industrial temperature measurement - cert-trak · industrial temperature measurement 3. temperature...

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Industrial temperature measurement 1. INTRODUCTION............................................................................................................................ 3 2. TEMPERATURE SCALES ............................................................................................................ 3 2.1 TEMPERATURE SCALES .............................................................................................................................................3 3. TEMPERATURE MEASUREMENT.............................................................................................. 4 3.1 THE DEFINITION OF TEMPERATURE ..........................................................................................................................4 4. PRINCIPLES OF TEMPERATURE MEASUREMENT ................................................................ 4 5. THERMOCOUPLES ...................................................................................................................... 4 5.1 TYPES OF THERMOCOUPLES .....................................................................................................................................7 5.2 MEASURING RANGE OF A THERMOCOUPLE ..............................................................................................................7 5.3 TOLERANCES ............................................................................................................................................................9 5.4 TEMPERATURE-VOLTAGE-RELATION ......................................................................................................................10 5.5 COMPENSATION CABLE...........................................................................................................................................10 5.5.1 Compensation cable ..........................................................................................................................................10 5.5.2 Extension cable .................................................................................................................................................10 5.5.3 Thermocouple wire............................................................................................................................................10 5.5.4 Colour codes......................................................................................................................................................10 5.6 APPLICATIONS AND LIMITATIONS ........................................................................................................................... 11 5.6.1 Type J. Fe-CuNi thermocouple ......................................................................................................................... 11 5.6.2 Type T. Cu-CuNi thermocouple ........................................................................................................................ 11 5.6.3 Type K. NiCr-Ni thermocouple ......................................................................................................................... 11 5.6.4 Type N. Nicrosil-NiSil thermocouple................................................................................................................12 5.6.5 Type S. Platinum 10% Rhodium-Platinum thermocouple ...............................................................................12 5.6.6 Type R. Platinum 13% Rhodium-Platinum thermocouple ..............................................................................12 5.6.7 Type B. Platinum 30% Rhodium-Platinum 6% Rhodium thermocouple ........................................................12 6. RESISTANCE THERMOMETER ................................................................................................ 13 6.1 PLATINUM RESISTANCE THERMOMETER.................................................................................................................13 6.1.1 Temperature – resistance relation ....................................................................................................................13 6.2 TOLERANCES ..........................................................................................................................................................14 6.2.1 Norm-related tolerances ...................................................................................................................................14 6.2.2 Commercial tolerances .....................................................................................................................................14 6.2.3 Company specific tolerances ............................................................................................................................14 6.3 MEASURING RESISTANCE TYPES AND MEASURING RANGE ....................................................................................15 6.3.1 Wire-wounded measuring resistors in ceramics ..............................................................................................15 6.3.2 Wire-wounded measuring resistors of glass.....................................................................................................15 6.3.3 Thin-film resistors .............................................................................................................................................15 6.4 COUPLING METHODS ..............................................................................................................................................15 6.4.1 2–wire coupling .................................................................................................................................................16 6.4.2 3-wire coupling..................................................................................................................................................16 6.4.3 4-wire coupling..................................................................................................................................................17 6.5 SELF-HEATING ........................................................................................................................................................17 6.6 APPLICATION ..........................................................................................................................................................18 7. SELECTION OF TEMPERATURE SENSOR............................................................................. 18 7.1 THE MOST IMPORTANT CONDITIONS FOR THE CHOICE OF A SENSOR ......................................................................18 7.2 TEMPERATURE RANGE ............................................................................................................................................19 7.3 CORROSION CONDITIONS........................................................................................................................................19 7.4 MECHANICAL LOAD PRESSURE, STATIC AND DYNAMIC INFLUENCE.....................................................................20 7.5 ACCURACY .............................................................................................................................................................21 7.6 RESPONSE TIME......................................................................................................................................................21 7.6.1 Response time ....................................................................................................................................................22 7.6.2 Other expressions of response time ..................................................................................................................22 Temperature Page 1 of 30

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Page 1: Industrial temperature measurement - CERT-TRAK · Industrial temperature measurement 3. TEMPERATURE MEASUREMENT 3.1 The definition of temperature The temperature of a medium is an

Industrial temperature measurement

1. INTRODUCTION............................................................................................................................ 3

2. TEMPERATURE SCALES............................................................................................................ 3 2.1 TEMPERATURE SCALES.............................................................................................................................................3

3. TEMPERATURE MEASUREMENT.............................................................................................. 4 3.1 THE DEFINITION OF TEMPERATURE ..........................................................................................................................4

4. PRINCIPLES OF TEMPERATURE MEASUREMENT ................................................................ 4

5. THERMOCOUPLES...................................................................................................................... 4 5.1 TYPES OF THERMOCOUPLES .....................................................................................................................................7 5.2 MEASURING RANGE OF A THERMOCOUPLE ..............................................................................................................7 5.3 TOLERANCES ............................................................................................................................................................9 5.4 TEMPERATURE-VOLTAGE-RELATION ......................................................................................................................10 5.5 COMPENSATION CABLE...........................................................................................................................................10

5.5.1 Compensation cable..........................................................................................................................................10 5.5.2 Extension cable .................................................................................................................................................10 5.5.3 Thermocouple wire............................................................................................................................................10 5.5.4 Colour codes......................................................................................................................................................10

5.6 APPLICATIONS AND LIMITATIONS ...........................................................................................................................11 5.6.1 Type J. Fe-CuNi thermocouple.........................................................................................................................11 5.6.2 Type T. Cu-CuNi thermocouple ........................................................................................................................11 5.6.3 Type K. NiCr-Ni thermocouple.........................................................................................................................11 5.6.4 Type N. Nicrosil-NiSil thermocouple................................................................................................................12 5.6.5 Type S. Platinum 10% Rhodium-Platinum thermocouple...............................................................................12 5.6.6 Type R. Platinum 13% Rhodium-Platinum thermocouple ..............................................................................12 5.6.7 Type B. Platinum 30% Rhodium-Platinum 6% Rhodium thermocouple........................................................12

6. RESISTANCE THERMOMETER................................................................................................ 13 6.1 PLATINUM RESISTANCE THERMOMETER.................................................................................................................13

6.1.1 Temperature – resistance relation ....................................................................................................................13 6.2 TOLERANCES ..........................................................................................................................................................14

6.2.1 Norm-related tolerances ...................................................................................................................................14 6.2.2 Commercial tolerances .....................................................................................................................................14 6.2.3 Company specific tolerances ............................................................................................................................14

6.3 MEASURING RESISTANCE TYPES AND MEASURING RANGE....................................................................................15 6.3.1 Wire-wounded measuring resistors in ceramics ..............................................................................................15 6.3.2 Wire-wounded measuring resistors of glass.....................................................................................................15 6.3.3 Thin-film resistors .............................................................................................................................................15

6.4 COUPLING METHODS ..............................................................................................................................................15 6.4.1 2–wire coupling.................................................................................................................................................16 6.4.2 3-wire coupling..................................................................................................................................................16 6.4.3 4-wire coupling..................................................................................................................................................17

6.5 SELF-HEATING ........................................................................................................................................................17 6.6 APPLICATION ..........................................................................................................................................................18

7. SELECTION OF TEMPERATURE SENSOR............................................................................. 18 7.1 THE MOST IMPORTANT CONDITIONS FOR THE CHOICE OF A SENSOR......................................................................18 7.2 TEMPERATURE RANGE............................................................................................................................................19 7.3 CORROSION CONDITIONS........................................................................................................................................19 7.4 MECHANICAL LOAD PRESSURE, STATIC AND DYNAMIC INFLUENCE.....................................................................20 7.5 ACCURACY .............................................................................................................................................................21 7.6 RESPONSE TIME......................................................................................................................................................21

7.6.1 Response time....................................................................................................................................................22 7.6.2 Other expressions of response time ..................................................................................................................22

Temperature Page 1 of 30

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Industrial temperature measurement

8. MOUNTING AND INSTALLATION............................................................................................. 23 8.1 MOUNTING POSSIBILITIES ......................................................................................................................................23 8.2 THE LENGTH OF THE SENSOR..................................................................................................................................24 8.3 ISOLATION...............................................................................................................................................................25

9. SOURCES OF ERROR............................................................................................................... 25 9.1 HEAT BALANCE.......................................................................................................................................................25

9.1.1 Heat transfer for a thermo pocket/well ............................................................................................................26 9.1.2 Radiation to and from thermo pocket/well.......................................................................................................27

10. SIGNAL CONDITIONING AND TRANSMISSION ................................................................. 28 10.1 DIRECT CABLE CONNECTION..................................................................................................................................28

10.1.1 Direct cable connection to a thermometer ..................................................................................................28 10.1.2 Electrical noise .............................................................................................................................................28 10.1.3 Direct cabling to resistance thermometers..................................................................................................28

10.2 TRANSMITTERS.......................................................................................................................................................29 10.2.1 2-wire transmitters .......................................................................................................................................29 10.2.2 4-wire transmitters .......................................................................................................................................29 10.2.3 Isolation ........................................................................................................................................................30

11. TABLES.................................................................................................................................... 30

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Industrial temperature measurement

1. INTRODUCTION

Temperature is one of the most measured parameters within industry and science. A cor-rect measurement is of great importance to the quality of the product, as well as to secu-rity and to energy consumption. Therefore, it is very important to choose the right sensor for the actual application. However, a 100% ideal solution for a measuring job is difficult to find if not to say impossible. The choice will often be a compromise between the require-ments of the user and the limitations set by the sensor types that are suitable for the con-ditions at the measuring point. The following paragraphs explain the theory behind electrical temperature sensors, choice of sensors and sources of error.

2. TEMPERATURE SCALES

2.1 Temperature scales Four temperature scales are available: Réaumur Fahrenheit Celsius Kelvin Kelvin is one of the basic units in the SI-system and is related to the thermodynamic tem-perature. The Kelvin scale is used in connection with scientific tasks. The Celsius scale and the Fahrenheit scale, on the contrary, are more commonly used and are as such the units that are used within the industry. The Celsius scale is used in Europe whereas the Fahrenheit scale is used in the USA. Formulas for conversion between the most used units. Celsius: °C = 5/9 (°F - 32) Fahrenheit: °F = 9/5 °C + 32 °C = K-273.15 °F = 9/5 K – 459.67 The international temperature scales from 1927 and on were all based on a number of temperature fix points. The numerical values of these had been determined based on the thermodynamic Kelvin scale. Temperatures in between were determined by using special standard thermometers and very thoroughly described interpolation methods. Until 1990, the platinum thermometer was used as standard thermometer in the range up till 630°C, above this temperature and up till 1064°C, Pt10%Rh-Pt thermocouples were used, and from 1064°C and up the scale was defined in accordance with Planck’s law of radiation. In connection with a revision per January 1, 1990, the range for the platinum thermometer was extended up to the freezing point of silver, i.e. 961.78°C and the law of radiation was extended downwards to the same point. In the process, the use of the thermocouple as standard thermometer was obsolete. It should also be mentioned that today only triple points and freezing points / melting points are used to determine the temperature scale. The previously used boiling points are left out due to the big dependence on pressure. According to the ITS-90 scale water no longer boils at 100°C but at 99.974°C.

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Industrial temperature measurement

3. TEMPERATURE MEASUREMENT

3.1 The definition of temperature

The temperature of a medium is an expression of its content of thermodynamic energy. The thermodynamic energy represents the average velocity of the unarranged molecular movement in the material. To measure a temperature is therefore different from measur-ing one of the other basic units. Metres for example can be measured with an inch rule without affecting or changing the length. To measure temperature is different. Actually, the content of thermodynamic energy in the medium should be measured, based on the defi-nition. This is of course not possible in practice and therefore a measuring principle is used, where the medium affects a sensor / a sensor element. The measurement must take so long that molecules in sensor and medium assume the same mean velocity. When this has been reached, the two bodies will have the same temperature (measure-ment medium and temperature sensor). To achieve this, the following 3 conditions must be fulfilled: The bodies must not exchange heat with external or internal sources. The bodies must be in mutual balance. The bodies have had thermal contact through sufficiently long time.

4. PRINCIPLES OF TEMPERATURE MEASUREMENT Electrical temperature measurement is based on electrically measurable changes that are taking place in materials when exposed to temperature changes. These changes could for example be: Changes in resistance in conducting materials Changes in resistance in semiconductors Thermal voltage Drop in diode voltage Drop in transistor voltage Changes in frequency Noise The principles are used for the following thermometers: Resistance thermometers Thermistors Thermocouples Frequency thermometers, etc. In the following, only thermocouples and resistance thermometers will be dealt with.

5. THERMOCOUPLES The thermocouple is an active temperature sensor that measures differences in tempera-ture without auxiliary power. In all metallic conductors a thermal voltage will appear, when a temperature difference be-tween the conductors’s free ends exists. This voltage is dependent on the temperature dif-

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Industrial temperature measurement

ference and on a material parameter called the thermal power S. Seebeck proved the phenomenon in 1821. T1 S T2 The relation between temperature difference and voltage is ∆U = S ⋅ (T2 – T1) The thermal power S of a material is called the absolute Seebeck coefficient [µV/°C]. It is not possible to measure this thermal power unless combined with another material. To achieve values with a common starting point, the precious metal of platinum is used as reference. If two metals are connected to a closed circuit, the current running will be dependent on the difference between the thermal power of the metals and the temperature difference between the junctions.

Material: A The junctions are normwelding. For practical temperatuused. The concept “relatpower for two random m Example: Iron (Fe) put to S Fe, FeCuNi = +15 If the circuit is cut up, the The thermocouple voltag

Temperature

T1

Material: B

T2

ally called soldering points, even though they are most often a

re measurement, the absolute Seebeck coefficient cannot be ive Seebeck-coefficient” is used, which is simply the total thermal aterials

I.e.:SAB = SA - SB

gether with constantan (FeCuNi)

µV/°C – (-38µV/°C) = 53µV/°C

thermal voltage may be measured with a sensitive millivoltmeter.

e is: Umeas = ( Smat A – Smat B) ⋅ (T2 – T1)

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Industrial temperature measurement

If you want to measure absolute temperature, one soldering point must be kept at a con-stant temperature. This soldering point is now called the cold junction point, and the other soldering point may be used as temperature sensor. As the ice point of water is fairly easy to realise, 0°C is often used as reference temperature. In tables on thermal voltages, 0°C is always used as reference. For industrial use, this method is not practical. In modern electronic instruments for tem-perature measuring, you let the cold soldering point assume the temperature inside the instrument. A special electronic circuit then measures this temperature and adds the nec-essary correction voltage to the thermal voltage. Such an arrangement is called "auto-matic cold junction compensation". A U T O M A T IC C O L D J U N C T IO N C O M P E N S A T IO N (C J C )

T R

T R

C u

C J C

T R

V o ltm e te r

U (T R )

C u

T

If you have no such instrument available for control of a thermocouple, you may use the following procedure provided that the ambient temperature is known and constant with good approximation: Example: Thermocouple: NiCr-Ni type K Umeasured = 44.221 mV Tref = 25°C The procedure is now that Tref = 25°C is converted into voltage - look into the table for type K. You will find the following Tref = 25°C ∼ 1.277mV. i.e. U(NiCr-Ni) + UTref = 44.221+1.277 = 45.498 mV Looking into the table you will find that 45.498 mV ∼ 800°C If instead, you first converted the measured voltage into °C and then added Tref, you would due to the non-linear characteristic get a wrong result, because Umeasured = 44.221 mV ∼ 780.2°C + Tref = 25°C = 805.2°C, i.e. an error of 5.2° C. The errors are dependent on type of thermocouple and level of tem-perature.

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Industrial temperature measurement

5.1 Types of thermocouples Two metals or alloys welded/joint together form a thermocouple, so the number of possi-bilities is infinite. It is a serious job to select the proper materials for a thermocouple. The types that for one reason or another are selected are defined very precisely as far as the composition of the alloy is concerned. This, together with the requirements to the accuracy tolerance makes it possible for different manufacturers to produce even complicated alloys completely uni-form themselves. The following thermocouples are international and described: Name of type/alloy

∗ T Cu-CuNi ∗ N NiCroSil –NiSil ∗ J Fe-CuNi ∗ S Pt10%Rh-Pt ∗ E NiCr-CuNi ∗ R Pt13%Rh-Pt ∗ K NiCr-Ni ∗ B Pt30%Rh-Pt6%Rh

This international standard is called IEC 584 and is based on an American standard. At the time when this took place, the Germans had their own standard in the field, the DIN 43710, which also had the types of Cu-CuNi and Fe-CuNi. Even though the alloys were basically the same, they nevertheless deviated so much that they did not give the same thermo voltage. Therefore, it was decided to keep these types, which are today used un-der the names of: Type designation/alloy U Cu-CuNi (DIN) L Fe-CuNi (DIN) When naming a thermocouple, the positive conductor is always mentioned first.

5.2 Measuring range of a thermocouple If you look at the number of thermocouples, they cover a large temperature range from –200 to 1800°C. The table below will give an overview of the temperature ranges, in which the thermocouples can be used. However, the recommended maximum operating temperature for the individual thermocouples is dependent on the diameter of the wire and the ambient atmosphere.

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Industrial temperature measurement

type

B P

t30%

Rh

- Pt6

%R

h

Normally not recommended

type

R P

t13%

Rh

- Pt

Temperature limits for thermocouple

2000

1600

1200

800

400

0

-200-273

Normally recommended

°C Temperaturety

pe E

NiC

r - C

uNi

type

T C

u - C

uNi

type

J F

e - C

uNi

type

K N

iCr -

Ni

type

N N

iCro

Sil -

NiS

il

type

S P

t10%

Rh

- Pt

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5.3 Tolerances

We distinguish between three tolerance classes. Class 1 is the most accurate. Class 2 is standard, i.e. this is the quality that is delivered if nothing else is mentioned. Below you will find an overview.

Tolerances for thermocouples acc. to IEC 584 - 2 Thermocouple Temperature range ToIerance 1) Class 1 Type T, Cu-CuNi -40 to 350°C ±0.5°C or ±0.004⋅tactual°C

Type E, NiCr-CuNi -40 to 800°C ±1.5°C or ±0.004⋅tactual°C

Type J, Fe-CuNi -40 to 750°C ±1.5°C or ±0.004⋅tactual°C

Type K, NiCr-Ni -40 to 1000°C ±1.5°C or ±0.004⋅tactual°C

Type N, Nicrosil-Nisil -40 to 1000°C ±1.5°C or ±0.004⋅tactual°C

Type S, Pt10%Rh-Pt

0 to 1100°C 1100 to 1600°C

±1.0°C ±(1.0°C +0,003(tactual – 1100))°C

Type R, Pt13%Rh-Pt

0 to 1100°C 1100 to 1600°C

±1.0°C ±(1.0°C +0,003(tactual – 1100))°C

Class 2 Type T, Cu-CuNi -40 to 350°C ±1.0°C or ±0.0075⋅tactual°C

Type E, NiCr-CuNi -40 to 900°C ±2.5°C or ±0.0075⋅tactual°C

Type J, Fe-CuNi -40 til 750°C ±2.5°C or ±0.0075⋅tactual°C

Type K, NiCr-Ni -40 to 1200°C ±2.5°C or ±0,0075⋅tactual°C

Type N, Nicrosil-Nisil -40 to 1200°C ±2,5°C or ±0,0075⋅tactual°C

Type S, Pt10%Rh-Pt

0 to 1100°C 1100 til 1600°C

±1,5°C or ±0,0025⋅tactual°C

Type R, Pt13%Rh-Pt

0 to 1600°C

±1,5°C or ±0,0025⋅tactual°C

Type B Pt30%Rh-Pt6%Rh

600 to 1700°C

±1,5°C or ±0,0025⋅tactual°C

Class 3 Type T, Cu-CuNi -200 to 40°C ±1,0°C or ±0,0015⋅tactual°C

Type K, NiCr-Ni -200 to 40°C ±2,5°C or ±0,0015⋅tactual°C

Type N, Nicrosil-Nisil -200 to 40°C ±2,5°C or ±0,0015⋅tactual°C

Pt30%Rh-Pt6%Rh Type B

600 to 1700°C ±4°C or ±0,005⋅tactual°C

Note 1) : The highest value is valid. I.e. for example for type K class 2 the tolerance in the range –40 to +333°C is ±2.5°C and above it is ±0.0075⋅tactual°C

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5.4 Temperature-voltage-relation

The temperature-voltage-relation is not based on a simple relation. The size of the thermal power or the thermal voltage has a most complicated relation to the temperature. This ap-pears from the fact that it takes a high power polynomial to describe this relation. Additionally tables calculated from these with polynomial are available with thermal volt-ages per °C.

5.5 Compensation cable The thermocouple goes from the hot junction in the sensor to the cold junction, which is normally found in the instrument, i.e. in principle a thermo wire should be used all the way. This is however unpractical as well as too expensive in many cases. Instead a special ca-ble is used. The requirements to this cable are that it does not add additional thermal volt-age to the measuring chain resulting in measurement errors. There are three cable types, which can solve this task: 5.5.1 Compensation cable The compensation cable is a cable made from metals or from alloys, which have the same thermoelectric characteristics as the thermocouple, but only in a limited temperature interval, typically up to 100°C. It is therefore important to ensure that the ambient tempera-ture at the junction remains within the interval recommended by the supplier. If not, it will be the same as to add an extra thermal point in the measuring circle. 5.5.2 Extension cable The designation extension cable covers a cable which holds the same alloy as the ther-mocouple or an alloy with the same thermoelectric characteristics as the thermocouple, but with a larger temperature interval than is valid for compensation cables, typically up to 200°C. 5.5.3 Thermocouple wire Thermocouple wire is the material that is used for the production of thermocouples. By us-ing this as extension cable you have eliminated minor errors coming from thermo junction. There are however two reasons for not using thermo wire as extension. First of all the price is high, especially in the case of thermocouples made of precious metals, secondly it is most often only produced as solid wire which is rather difficult to use for installation pur-poses. 5.5.4 Colour codes As there are many types of thermocouples and as you cannot see the alloy of a cable immediately, a colour code has been introduced. The standard valid today is IEC584-4. According to this standard all negative conductors are white, while the positive conductors and common isolation have the same colour. Before this standard was introduced, the DIN 43710 was used in Europe. In this standard all positive conductors were red, so one has to pay attention to what is connected together. The below table indicates the colour codes according the IEC norm and other national standards.

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Colour Codes for compensation cables

Standard Thermocouples Common Isolation

Isolation Positive

Isolation Negative

Cu-CuNi Type T Brown Brown White NiCr-CuNi Type E Violet Violet White Fe-CuNi Type J Black Black White NiCr-Ni Type K Green Green White Nicrosil-Nisil Type N Pink Pink White Pt10%Rh-Pt Type S Orange Orange White Pt13%Rh-Pt Type R Orange Orange White

IEC 584 - 4

Pt30%Rh-Pt6%Rh Type B Grey White White Cu-CuNi Type U Brown Red Brown Fe-CuNi Type L Blue Red Blue NiCr-Ni Type K Green Red Green Pt10%Rh-Pt Type S White Red White

DIN

Pt13%Rh-Pt Type R White Red White Cu-CuNi Type T Blue Blue Red NiCr-CuNi Type E Purple Purple Red Fe-CuNi Type J Black White Red NiCr-Ni Type K Yellow Yellow Red Pt10%Rh-Pt Type S Green Black Red Pt13%Rh-Pt Type R Green Black Red

ANSI

Pt30%Rh-Pt6%Rh Type B Grey Grey Red

5.6 Applications and limitations A good knowledge of the conditions under which the measurement shall take place gives the best possibility for choosing the right type of thermocouple. For the thermocouples most often used the following should be observed as to applications and limitations: 5.6.1 Type J. Fe-CuNi thermocouple ∗ Cannot be used below 0°C, because condensation on the Fe-conductor will cause rust-

ing. ∗ Most suitable for reducing atmospheres ∗ May be used up to 500°C as a max. Above this temperature the oxidation will be very

heavy. Besides, both thermocouple wires will be attacked and destroyed by sulphur. ∗ Shows too high temperature after ageing. 5.6.2 Type T. Cu-CuNi thermocouple ∗ May be used below 0°C even with very high accuracy. ∗ May be used both in slightly oxidizing and slightly reducing atmospheres. Should, however, not be used for temperatures above 400°C.

∗ Not sensible to humidity. ∗ Both threads may be annealed to remove non-homogeneous stuff. In this way faulty

voltages are omitted. 5.6.3 Type K. NiCr-Ni thermocouple ∗ Type K is widely used in numerous applications from –100°C to max. +1000°C ((rec-

ommended), depending on the wire diameter). ∗ For a short time up to 1200°C.

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∗ In the range from 200 to 500°C a so-called hysteresis effect may occur, i.e. you do not reach the same value in heating and cooling. There may be a difference of up to 5°C.

∗ To be used in neutral or oxidizing atmospheres. ∗ Shows too low temperature after ageing. ∗ Is not recommended to be used in reducing atmospheres. In this case chromium will

come out of the NiCr-conductor, the so-called migration. The thermocouple will change thermal voltage and show too low temperature. This error effect is called Green-rot.

∗ Sulphurous atmospheres are poisonous, because sulphur will attack both threads. 5.6.4 Type N. Nicrosil-NiSil thermocouple The type N thermocouple is of a relatively new date and is constructed based on a type K thermocouple. The type K thermocouple is easily polluted at high temperatures by foreign bodies. By alloying both conductors with among others silicon, you have "polluted" the thermocouple in advance and in this way it is less exposed to pollution from other materi-als. ∗ The recommended max. working temperature is 1200°C (depending on the wire diame-

ter). ∗ For a short time up to 1250°C. ∗ High stability in the range from 200 to 500°C (no hysteresis effect like for type K). 5.6.5 Type S. Platinum 10% Rhodium-Platinum thermocouple ∗ The recommended max. working temperature is 1350°C (depending on the wire diame-

ter). ∗ For a short time up to 1750°C. ∗ Will be polluted at temperatures above 900°C by hydrogen, carbon and metallic gasses

from copper and iron. Already at absorption of 0.1% iron in the platinum wire, the ther-mal voltage will change by more than 1 mV at 1200°C and 1.5 mV at 1600°C. The con-sequence is an indication error of more than 100°C and 160°C, respectively. The same pattern takes place in connection with absorption of copper. Therefore, you should never use a platinum thermocouple with a steel tube, unless the steel tube has a gas proof ceramic tube inside.

∗ May be used in oxidizing atmospheres. ∗ At temperatures above 1000°C, the thermocouple is also polluted by silicon. This silicon

exists in some types of ceramic protection tubes used for the thermocouple. Therefore, it is important to use thermocouples with protection tubes of extremely pure aluminium oxide.

∗ Applications below 400°C cannot be recommended, as the thermal voltage here is very low and non-linear.

5.6.6 Type R. Platinum 13% Rhodium-Platinum thermocouple ∗ Same as for Type S above. 5.6.7 Type B. Platinum 30% Rhodium-Platinum 6% Rhodium thermocouple ∗ Recommended max. working temperature 1500°C (depending on the wire diameter) ∗ For a short time up to 1750°C. ∗ Will be polluted at temperatures above 900°C by hydrogen, carbon and metallic gasses

from copper and iron, however less than type S and type R. ∗ At temperatures above 1000°C, the thermocouple is also polluted by silicon. This silicon

exists in some types of the ceramic protection tubes, which are used for the thermo-couple Therefore, it is important to use thermocouples with protection tubes of ex-tremely pure aluminium oxide.

∗ May be used in oxidizing atmospheres.

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∗ Applications below 600°C cannot be recommended, as the thermal voltage here is very low and non-linear.

6. RESISTANCE THERMOMETER

The resistance thermometer is a passive temperature sensor, based on the physical phe-nomenon that an electric conductor changes its conductivity as a function of the tempera-ture. Resistance thermometers can be split into two main groups: Metal resistance thermometers Semiconductor resistance thermometers Within technical temperature measurement, the metals of platinum, nickel, copper and nickel-iron are used, but even high in price, especially platinum is the preferred metal. This is mostly due to the fact that being a precious metal, platinum has an eminent chemical stability towards most media and high stability at high temperatures. In addition, platinum has an excellent reproduction of its electrical characteristics due to its homogeneity. Therefore, the platinum resistance thermometer is used as interpolation instrument when determining the ITS, the International Temperature Scale. The following will only deal with the platinum resistance thermometer.

6.1 Platinum resistance thermometer

6.1.1 Temperature – resistance relation The relation between temperature and resistance has been laid down in the IEC 751 as table value and as an equation. For Pt100 the following equations apply: For the temperature range from –200°C to 0°C the following will apply: Rt = R0 ⋅ (1 + A ⋅ t + B ⋅ t 2 + C ⋅ (t – 100) ⋅ t 3)) For the temperature range from 0°C to 850°C the following will apply: Rt = R0 ⋅ (1 + A ⋅ t + B ⋅ t 2 ) The constants have been fixed as follows:

A = 3.90803 ⋅ 10 -3 B = - 5.775 ⋅ 10 -7

C = - 4.183 ⋅ 10 –12

The temperature coefficient α is a value of the sensitivity of the resistance thermometer. It is also an expression of the mean value for the relative change in resistance per °C be-tween 0 and 100°C. α = (R100 - R0)/ R0 ⋅ 100 [°C-1 ] R100 = the resistance at 100°C R0 = the resistance at 0°C For Platinum α = 0.3850/°C

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6.2 Tolerances

A tolerance is an indication of the highest permittable deviation from true value under non-calibrated conditions. There are four different tolerances: ∗ Norm-related tolerances ∗ Commercial tolerances ∗ Company specific tolerances ∗ Relative tolerances

6.2.1 Norm-related tolerances Norm-related tolerances are the tolerances that can be found in national or international norms on resistance elements. DIN43760, the German industrial norm, has been elevated into the international norm of IEC751 and indicates tolerances for platinum sensors as fol-lows: Class A: ± (0.15 + 0.002 tactual ) [°C] Class B: ± ( 0.3 + 0.005 tactual ) [°C] Where tactual is the actual value of the temperature. Based on these formulas it is seen that tolerances consist of two contributions, i.e. the zero point tolerance (0°C) and the temperature-dependant additional tolerance (inclina-tion). Norm tolerances are in general valid, i.e. they are in force no matter whether it con-cerns Pt100 or Pt500, etc.

6.2.2 Commercial tolerances Mercantile tolerances are a supplementary to the norm-related tolerances. Increasing demands to being able to measure more accurately and the fact that the norms only dif-ferentiate between two tolerance classes, have resulted in the concept called mercantile tolerances. These are described in 1/3 DIN, 1/6 DIN, and 1/10 DIN. The mercantile toler-ances are so well integrated that they are accepted as an ordinary standard. Unfortu-nately, these norms may be abused to let the customer believe that he buys something, which is better than it actually is. It is an error that some suppliers wrongly inform that both the zero point tolerance and the temperature-dependant tolerance are a fraction of the norm tolerance. The normal is that only the zero point tolerance is improved. Ametek Denmark A/S defines it in the following way: 1/3 Cl. B at 0°C: ±(0.1+0.005⋅ tactual) [°C] 1/6 Cl. B at 0°C: ±(0.05+0.005⋅ tactual) [°C]

6.2.3 Company specific tolerances Company specific tolerances are yet another supplement to the norm tolerances. Some companies use tolerance classes, which are completely their own. This is most often the case, if a company can offer platinum elements that are better than what can be described with norm tolerances as well as mercantile tolerances. For example: SDL band 5: ±(0.045+0.001x tactual )[°C] in the range -50+400°C

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Relative tolerances are another form of tolerance. Here, the tolerance or the per-mittable deviation is not measured in relation to the correct value, but in relation to another platinum resistance. In connection with measurement of energy amounts there is a need for measuring relatively between supply and return. It is for exactly such measurements that relative tolerances are used. The tolerance may also be indicated as: ±0.1°C variance at 0°C and 100°C (group-paired)

6.3 Measuring resistance types and measuring range The measuring element can be divided into the following groups: Types ∗ Wire-wounded in ceramics ∗ Wire- wounded in glass ∗ Thin-film resistors Measuring range When evaluating the temperature ranges, it is necessary to differentiate between the ba-sic values and whether the carrier material is ceramics or glass. Generally, resistance thermometers are suited for the range from -50 to 400°C. For measurement of temperatures higher than 600°C, the use of thermocouples should be considered. 6.3.1 Wire-wounded measuring resistors in ceramics For industrial use, the platinum wire has been completely or partly embedded to ensure optimum mechanical strength against impacts, chocks and vibrations. In the reference resistor the platinum wire is loose to avoid differences in the expansion coefficients between platinum and ceramics and thereby influence the accuracy in nega-tive direction. The consequence is naturally that these measuring resistors are not very robust and cannot stand impacts or vibrations. 6.3.2 Wire-wounded measuring resistors of glass Glass resistors have the very big advantage of not being hydrostatic, i.e. they do not ab-sorb water from the surroundings. So, if you have to make a temperature measurement in air with a quick reaction time it is quite obvious to use a glass-measuring resistor. The glass-measuring resistor is the most expensive one of the three types.

6.3.3 Thin-film resistors The production process of thin-film resistors is as follows: a thin ceramic substrate is fused on to the platinum and a pattern is cut into the platinum until the desired basic value has been achieved. This type of measuring resistor shows very good characteristics to-wards vibrations. The thin-film resistors are cheaper than the wire-wounded resistors.

6.4 Coupling methods Today the following different coupling methods may be chosen: Temperature Page 15 of 30

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∗ 2-wire ∗ 3-wire ∗ 4-wire 6.4.1 2–wire coupling This coupling method will always result in measuring errors, because you cannot avoid also measuring the lead wires. If the measurement is done by means of a Wheatstone bridge, this measuring error can be adjusted away, but only at one temperature. If only a narrow temperature range is measured, the measuring bridge is adjusted to be correct in the middle of the range. So, in this case it is possible to use the cheap 2-wire coupling. As an example this means that a lead wire resistance of 0.5Ω will give the fol-lowing error depending on the basic value R0 R0 : Pt100 Pt500 Pt1000 Measuring error : 2,6°C 0,52°C 0.25°C As expected the error declines as the value of R0 increases. 6.4.2 3-wireHere the meascourse due to tsame size. CoThis means thperature 0°C conly occurs, wthe error will grchanges in the1/10 of the err10Ω. Temperature

2-WIRE

coupling uring error will be 0°C, when the temperature 0°C is measured. This is of he fact that the measuring bridge is in balance, when all resistors have the nsequently, the lead wire resistance must be the same in the three wires. at a 3-wire coupling gives a fully compensated measurement at the tem-ompletely independent of the size of the lead wire resistance. The error hen the measured temperature is different from 0°C, and then the size of ow along with increasing lead wire resistance. In this case it is a matter of sensibility of the measuring bridge. The size of the error will be less than or in a 2-wire system, if the resistance in the individual lead wire is max.

3-WIRE

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6.4.3 4-wire coupling With the 4-wire coupling you are not using the Wheatstone bridge as measuring circuit. A constant measuring current is sent to the measuring resistor through two of the wires. The voltage that is created above the resistor is measured with a high impedance voltme-ter over the two other wires. When the input impedance is within the mega-ohm range, the current and thereby the voltage drop in the measuring wires will be approximately zero. In this way you avoid including the lead wires in the measurement.

4-WIREIconst Umeas

I1

U1

U2

I2

Pt 100

6.5 Self-heating The current that is sent through a measuring resistor to measure the voltage has an elec-trical effect (Joule) that will heat the measuring resistor. The effect can be found from the relation. tself heating = P/EK = RT ⋅ I2/EK Manufacturers of measuring resistors indicate a self-heating coefficient EK for the measur-ing resistor itself. This figure cannot be used for the entire sensor, because the size of the self-heating coefficient is dependent on the surface that is in contact with the medium, the coefficients of heat transfer and the temperature delay (sensor medium). Examples Medium: Water at 0.2 m/s Ceramics measuring resistor EK = 300mW/°C Measuring resistor in measuring insert EK = 80mW/°C Measuring resistor in fittings EK = 10mW/°C In air the values are typical in the range 25-100µW/°C. When the values are known, the spontaneous heating may be calculated based on the following: You normally try to keep the measuring current so low (typically<1mA) that the self-heating max. becomes 0.1°C, or you use a pulsating current.

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6.6 Application Resistance thermometers are in general used where the following requirements and work-ing conditions exist: ∗ Temperature range -50+400°C ∗ High absolute accuracy is a demand ∗ High relative accuracy is a demand ∗ High repeatability ∗ Not too heavy vibration conditions ∗ Mean response time ∗ Interchangeability

7. SELECTION OF TEMPERATURE SENSOR An ideal solution to a temperature measurement task seldom exists. Selection of tempera-ture sensor will invariably be a compromise between the requirements of the user and the limitations that are set by the possible types of sensor in connection with the conditions on the measuring point. The following indicates the most important conditions for an appropriate selection of sen-sor. Attention should be paid to the fact that a sensor measures its own temperature. There-fore it is quite decisive for the accuracy that the sensor assumes the temperature that is to be measured, that is without having any effect on this. A surface sensor with thermocou-ple could for example very well measure more accurately than a corresponding sensor made as a resistance thermometer.

7.1 The most important conditions for the choice of a sensor Selection of sensors in practice should be based on a total evaluation, in which a.o. the following parameters are considered: ∗ Temperature range ∗ Corrosion conditions ∗ Breaking down due to wear and tear ∗ Static mechanical influence ∗ Dynamic influence ∗ Accuracy ∗ Pressure conditions ∗ Interchangeable (with pocket, interchange without stopping the process) ∗ Response time ∗ Conditions of pollution ∗ Variations in temperature – temperature shock ∗ Sensitivity In the following some tools are given to simplify the necessary choice. It should be men-tioned that these are not a “finial” solution but considerations to evaluate when selecting a sensor for a specific task.

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7.2 Temperature range This is normally one of the first things to evaluate, because the range of the individual thermo sensors easily determines the choice. At temperatures below 400°C resistance thermometers are often a natural choice. In the range 400 to 600°C thermocouples as well as resistance thermometers may be considered. If the measuring range is above 600°C, a thermocouple is often chosen. Below table gives a general view of the temperature ranges that can be measured with a thermocouple and a resistance thermometer, respectively. Only remember to consider not only the normal temperature but also maximum and minimal temperatures that may occur. Furthermore, it may also be decisive how long the sensor is used.

2000

1600

1200

800

400

0

-200-273

Normally recommended

Normally not recommended

°CSelection of sensor depending on temperature range

7.3 Corrosion conditions Corrosion conditions are decisive for choice of fittings and thermo pockets, if any. If you suspect the medium you are going to measure to be aggressive, the following information must be available: ∗ Medium/media ∗ Concentration ∗ Temperature

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This information will form the basis for finding the best-suited material for the job. Here the supplier will use public information about steel types and, above all, corrosion tables to find the best-suited material. In some cases it is difficult to find a suitable alloy, which is why also other possibilities such as rubberizing, Teflon coating or plast coating are taken into consideration. Naturally, it is always helpful to have information about what other material sensors and the con-tainer are made of. The solution to such a problem could also be to measure on the outside of the container using a surface sensor. A quite special problem may occur, if the electrical conditions make a galvanic corrosion occur. In such cases the least precious of the metals involved will be corroded. If the medium, in which the measurement should be done, is a gas type, you will only very seldom see corrosion at low temperatures, but at higher temperatures even air may be aggressive due to oxidation. The same goes for fuel gases with content of carbon monoxide, hydrocarbons or sulphur compounds. The material will be damaged or the protection tube become fragile due to decarburization, just as sulphides will be cre-ated. Luckily, a number of heat-resistant or inoxidizable materials on iron-chromium-nickel basis is available, all even with a very low content of silicium or manganese. In oxygenic gases a thick, sticky oxidation deposit is created acting as a protective layer, as long as it is not damaged by settlement of dust, oil ash or flux. When metallic protection tubes are unable to give sufficient protection, ceramic tube of porcelain or Al203 must be used. As to chemi-cals these tubes are superior to metallic tubes in every way, but unfortunately they have only poorer mechanical strength and they are more sensitive towards quick deviations in temperature.

7.4 Mechanical load pressure, static and dynamic influence Temperature sensors are normally exposed to mechanical influence, which can reach from pure static load (for example the self-weight of long thermocouples) over mixed static and dynamic load to high frequency vibrations from fast moving floating media or swinging machine parts. To this should be added pressure influence from containers or pipelines. If the pressure conditions, under which a temperature sensor must be placed, are known, these are compared with data informed in the individual data sheets, and a pocket/protective tube that fulfils the desired requirements is chosen. Load diagrammes are based on DIN 43763. Sensors placed in a tube with floating media are very often exposed to heavy mechanical vibrations. In this respect please note that load curves for thermo wells/pockets as func-tion of pressure, material, temperature, velocity of medium in DIN 43763 only consider in-fluence caused by force from the medium, and not the load that comes from vibrations. The size of this influence is especially dependent of the flow velocity (laminar or turbulent flow) and the built-in length. Ametek Denmark A/S can offer consulting around dynamic influence on sensors a.o. by means of special developed software programs.

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7.5 Accuracy To achieve the desired accuracy, a choice is made based on the norms. Please see page 12 for tolerance on resistance thermometers and page 7 for tolerance for thermocouples. Below graph will give a total picture.

Cl. 3

-100

Pt100 Class AType R,S Class 1Type E, J,

K, N C

lass 1

Allo

wed

dev

iatio

n

°C

400 800 1200 1600 °CTemperature

Type

E, J

, K, N

Cla

ss 2

Type R, S Class 2Pt10

0 Clas

s B

±10

±8

±6

±4

±2

If you are in the situation that the accuracy is not good enough, you will have to choose calibrated sensors or calibrated systems.

7.6 Response time It is not a guarantee for the final achieved accuracy to choose resistance sensors with the absolutely best tolerance. As described earlier, a thermometer cannot show the temperature without having as-sumed the level of energy corresponding to the actual temperature. The sensing element – be it thermocouple or resistance element - is the last part that is influenced by the tem-perature. So, if you have a dynamic process, the temperature sensor may chronically halt after the temperature. A temperature sensor’s response time is a.o. influenced by the following conditions: ∗ Dimension of sensor ∗ Heat transfer number between medium and sensor ∗ Static or dynamic medium ∗ Type of medium. Liquid or gas ∗ Production method

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For a quantitive description of the response time of a temperature sensor you make the assumption that the sensor is a first order system. I.e. you define that there is only a delay of the heat transfer between the medium and the sensor itself. This is rarely the case in practice, as a sensor most often consists of various heat delaying layers, such as pocket, protective tube, ceramic powder, and cavities. When simplifying nevertheless, it is partly because it gives relatively good agreement with the actual conditions and partly because it is easy to create formulas that can be used for calculations. 7.6.1 Response time If a temperature sensor is exposed to a temperature response, its response or reaction can be described with the below graph.

RESPONSE TIME

Temperature

Timeτ

63,2 %

If the time constant τ is known for a temperature sensor, it is also possible to state how many percent of the final value it has reached. If you determine that the acceptable error percentage must not exceed the tolerance for the sensor, the following relation will give how many time constants that have to be passed, before the accuracy has been achieved: Z = ln (100/X) Where X is the error percentage that can be accepted, Z is the number of time constants to be passed to achieve the desired accuracy. Z is typically 4-6 τ 7.6.2 Other expressions of response time As the response time is not a simple 1. order system, as mentioned, Ametek Denmark A/S indicates a more differentiated value than just a time constant. In the indication of the response time, different conditions have been included such as medium involved, and movements of the medium compared to the sensor. Two times are indicated:

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T0,5 is the time it takes the sensor to reach 50% of a change in temperature. T0,9 is the time it takes the sensor to reach 90% of a change in temperature. The indicated times have been found by testing the given type of sensor. There are there-fore no approaches to a 1. order system.

RESPONSE TIME

Temperature

t0,5 t0,9

Time

50 %

90 %

τt0,1

63,2 %

Time constant τ in relation to other expressions of response time

t1

It is possible to convert from this system to a time constant system with the purpose of be-ing able to make calculations with the indicated formulas for the spring response, the ramp function or the sinus function. This is done in the following way: τ = T 0.9 / 2.3 or τ = T 0.5 / 0.7 It should be emphasized that the above methods of calculation are approaches. One of the factors that have major influence on the response time is the thermal mass of the sensor or in plain words its size. This fact makes it possible that values informed by a supplier with a good approach can be used on similar products from other manufacturers. Another factor that has great impact on the size of the time of reaction, is the heat transfer ability between the sensor and the actual medium. In general, the heat transfer between sensor and liquid is much easier than between sensor and a gas.

8. MOUNTING AND INSTALLATION Many things have to be considered in connection with mounting and installation of tem-perature sensors. The following is only mechanical, practical considerations.

8.1 Mounting possibilities Temperature Page 23 of 30

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There are three different ways: ∗ Mounted at right angles to the tube (standard) ∗ Mounted counter the flow direction, most often angled 45° ∗ Mounted counter the flow direction in an angle piece. Elbow placing Mounting methods are illustrated below.

Mounted in an angleagainst flow direction

Standard mountingMounted in an angleor elbow

Installation of screw - in sensor

No unique prescriptions are given here as to which mounting should be used for specific measurements. Each individual installation must be evaluated separately. The length of the sensor can be decisive for the way of placing.

8.2 The length of the sensor It is of decisive importance to choose the correct sensor length with a view to errors caused by heat dissipation from sensor tip to the surroundings. On this point you should choose length according to the following guidelines. The numbers in the table indicate the factor by which the sensor diameter has to be multiplied to calculate the length of the sen-sor.

Medium Dynamic Static Liquid 5-10 10-20 Air 10-20 20-40

For example: A sensor with a diameter of 9 mm placed in a dynamic air stream should have an insertion depth of between 90 and 180 mm. To this insertion depth should further be added the physical length of the sensor element or the temperature sensitive length (TSL), which may vary from a few mm to 50-60 mm. If the length after these calculations is bigger than the radius of the medium tube, you have the possibility of placing the sensor in an angle. Or if this is not sufficient, the sensor may be placed in an elbow.

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The length of the sensor also has to be evaluated as regards vibrations, shocks and reso-nance frequency. Here it is important to ensure that the sensor does not get too long if mounted in a very turbulent liquid medium. Finally, the mounting should be done in such a way that it leaves room around the sensor with a view to replacing the measuring insert.

8.3 Isolation In cases where the measurement is carried out on media that have a temperature very different from the surroundings, the medium tube has to be isolated to minimize the effect from heat conduction. To ensure that heat transfer errors are eliminated, the sensor is some times isolated with a layer so thick that the connection head of the sensor is inside the isolation.

9. SOURCES OF ERROR There are many possible errors in connection with temperature measurement. In the fol-lowing is dealt with the types of error that are either caused by the physical conditions or general electrical conditions. If the error is connected to the measuring element (or the transducer) please refer to these sections. Sources of error: ∗ Heat conduction in the temperature sensor ∗ Radiation to and from the surroundings ∗ Heat capacity of the temperature sensor ∗ Dynamic temperature ∗ Earth currents ∗ Electric noise ∗ Non-tempered measuring instrument

9.1 Heat balance Heat energy is like electric current it follows the easiest way. That is the reason why measuring errors can occur in connection with heat conduction along a temperature sen-sor. On the below figure are shown the different factors contributing to the heat balance of a temperature sensor.

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qf

qv,f qf,v

Radiation

qm,f

tv

tf

. tm

Radiation

heat-conduction

Convection

Heat balance for a thermometer Where: tm temperature of the medium tf temperature of the sensor tv temperature of the tube wall These contributions will have the effect that the temperature tf of the sensor will be differ-ent from the temperature tm. of the medium. It is very complicated to find a true correction for the entire system and we would therefore like to split up the problem in two cases. 9.1.1 Heat transfer for a thermo pocket/well The size of the measurement error for a tube-formed pocket with thin wall is dependent of the convection contribution (medium – sensor) qm,f and the heat conduction contribution qf. It can be expressed as follows

)cosh( xLttttt vm

fmconvection ⋅−

=−=∆

Where: L Built-in length in mm

AkUhx

⋅⋅

=

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h Heat conduction coefficient (medium-pocket) in J/m2 s °C k Thermal heat conductivity for thermal pocket in J/m2 s °C A Heat conducting cross-sectional area in mm2 (metal thickness of the pocket) U Circumference in mm of the thermo pocket From this expression can be seen that the size of the product L⋅ x has big impact on the error, i.e. diameter, metal thickness, and insertion length. Practical actions to minimize the error as follows: ∗ Ensure a good isolation around process tube or container ∗ Use sufficiently small metal thickness for the thermo pocket ∗ Use big insertion depth ∗ Use an earthed version of thermocouple ∗ Place the sensor where the medium is in motion to ensure that the mounting spot is not

a cold spot that may conduct heat from the sensor ∗ Choose a sensor type with short time of reaction ∗ Keep the part of the sensor that is not placed inside the hose or the container isolated

in order to minimise the temperature potential that pulls the heat flow out through the sensor

Also, some parts of steel may be replaced by parts of synthetic materials to increase the heat transfer resistance. 9.1.2 Radiation to and from thermo pocket/well We know that energy may be transmitted by radiation through transparent material, if a temperature potential is present. In practice this means that the heat energy that a sensor absorbs from the medium by means of convection and conduction is radiated to the sur-roundings instead of being conducted to the sensor. Provided that the surface area of the pocket is small compared with that of the wall, the correction for the contribution from radiation may be expressed as follows

hTT

ttt vffmradiation

)( 44 −⋅⋅=−=∆ δε

Where: h Energy transfer coefficient (medium-pocket) in J/m2 s °C ε The emissivity of the thermo pocket/well (a quantity to account for non-blackness of the sensor 0<ε<1 δ The radiation value for a “Black” body, Stefan – Boltzmann’s constant Tf ,Tv The absolute temperature of the sensor and the wall in K From the expression one can see that the radiation correction is decreased, if you ensure a high energy exchange rate (medium – pocket), a low emissivity number for the pocket (brightness), and a good heat isolation of the walls. Errors due to radiation exchange can be pretty big. In an incinerator with a temperature of approx. 850°C and a wall temperature of approx. 250°C, i.e. a temperature potential of 600°C, the measuring errors may be as high as 50°C. So, this error source contributes with errors so big that compensating actions must be taken. The following is an example: Temperature Page 27 of 30

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∗ Distance as big as possible between heat radiation exchangers ∗ Reduction of sensor diameters ∗ Placing of sensors, where the surrounding walls seem to be most hot ∗ Mounting of one or more radiation shields on the temperature sensor

10. SIGNAL CONDITIONING AND TRANSMISSION In a process the temperature often has to be measured in one place and the measure-ment data have to be sent to another place – often to a control room several hundred me-ters away – where the measurement data are used. In this respect, accuracy, stability, life-time and costs have to be optimised. The most important factor in temperature control is good, reliable temperature data. To choose the right temperature sensor and the right method to transmit temperature data is the most important task. In this section we will concentrate on the signal transmission task. Having chosen the optimal temperature sensor for a measuring task, next step in remote temperature measurement is to send information from the temperature sensor to the con-trol room. Connecting the thermocouple or the resistance thermometer directly with a ca-ble can do this, or you can have a transmitter placed close to the temperature sensor, from which an amplified signal is sent to the control room.

10.1 Direct cable connection The direct cable connection has been used for many years and is easy to handle. 10.1.1 Direct cable connection to a thermometer It takes great care to install compensation cables to thermocouples. Each type of thermo-couple must have its own special compensation cable, which is described with a colour code in accordance with the standards.

Shielded compensation cable Indicator for TC

TC °C 10.1.2 Electrical noise Electrical noise is often varying or is periodical and therefore it is difficult to locate and eliminate errors. The easiest way to avoid noise is by keeping as much distance between signal cables and noise sources as possible. Shielded cables reduce the problem but in-crease the costs. 10.1.3 Direct cabling to resistance thermometers Contrary to thermocouples, resistance thermometers do not require a special cable. Cop-per cables are sufficient to send temperature information from resistance thermometers to a control room. If you only use a 2-wire connection between the temperature sensor and the control room, i.e. two wires in the cable, the resistance of these two wires will be added to the resistance in the resistance thermometer, which will of course result in a permanent measuring error of several degrees depending on the length of the cable. Add to this that variations in temperature along the two wires in the cable will change resis-

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tance of the cable. This will cause variation in the temperature indication up to several de-grees, depending on the length of the cable and the variation in temperature. Therefore, it is recommended to use at least three and preferably four wires in the cable, so-called 3- or 4-wire configuration between the resistance thermometer and the control room. 3- or 4-wire configurations can only be used, if the instrumentation in the control room is designed for this. Instrumentation in conventional 3-wire configuration compensates for the resis-tance itself and the variation contained in this, but the measuring principle with 3-wire con-figuration has built-in errors. Only instrumentation with 4-wire configuration or a special 3-wire configuration, which simulates 4-wire configuration gives the correct compensation for the cable resistance and thereby the best accuracy, when resistance thermometers are used for measurement of temperature.

Indicator for Pt100

°CPt100

Shielded 3 or 4 wire cable

10.2 Transmitters Transmitters are electronic instruments that transform a measured value from one repre-sentation to another. This new representation is normally standardized and can be sent over several thousand metres without problems. Always consider using transmitters, when the temperature information has to be sent over distances that are bigger than 70 metres. In surroundings with electrical noise, where an accurate and reliable signal transmission is important, the use of transmitters should be considered even in connec-tion with very short distances. This means of course that the transmitter you are using must not be affected by electrical noise and must be stable in the environment where it has to be used. Transmitters can be split up based on different characteristics: 1. 2-wire or 4-wire transmitters 2. Transmitters with voltage, current or digital output signal 3. Isolated or non-isolated transmitters 4. Analogue or “smart” transmitters 10.2.1 2-wire transmitters 2-wire transmitters are using the same two wires for receiving energy to the transmitter as well as for sending the signal from the transmitter to the control room. The output signal is a standardised current signal, which alternates from 4-20 mA, determined by the meas-ured temperature. The lowest temperature normally corresponds to 4 mA, and the highest temperature to 20 mA. The energy that powers the transmitter is lower than 4 mA so that the measuring signal is never affected. As the output signal always has to be at least 4 mA, breakage on the wires from the transmitter to the control room will be detected, if the output signal becomes 0 mA. 2-wire transmitters are naturally cheaper to install than the 4-wire transmitters. That is often the reason to choose 2-wire transmitters. 10.2.2 4-wire transmitters 4-wire transmitters are using two wires to receive power to the transmitter and two other wires to send the signal from the transmitter. 4-wire transmitters are necessary when the output signal must refer to zero, for example from 0-20 mA, or when 0-5 V is desired. The

Temperature Page 29 of 30

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Industrial temperature measurement

Temperature Page 30 of 30

power consumption of the 4-wire transmitters is not limited to 4 mA, and therefore the quality of the 4-wire transmitter was previously of a higher quality than the 2-wire transmit-ter. In general, 2-wire transmitters are preferred, because cable costs are lower and be-cause the price difference between 2-wire and 4-wire transmitters in the same quality is small. 10.2.3 Isolation The isolation to earth of isolated temperature sensors is minimised dramatically with the increase in temperature. Due to the difference in the electrical potential in the earth, where the temperature sensor is mounted, and the potential where the instrument is mounted, an earth current will flow in the transmission cables. The Power Regulation from 1994, which is based on European recommendations, means in practice that the receiving instrument is often connected to earth. Therefore it is rec-ommended to use isolated transmitters, especially when operating with high temperatures in the temperature sensor. This will be valid for many resistance thermometer systems and most thermocouple systems.

11. TABLES Enclosed tables for thermal voltages are based on the latest temperature scale ITS 90 and the resistance table for Pt100.

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Thermocouple reference tables acc. to IEC 584 - 1

Termo-couple

Type U IPTS68

Type T ITS90

Type L IPTS68

Type J ITS90

Type K ITS90

Type N ITS90

Type S ITS90

Type R ITS90

Type B ITS90

Temp. in °C mV µV mV µV µV µV µV µV µV

-200 -5,70 -5603 -8,15 -7890 -5891 -3990-150 -4,69 -4648 -6,60 -6500 -4913 -3336-100 -3,40 -3379 -4,75 -4633 -3554 -2407-50 -1,85 -1819 -2,51 -2431 -1889 -1269 -236 -226-40 -1,50 -1475 -2,03 -1961 -1527 -1023 -194 -188-30 -1,14 -1121 -1,53 -1482 -1156 -772 -150 -145-20 -0,77 -757 -1,02 -995 -778 -518 -103 -100-10 -0,39 -383 -0,51 -501 -392 -260 -53 -510 0,00 0 0,00 0 0 0 0 0 010 0,40 391 0,52 507 397 261 55 54 -220 0,80 790 1,05 1019 798 525 113 111 -330 1,21 1196 1,58 1537 1203 793 173 171 -240 1,63 1612 2,11 2059 1612 1065 235 232 050 2,05 2036 2,65 2585 2023 1340 299 296 260 2,48 2468 3,19 3116 2436 1619 365 363 670 2,91 2909 3,73 3650 2851 1902 433 431 1180 3,35 3358 4,27 4187 3267 2189 502 501 1790 3,80 3814 4,82 4726 3682 2480 573 573 25

100 4,25 4279 5,37 5269 4096 2774 646 647 33110 4,71 4750 5,92 5814 4509 3072 720 723 43120 5,18 5228 6,47 6360 4920 3374 795 800 53130 5,65 5714 7,03 6909 5328 3680 872 879 65140 6,13 6206 7,59 7459 5735 3989 950 959 78150 6,62 6704 8,15 8010 6138 4302 1029 1041 92160 7,12 7209 8,71 8562 6540 4618 1110 1124 107170 7,63 7720 9,27 9115 6941 4937 1191 1208 123180 8,15 8237 9,83 9669 7340 5259 1273 1294 141190 8,67 8759 10,39 10224 7739 5585 1357 1381 159200 9,20 9288 10,95 10779 8138 5913 1441 1469 178210 9,74 9822 11,51 11334 8539 6245 1526 1558 199220 10,29 10362 12,07 11889 8940 6579 1612 1648 220230 10,85 10907 12,63 12445 9343 6916 1698 1739 243240 11,41 11458 13,19 13000 9747 7255 1786 1831 267250 11,98 12013 13,75 13555 10153 7597 1874 1923 291260 12,55 12574 14,31 14110 10561 7941 1962 2017 317270 13,13 13139 14,88 14665 10971 8288 2052 2112 344280 13,71 13709 15,44 15219 11382 8637 2141 2207 372290 14,30 14283 16,00 15773 11795 8988 2232 2304 401300 14,90 14862 16,56 16327 12209 9341 2323 2401 431310 15,50 15445 17,12 16881 12624 9696 2415 2498 462320 16,10 16032 17,68 17434 13040 10054 2507 2597 494330 16,70 16624 18,24 17986 13457 10413 2599 2696 527340 17,31 17219 18,80 18538 13874 10774 2692 2796 561350 17,92 17819 19,36 19090 14293 11136 2786 2896 596360 18,53 18422 19,92 19642 14713 11501 2880 2997 632370 19,14 19030 20,48 20194 15133 11867 2974 3099 669380 19,76 19641 21,04 20745 15554 12234 3069 3201 707390 20,38 20255 21,60 21297 15975 12603 3164 3304 746400 21,00 20872 22,16 21848 16397 12974 3259 3408 787410 21,62 22,72 22400 16820 13346 3355 3512 828420 22,25 23,29 22952 17243 13719 3451 3616 870430 22,88 23,86 23504 17667 14094 3548 3721 913440 23,51 24,43 24057 18091 14469 3645 3827 957450 24,15 25,00 24610 18516 14846 3742 3933 1002460 24,79 25,57 25164 18941 15225 3840 4040 1048470 25,44 26,14 25720 19366 15604 3938 4147 1095480 26,09 26,71 26276 19792 15984 4036 4255 1143490 26,75 27,28 26834 20218 16366 4134 4363 1192500 27,41 27,85 27393 20644 16748 4233 4471 1242

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Thermocouple reference tables acc. to IEC 584 - 1

Termo-couple

Type U IPTS68

Type T ITS90

Type L IPTS68

Type J ITS90

Type K ITS90

Type N ITS90

Type S ITS90

Type R ITS90

Type B ITS90

Temp. in °C mV µV mV µV µV µV µV µV µV510 28,08 28,43 27953 21071 17131 4332 4580 1293520 28,75 29,01 28516 21497 17515 4432 4690 1344530 29,43 29,59 29080 21924 17900 4532 4800 1397540 30,11 30,17 29647 22350 18286 4632 4910 1451550 30,80 30,75 30216 22776 18672 4732 5021 1505560 31,49 31,33 30788 23203 19059 4833 5133 1561570 32,19 31,91 31362 23629 19447 4934 5245 1617580 32,89 32,49 31939 24055 19835 5035 5357 1675590 33,60 33,08 32519 24480 20224 5137 5470 1733600 34,31 33,67 33102 24905 20613 5239 5583 1792610 34,26 33689 25330 21003 5341 5697 1852620 34,85 34279 25755 21393 5443 5812 1913630 35,44 34873 26179 21784 5546 5926 1975640 36,04 35470 26602 22175 5649 6041 2037650 36,64 36071 27025 22566 5753 6157 2101660 37,25 36675 27447 22958 5857 6273 2165670 37,85 37284 27869 23350 5961 6390 2230680 38,47 37896 28289 23742 6065 6507 2296690 39,09 38512 28710 24134 6170 6625 2363700 39,72 39132 29129 24527 6275 6743 2431710 40,35 39755 29548 24919 6381 6861 2499720 40,98 40382 29965 25312 6486 6980 2569730 41,62 41012 30382 25705 6593 7100 2639740 42,27 41645 30798 26098 6699 7220 2710750 42,92 42281 31213 26491 6806 7340 2782760 43,57 42919 31628 26883 6913 7461 2854770 44,23 43559 32041 27276 7020 7583 2928780 44,89 44203 32453 27669 7128 7705 3002790 45,55 44848 32865 28062 7236 7827 3078800 46,22 45494 33275 28455 7345 7950 3154810 46,89 46141 33685 28847 7454 8073 3230820 47,57 46786 34093 29239 7563 8197 3308830 48,25 47431 34501 29632 7673 8321 3386840 48,94 48074 34908 30024 7783 8446 3466850 49,63 48715 35313 30416 7893 8571 3546860 50,32 49353 35718 30807 8003 8697 3626870 51,02 49989 36121 31199 8114 8823 3708880 51,72 50622 36524 31590 8226 8950 3790890 52,43 51251 36925 31981 8337 9077 3873900 53,14 51877 37326 32371 8449 9205 3957910 52500 37725 32761 8562 9333 4041920 53119 38124 33151 8674 9461 4127930 53735 38522 33541 8787 9590 4213940 54347 38918 33930 8900 9720 4299950 54956 39314 34319 9014 9850 4387960 55561 39708 34707 9128 9980 4475970 56164 40101 35095 9242 10111 4564980 56763 40494 35482 9357 10242 4653990 57360 40885 35869 9472 10374 47431000 57953 41276 36256 9587 10506 48341010 58545 41665 36641 9703 10638 49261020 59134 42053 37027 9819 10771 50181030 59721 42440 37411 9935 10905 51111040 60307 42826 37795 10051 11039 52051050 60890 43211 38179 10168 11173 52991060 61473 43595 38562 10285 11307 53941070 62054 43978 38944 10403 11442 54891080 62634 44359 39326 10520 11578 55851090 63214 44740 39706 10638 11714 56821100 63792 45119 40087 10757 11850 57801110 64370 45497 40466 10875 11986 58781120 64948 45873 40845 10994 12123 59761130 65525 46249 41223 11113 12260 60751140 66102 46623 41600 11232 12397 61751150 66679 46995 41976 11351 12535 6276

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Thermocouple reference tables acc. to IEC 584 - 1

Termo-couple

Type U IPTS68

Type T ITS90

Type L IPTS68

Type J ITS90

Type K ITS90

Type N ITS90

Type S ITS90

Type R ITS90

Type B ITS90

Temp. in °C mV µV mV µV µV µV µV µV µV1160 67255 47367 42352 11471 12673 63771170 67831 47737 42727 11590 12812 64781180 68406 48105 43101 11710 12950 65801190 68980 48473 43474 11830 13089 66831200 69553 48838 43846 11951 13228 67861210 49202 44218 12071 13367 68901220 49565 44588 12191 13507 69951230 49926 44958 12312 13646 71001240 50286 45326 12433 13786 72051250 50644 45694 12554 13926 73111260 51000 46060 12675 14066 74171270 51355 46425 12796 14207 75241280 51708 46789 12917 14347 76321290 52060 47152 13038 14488 77401300 52410 47513 13159 14629 78481310 52759 13280 14770 79571320 53106 13402 14911 80661330 53451 13523 15052 81761340 53795 13644 15193 82861350 54138 13766 15334 83971360 54479 13887 15475 85081370 54819 14009 15616 86201380 14130 15758 87311390 14251 15899 88441400 14373 16040 89561410 14494 16181 90691420 14615 16323 91821430 14736 16464 92961440 14857 16605 94101450 14978 16746 95241460 15099 16887 96391470 15220 17028 97531480 15341 17169 98681490 15461 17310 99841500 15582 17451 100991510 15702 17591 102151520 15822 17732 103311530 15942 17872 104471540 16062 18012 105631550 16182 18152 106791560 16301 18292 107961570 16420 18431 109131580 16539 18571 110291590 16658 18710 111461600 16777 18849 112631610 16895 18988 113801620 17013 19126 114971630 17131 19264 116141640 17249 19402 117311650 17366 19540 118481660 17483 19677 119651670 17600 19814 120821680 17717 19951 121991690 17832 20087 123161700 17947 20222 124331710 18061 20356 125491720 18174 20488 126661730 18285 20620 127821740 18395 20749 128981750 18503 20877 130141760 18609 21003 131301770 132461780 133611790 134761800 13591

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Resistance values in ohm for PT100 acc. to IEC 751

°C (ITS90) 0,00 1 2 3 4 5 6 7 8 9

-200 18,52-190 22,83 22,40 21,97 21,54 21,11 20,68 20,25 19,82 19,38 18,95-180 27,10 26,67 26,24 25,82 25,39 24,97 24,54 24,11 23,68 23,25-170 31,34 30,91 30,49 30,07 29,64 29,22 28,80 28,37 27,95 27,52-160 35,54 35,12 34,70 34,28 33,86 33,44 33,02 32,60 32,18 31,76-150 39,72 39,31 38,89 38,47 38,05 37,64 37,22 36,80 36,38 35,96-140 43,88 43,46 43,05 42,63 42,22 41,80 41,39 40,97 40,56 40,14-130 48,00 47,59 47,18 46,77 46,36 45,94 45,53 45,12 44,70 44,29-120 52,11 51,70 51,29 50,88 50,47 50,06 49,65 49,24 48,83 48,42-110 56,19 55,79 55,38 54,97 54,56 54,15 53,75 53,34 52,93 52,52-100 60,26 59,85 59,44 59,04 58,63 58,23 57,82 57,41 57,01 56,60-90 64,30 63,90 63,49 63,09 62,68 62,28 61,88 61,47 61,07 60,66-80 68,33 67,92 67,52 67,12 66,72 66,31 65,91 65,51 65,11 64,70-70 72,33 71,93 71,53 71,13 70,73 70,33 69,93 69,53 69,13 68,73-60 76,33 75,93 75,53 75,13 74,73 74,33 73,93 73,53 73,13 72,73-50 80,31 79,91 79,51 79,11 78,72 78,32 77,92 77,52 77,12 76,73-40 84,27 83,87 83,48 83,08 82,69 82,29 81,89 81,50 81,10 80,70-30 88,22 87,83 87,43 87,04 86,64 86,25 85,85 85,46 85,06 84,67-20 92,16 91,77 91,37 90,98 90,59 90,19 89,80 89,40 89,01 88,62-10 96,09 95,69 95,30 94,91 94,52 94,12 93,73 93,34 92,95 92,55-0 100,00 99,61 99,22 98,83 98,44 98,04 97,65 97,26 96,87 96,480 100,00 100,39 100,78 101,17 101,56 101,95 102,34 102,73 103,12 103,5110 103,90 104,29 104,68 105,07 105,46 105,85 106,24 106,63 107,02 107,4020 107,79 108,18 108,57 108,96 109,35 109,73 110,12 110,51 110,90 111,2930 111,67 112,06 112,45 112,83 113,22 113,61 114,00 114,38 114,77 115,1540 115,54 115,93 116,31 116,70 117,08 117,47 117,86 118,24 118,63 119,0150 119,40 119,78 120,17 120,55 120,94 121,32 121,71 122,09 122,47 122,8660 123,24 123,63 124,01 124,39 124,78 125,16 125,54 125,93 126,31 126,6970 127,08 127,46 127,84 128,22 128,61 128,99 129,37 129,75 130,13 130,5280 130,90 131,28 131,66 132,04 132,42 132,80 133,18 133,57 133,95 134,3390 134,71 135,09 135,47 135,85 136,23 136,61 136,99 137,37 137,75 138,13

100 138,51 138,88 139,26 139,64 140,02 140,40 140,78 141,16 141,54 141,91110 142,29 142,67 143,05 143,43 143,80 144,18 144,56 144,94 145,31 145,69120 146,07 146,44 146,82 147,20 147,57 147,95 148,33 148,70 149,08 149,46130 149,83 150,21 150,58 150,96 151,33 151,71 152,08 152,46 152,83 153,21140 153,58 153,96 154,33 154,71 155,08 155,46 155,83 156,20 156,58 156,95150 157,33 157,70 158,07 158,45 158,82 159,19 159,56 159,94 160,31 160,68160 161,05 161,43 161,80 162,17 162,54 162,91 163,29 163,66 164,03 164,40170 164,77 165,14 165,51 165,89 166,26 166,63 167,00 167,37 167,74 168,11180 168,48 168,85 169,22 169,59 169,96 170,33 170,70 171,07 171,43 171,80190 172,17 172,54 172,91 173,28 173,65 174,02 174,38 174,75 175,12 175,49200 175,86 176,22 176,59 176,96 177,33 177,69 178,06 178,43 178,79 179,16210 179,53 179,89 180,26 180,63 180,99 181,36 181,72 182,09 182,46 182,82220 183,19 183,55 183,92 184,28 184,65 185,01 185,38 185,74 186,11 186,47230 186,84 187,20 187,56 187,93 188,29 188,66 189,02 189,38 189,75 190,11240 190,47 190,84 191,20 191,56 191,92 192,29 192,65 193,01 193,37 193,74250 194,10 194,46 194,82 195,18 195,55 195,91 196,27 196,63 196,99 197,35260 197,71 198,07 198,43 198,79 199,15 199,51 199,87 200,23 200,59 200,95270 201,31 201,67 202,03 202,39 202,75 203,11 203,47 203,83 204,19 204,55280 204,90 205,26 205,62 205,98 206,34 206,70 207,05 207,41 207,77 208,13290 208,48 208,84 209,20 209,56 209,91 210,27 210,63 210,98 211,34 211,70300 212,05 212,41 212,76 213,12 213,48 213,83 214,19 214,54 214,90 215,25

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Resistance values in ohm for PT100 acc. to IEC 751

°C (ITS90) 0,00 1 2 3 4 5 6 7 8 9

310 215,61 215,96 216,32 216,67 217,03 217,38 217,74 218,09 218,44 218,80320 219,15 219,51 219,86 220,21 220,57 220,92 221,27 221,63 221,98 222,33330 222,68 223,04 223,39 223,74 224,09 224,45 224,80 225,15 225,50 225,85340 226,21 226,56 226,91 227,26 227,61 227,96 228,31 228,66 229,02 229,37350 229,72 230,07 230,42 230,77 231,12 231,47 231,82 232,17 232,52 232,87360 233,21 233,56 233,91 234,26 234,61 234,96 235,31 235,66 236,00 236,35370 236,70 237,05 237,40 237,74 238,09 238,44 238,79 239,13 239,48 239,83380 240,18 240,52 240,87 241,22 241,56 241,91 242,26 242,60 242,95 243,29390 243,64 243,99 244,33 244,68 245,02 245,37 245,71 246,06 246,40 246,75400 247,09 247,44 247,78 248,13 248,47 248,81 249,16 249,50 249,85 250,19410 250,53 250,88 251,22 251,56 251,91 252,25 252,59 252,93 253,28 253,62420 253,96 254,30 254,65 254,99 255,33 255,67 256,01 256,35 256,70 257,04430 257,38 257,72 258,06 258,40 258,74 259,08 259,42 259,76 260,10 260,44440 260,78 261,12 261,46 261,80 262,14 262,48 262,82 263,16 263,50 263,84450 264,18 264,52 264,86 265,20 265,53 265,87 266,21 266,55 266,89 267,22460 267,56 267,90 268,24 268,57 268,91 269,25 269,59 269,92 270,26 270,60470 270,93 271,27 271,61 271,94 272,28 272,61 272,95 273,29 273,62 273,96480 274,29 274,63 274,96 275,30 275,63 275,97 276,30 276,64 276,97 277,31490 277,64 277,98 278,31 278,64 278,98 279,31 279,64 279,98 280,31 280,64500 280,98 281,31 281,64 281,98 282,31 282,64 282,97 283,31 283,64 283,97510 284,30 284,63 284,97 285,30 285,63 285,96 286,29 286,62 286,95 287,29520 287,62 287,95 288,28 288,61 288,94 289,27 289,60 289,93 290,26 290,59530 290,92 291,25 291,58 291,91 292,24 292,56 292,89 293,22 293,55 293,88540 294,21 294,54 294,86 295,19 295,52 295,85 296,18 296,50 296,83 297,16550 297,49 297,81 298,14 298,47 298,80 299,12 299,45 299,78 300,10 300,43560 300,75 301,08 301,41 301,73 302,06 302,38 302,71 303,03 303,36 303,69570 304,01 304,34 304,66 304,98 305,31 305,63 305,96 306,28 306,61 306,93580 307,25 307,58 307,90 308,23 308,55 308,87 309,20 309,52 309,84 310,16590 310,49 310,81 311,13 311,45 311,78 312,10 312,42 312,74 313,06 313,39600 313,71 314,03 314,35 314,67 314,99 315,31 315,64 315,96 316,28 316,60610 316,92 317,24 317,56 317,88 318,20 318,52 318,84 319,16 319,48 319,80620 320,12 320,43 320,75 321,07 321,39 321,71 322,03 322,35 322,67 322,98630 323,30 323,62 323,94 324,26 324,57 324,89 325,21 325,53 325,84 326,16640 326,48 326,79 327,11 327,43 327,74 328,06 328,38 328,69 329,01 329,32650 329,64 329,96 330,27 330,59 330,90 331,22 331,53 331,85 332,16 332,48660 332,79 333,11 333,42 333,74 334,05 334,36 334,68 334,99 335,31 335,62670 335,93 336,25 336,56 336,87 337,18 337,50 337,81 338,12 338,44 338,75680 339,06 339,37 339,69 340,00 340,31 340,62 340,93 341,24 341,56 341,87690 342,18 342,49 342,80 343,11 343,42 343,73 344,04 344,35 344,66 344,97700 345,28 345,59 345,90 346,21 346,52 346,83 347,14 347,45 347,76 348,07710 348,38 348,69 348,99 349,30 349,61 349,92 350,23 350,54 350,84 351,15720 351,46 351,77 352,08 352,38 352,69 353,00 353,30 353,61 353,92 354,22730 354,53 354,84 355,14 355,45 355,76 356,06 356,37 356,67 356,98 357,28740 357,59 357,90 358,20 358,51 358,81 359,12 359,42 359,72 360,03 360,33750 360,64 360,94 361,25 361,55 361,85 362,16 362,46 362,76 363,07 363,37760 363,67 363,98 364,28 364,58 364,89 365,19 365,49 365,79 366,10 366,40770 366,70 367,00 367,30 367,60 367,91 368,21 368,51 368,81 369,11 369,41780 369,71 370,01 370,31 370,61 370,91 371,21 371,51 371,81 372,11 372,41790 372,71 373,01 373,31 373,61 373,91 374,21 374,51 374,81 375,11 375,41800 375,70 376,00 376,30 376,60 376,90 377,19 377,49 377,79 378,09 378,39810 378,68 378,98 379,28 379,57 379,87 380,17 380,46 380,76 381,06 381,35820 381,65 381,95 382,24 382,54 382,83 383,13 383,42 383,72 384,01 384,31830 384,60 384,90 385,19 385,49 385,78 386,08 386,37 386,67 386,96 387,25840 387,55 387,84 388,14 388,43 388,72 389,02 389,31 389,60 389,90 390,19850 390,48

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