163257839 ⋅10 -1 -1.441693666 ⋅10 -2 6.247205420 ⋅10 -1 4.2527777 ⋅10 -1 -2.165394 ⋅10 -3 b5 1.88821343 ⋅10 2 3.187963771 ⋅10 -2 2.081618890 ⋅10 -4 0.000000000 ⋅100 1.3304473 ⋅10 -1 6.048144 ⋅10 -5 b6 -1.59085941 ⋅10 2 -1.291637500 ⋅10 -3 0.000000000 ⋅10 0 0.000000000 ⋅100 2.0241446 ⋅10 -2 -7.293422 ⋅10 -7 b7 8.23027880 ⋅10 1 2.183475087 ⋅10 -5 0.000000000 ⋅10 0 0.000000000 ⋅100 1.2668171 ⋅10 -3 0.000000 ⋅10 0 b8 -2.34181944 ⋅10 1 -1.447379511 ⋅10 -7 0.000000000 ⋅10 0 0.000000000 ⋅100 b9 2.79786260 ⋅10 0 8.211272125 ⋅10 -9 0.000000000 ⋅10 0 0.000000000 ⋅100 b10

Error ( °C) -0.02 to 0.02 -0.01 to 0.01 -0.0002 to 0.0002 -0.002 to 0.002 -0.02 to 0.04 -0.03 to 0.03

Unfortunately, the standards used are not the same for all countries. The wires of thermocouplesand the corresponding compensation wires (extension grades) have standardized colours too (see forinstance Table 8.6), but also these differ completely from country to country. For some popular typesthere are now European colour codes (see e.g. www.omega.com).

The Seebeck voltage does not depend on the geometry of the junction. A good electrical contactwill do. Small sized, bear junctions (exposed junctions) react quickly to temperature changes but areonly applicable in a non-corrosive environment. Also ‘sheet-shaped’ types are available, and are suit-able to be glued on a flat surface. An insulating layer around the junction protects the device againstmechanical and chemical damage but lowers the response time, as is clearly shown in Figure 8.24.

The market offers a wide variety of thermocouples, with various shapes, dimensions and protectingcovers. Thermocouples manufactured as separate sensing elements are displayed in Fig. 8.25, thermo-

couples delivered as measuring probes are shown in Fig. 8.26. A measuring probe intended for mount-ing into a wall opening is shown in Fig. 8.27.

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Table 8.6 Color designation of thermocouples and compensation wiring (source Newport Omega,www.omega.com)

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Fig. 8.24 Different types of the measuring junction designa) exposed junction, b) grounded junction, c) insulated junction, d) comparison of the response time

Fig. 8.25 Thermocouples manufactured as separate sensing elementsa) basic type with non-protected connecting wires, b) two separate tubes protecting the connecting wires, c) onetube with two separate holes protecting the connecting wires, d) protecting tubes shielded by metal net, e) ther-

mocouple with opened measuring junction, f) thermocouple with opened measuring junction and metal cover, g) sensing junction protected by metal cover with openings, h) design for surface temperature measurement

Metal thermocouples have a relatively low sensitivity. To obtain a sensor with a higher sensitivity,a number of couples are electrically connected in series; all cold junctions are thermally connected toeach other, as well as all hot junctions (Figure 8.28). The sensitivity of such a thermopile is n timesthat of a single junction where n is the number of couples.

Not only junctions of different metals generate thermovoltages, it also happens at a junction of dif-ferent semiconductors and a junction of a metal and a semiconductor. In particular, p-type silicon andn-type silicon are used for temperature measurements, because of the compatibility of these materialswith integrated circuit technology. The Seebeck coefficient of silicon strongly depends on the dopinglevel of the p or n materials, on the temperature and on the structure (monocrystalline silicon, polysili-con, amorphous silicon). Most integrated silicon thermocouples consist of junctions from single-crystal p- or n-doped silicon and aluminium, because these materials are present in standard IC tech-nology. Typical values of the absolute Seebeck coefficient of such junctions at 300 K are around 1mV/K, so much higher than metal-metal junctions.

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Fig. 8.26 Measuring probes provided by thermocouplesa) design for easy measurement of surface temperature, b) handy probe for the measurement of surface tem-

perature, c) penetrating measuring probe, d) probe for flowing non-oxidation liquid

As with the metal thermocouples, the sensitivity of semiconductor thermoelectric sensors can beincreased by a thermopile configuration. The planar technology allows the construction of several tensof junctions on a single silicon chip. Such silicon thermopiles are used for instance in infrared detec-tors, pyrometers and other thermal sensing instruments. The integration with read-out electronics is an

advantage; the restricted temperature range (450 K) limits the applicability.

8.4.4 Temperature sensors based on bipolar transistors

The relation between the current through a pn-junction and the voltage across it is given by:

s I I

qkT

U ln= (8.25)

where I s is the saturation current. This equation holds for a pn-diode, and also for a bipolar transistor,for which I = I C (the collector current) and U = U BE (the base-emitter voltage) applies. The saturationcurrent varies with temperature according to:

kT

U m

s

g

eT I 0−

∝ (8.26)

with U g 0 the extrapolated bandgap voltage at 0 K. To use these properties for temperature measure-ment, the current through the device is kept at a fixed value. Applying this to a bipolar transistor withzero base-collector voltage yields:

)()(0BEBE

T RT U T U ++= λ (8.27)

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Fig. 8.27 Measuring probe intended for buildinginto a measuring opening in a wall

(1 – sensitive element (thermocouple, resistancethermometer, ...), 2 – protecting tubes, 3 – metal

protecting bushing, 4 – interpiece, 5 – lengtheningbushes, 6 – connecting pieces, 7 – probe head con-

taining terminals, 8 – metal bushing, 9 – screwingcover)

Fig. 8.28 Layout of a thermopile

where

U BE0 is the extrapolated base-emitter voltageat 0 K,

λ is the thermal sensitivity, R(T ) is a small temperature dependent non-

linearity term (of the second order).

In integrated temperature sensors, a combina-tion of two transistors is used, having a fixedemitter area ratio a and carrying different cur-rents with a fixed ratio r , to cancel the non-linearities and other common effects. Then, thedifference between the two base-emitter volt-ages satisfies the relation

r aq

kT T U ⋅==∆ ln)(

BE (8.28)

This voltage is proportional to the absolutetemperature, and a temperature sensor based onthis property is called a PTAT sensor . The mar-ket offers several types of integrated circuitscontaining a PTAT circuit. Table 8.7 showssome typical specifications of such a device.Obviously, the temperature range is limited bythe technology used. Advantages are the easyinterfacing and the low price.

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Tab. 8.7 Typical specification of such devices

Property Value/Range Unit

Operating range -25, ... +105 °C

Non-linearity (full range) 0,2 °C

Output sensitivity 1 µA/K

8.4.5 Radiation thermometers

8.4.5.1 Physical background

A radiation thermometer responds to the thermal radiation of the body whose temperature has to bemeasured. The measurement is essentially contact-free. The total heat flux W of a radiating body is

proportional to the fourth power of its temperature T r :

4r r T W ⋅⋅= σ ε (8.29)

where

σ is the Stefan-Boltzmann constant (5.669 ⋅10 -8 W ⋅m-2K -4),ε r is the coefficient of emission or the emissivity of the radiating surface.

Since the detector itself also radiates heat, the net heat flux as detected by the instrument is

( )4dd4r r T T W ε ε σ −= (8.30)where

T d is the detector temperature,ε d is the emissivity of the detector material. The emissivity of a metal surface ranges from 0.03

(highly polished) to 0.8 (rough surface), and amounts 0.96 for graphitized surfaces. A properthermal detector should have an emissivity close to 1.

The heat flux radiated by a body covers a wave-length range that depends on the temperature. Thewavelength where the radiation is a maximum, decreases with increasing temperature (Wien’s law ofradiation, see Figure 8.29). For instance, at room temperature this maximum occurs at 9.6 µm (IR). A

body at 1000K has its maximum emission at about 3.5 µm, but part of the emission is within the visible range of the spectrum (Figure 8.30). Since radiation thermometers operate contact free, they allowthe measurment of very high temperatures, up to 3500 °C. Another important advantage is the possi-

bility to measure temperatures of materials having a low thermal conductivity, for instance stone.A correct temperature measurement using the radiation method requires knowledge of the emissiv-

ity. The emissivity is the ratio of the emitted radiation of the actual radiating surface to that of a black body. Its value depends on the material, the surface condition and the wavelength. Usually, a pyrome-ter is calibrated using a surface with emissivity equal to 1. If the emissivity differs from 1, the meas-urement result should be corrected. Since the heat is proportional to T 4 (see the equation given above),the relative measurement error due to an unknown emissivity is ε 1/4. For example, if the emissivity of

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the radiating surface is 0.6, the correction factor is 0.13. At known emissivity, the inaccuracy of a ra-diation thermometer is about 0.5 °C (at ambient).

Fig. 8.29 Spectral radiation of a black body as a function of wavelength and temperature(picture adapted from the site http://www.omega.com/techref/iredtempmeasur.html)

Fig. 8.30 The electromagnetic spectrum

Figure 8.31 shows the correction in terms of temperature, for various values of emissivity.

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Fig. 8.31 Temperatures t k with which the measured temperature t s should be corrected, for various values of theemissivity ε

(picture adapted from the site http://www.omega.com/techref/iredtempmeasur.html)

8.4.5.2 Pyrometers

Two types of pyrometers are distinguished - the radiation pyrometer and the optical pyrometer.

In a radiation pyrometer the radiation is focussed on a temperature sensitive sensor that will heatup by the radiation (Figure 8.32). The temperature sensor in a radiation thermometer can be any of thedevices discussed before. If the sensor is a resistive temperature sensor, such as a platinum sensor or athermistor, the instrument is called a bolometer . When the heat is measured using a thermoelectricsensor (a thermocouple, a thermopile or a pyroelectric sensor), it is called a pyrometer .

Fig. 8.32 Radiation pyrometer1 – lens, 2 – protecting screen, 3 – gold-plated (silver-plated) mirror, 4 – sensing element, 5 – gearing, 6 – ad-

justing button, 7 – input screen

An optical pyrometer contains a filament, which can be electronically heated to a known tempera-ture. In the optical pyrometer presented in Fig. 8.33, the filament is viewed with the hot body in the

background. The temperature of the filament is adjusted until it appears to vanish (when it has the

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same color as the background). So, at this point the filament temperature is the same as the tempera-ture to be measured.

Fig. 8.33 Spectral pyrometer with a changeable intensity of the lampa) design, b) bulb filament lighter than measured object, c) measured object lighter than bulb filament

1 – input lens, 2 – ocular lens, 3 – filter, 4 – pyrometric bulb

A similar approach is shown in Figure 8.34, where the bulb has a fixed temperature (intensity). Inthis case the intensity of the incoming radiation is made equal to that of the bulb using a rotatablewedge with grading thickness. The wedge’s position at equal intensity is a measure for the temperatureof the radiating body.

Fig. 8.34 Spectral pyrometer with fixed bulb intensitya) design scheme, b) gray wedge with graded thickness

1 – input lens, 2 – ocular lens, 3 – filter, 4 – pyrometric bulb, 5 – grey wedge, 6 – index

An alternative construction is shown in Figure 8.35, with two manually adjustable wedges: theColour comparison pyrometer. Again, it compares the radiation from the measurement object to thatof a pyrometric bulb. This comparison is now made at two wavelengths. The pyrometer works withinthe visible part of the electromagnetic spectrum, so the wavelengths are λ 1 = 0.65 µm (correspondingto red) and λ 2 = 0.55 µm (corresponding to green). Both wavelenghts are complementary: togetherthey yield white light.

When observing the principle design presented in Fig. 8.35, radiation from the measurement objectenters the pyrometer through lens 1 and passes the two-color rotable wedge 2. Here two colours areseparated into red and green rays. The observer rotates the two-colour wedge (i.e. changing the ratio

between red and green rays) until the incoming radiation seems to be white. The radiation from themeasurement object passes the neutral wedge 3 and enters the semi-transparent optical prism 4 with asilver-coated centre. The pyrometric bulb 5 is heated by a constant current. Its radiation passes filter 6

and the eye observes it as white light. The radiation produced by the pyrometric bulb is then reflected

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Module M08 Measurement of temperatu

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