Thermocouple

A thermocouple is a pair of metallic conductors made of different materials that are connected at one end and are suitable for temperature measurement due to the thermoelectric effect . In principle, the thermocouple delivers electrical energy from heat at a temperature difference along the electrical conductor. The electrical voltage that occurs at the ends of the metallic conductors is comparatively small and is in the range of a few 10 µV per 1 ° C temperature difference. Even with high temperature differences above 1000 ° C and selected materials with high sensitivity , the achievable electrical voltages are below or in the order of magnitude of 0.1 V. Several thermocouples connected in series form a thermal chain , which supplies an electrical voltage that is higher by the number.

Symbol of the thermocouple for circuit diagrams in accordance with standardization with indication of polarity or identification of the negative pole with a wider line

Thermoelectric generators ( TEG ) usually use a thermal chain and serve as an electrical generator to provide electrical energy. The functional reversal of this principle - pumping thermal energy by means of an externally supplied electrical power - turns the thermo into a Peltier element .

Note: The graph of type R is reversed with that of type S.

Basics

Schematic measuring circuit with a thermocouple

Seebeck effect

Tip of a type J welded thermocouple

The thermoelectric or Seebeck effect is the term used to describe the occurrence of a thermal voltage due to a temperature gradient along an electrical conductor. This electrical voltage or potential difference is a function of the temperature difference along the conductor and is different for each conductor material. The characteristics are only approximately linear.

In order to be able to measure an electrical voltage at the two conductor ends, the return conductor must be made of a different material than the forward conductor, as shown in the schematic measurement circuit shown here. With the same material in both conductors, the same amount of potential differences would arise, which would cancel each other out in a closed circuit . The connection point of a thermocouple that is exposed to the temperature to be measured has the function of a measuring point , the transition to the (copper) lines leading to the voltage measuring device has the function of a reference point . (Any further temperature-related potential difference along the supply lines is excluded from the voltage measurement if the lines are the same.)

Each thermal voltage stands for a temperature difference between the measuring and reference junction. In order to be able to determine the actual temperature of the measuring point, the temperature of the comparison point must be known, see below . This temperature must also be known because, due to the non-linear relationship, depending on the reference junction temperature, each thermal voltage has a different temperature difference.

The sensitivity of a single conductor cannot be measured in the measuring arrangement; it is given as a thermoelectric coefficient in comparison to a reference material, platinum is common . These material data, which are specified for a fixed temperature and sorted by size, form the thermoelectric voltage series . The values of these thermoelectric coefficients depend on the alloy ratio or degree of purity of the metals used. Targeted admixtures can be used to produce materials with reproducible, reasonably long-term stable thermoelectric coefficients.

Mathematical description

Type K thermocouple with a plug; Its contact pins are also made of thermal material; they cannot be interchanged when plugging in

The relationship between electrical voltage and measuring point temperature at the reference junction temperature is established for some pairs of materials by standardization in reference functions , namely in several different equations for different temperature ranges. The characteristics are curved, the equations are complicated, the relationships are preferably shown in tables. ${\ displaystyle U _ {\ mathrm {th}}}$ ${\ displaystyle t _ {\ mathrm {M}}}$ ${\ displaystyle t _ {\ mathrm {V}} = 0 \, ^ {\ circ} \ mathrm {C}}$ ${\ displaystyle U _ {\ mathrm {th}} = f (t _ {\ mathrm {M}})}$

A linear approximation can be used for rough calculations in a certain subrange . The following example shows the voltage on a type K thermocouple. This consists of a nickel-chromium alloy and nickel. With the thermoelectric coefficients and we get: ${\ displaystyle k _ {\ mathrm {NiCr}}}$ ${\ displaystyle k _ {\ mathrm {Ni}}}$

{\ displaystyle U _ {\ mathrm {th}} = (k _ {\ mathrm {NiCr}} -k _ {\ mathrm {Ni}}) \ cdot \ Delta t}

With

{\ displaystyle \ Delta t = t _ {\ mathrm {M}} -t _ {\ mathrm {V}}}

However, the coefficients themselves depend on the temperature, just like the Seebeck coefficient of the thermocouple, which indicates the sensitivity . ${\ displaystyle \ mathrm {d} U _ {\ mathrm {th}} / \ mathrm {d} t _ {\ mathrm {M}}}$

The resolution of the reference functions is easy with a linear approach. For the non-linear case, the standard also gives these inverse equations. ${\ displaystyle t _ {\ mathrm {M}} = f (U _ {\ mathrm {Th}})}$

Materials for measuring purposes

Bendable sheathed thermocouple in stainless steel jacket of 0.5 mm ⌀

Industrial thermocouple in protective tube with connection head.
The broken part shows the thermal wires including the insulation in the protective tube of the measuring insert (mostly made of ceramic), which is inserted in an outer protective tube (made of ceramic or metal, depending on the application)

When selecting a material pairing for measurement purposes, one strives for high thermal voltage, high linearity and high corrosion resistance at high temperatures. These goals cannot be achieved with a single combination. Therefore, different material pairings are used depending on the application.

Ten thermocouples are internationally standardized, each of which is identified by a capital letter. Widespread are:

Nickel-chromium / nickel (type K; most common type with thermal voltages between −6.458 mV at −270 ° C and 52.410 mV at 1300 ° C) with a sensitivity of about 40 µV / ° C (above 0 ° C)
Iron / copper-nickel (type J; for industrial applications with thermal voltages between −8.095 mV at −210 ° C and 69.553 mV at 1200 ° C) with slightly higher sensitivity, but less linear
Platinum-rhodium / platinum (types R and S; for high temperatures, up to approx. 20 mV) with a sensitivity of 5… 12 µV / ° C depending on the temperature

The respective positive conductor is given first; it has a positive potential compared to the other conductor at a positive temperature difference at which the measuring point is warmer than the reference point.

In addition, two high-purity thermocouples gold-platinum and platinum-palladium are standardized, but their handling is difficult.

Brand names such as Chromel or Konstantan are no longer used in standardization.

For the measurement of high temperatures, the standardization has been expanded to include tungsten-based thermocouples up to 2500 ° C. For the measurement of low temperatures, gold-based thermocouples have been developed, but their thermal voltages are not (yet) reproducible enough for a uniform definition.

To protect against contaminating, corrosive or abrasive influences from the environment, thermocouples are manufactured for industrial use as sheathed thermocouples or as measuring inserts with a protective tube. The measuring insert is operated in an outer protective tube with a connection head for easy interchangeability - even during operation.

history

The first thermocouple was described by Thomas Johann Seebeck in 1821 . In 1826, as a result of his research on thermoelectricity , Antoine César Becquerel recommended the use of a thermocouple made of platinum and palladium and thus was the first to introduce platinum into thermoelectric measurement technology, which is still the most common material for the construction of precious metal thermocouples today. In 1885, Henry Le Chatelier developed the first thermocouple that was used in practical measurement technology. Its positive leg consisted of a platinum - rhodium - alloy having a rhodium content of 10%, the negative leg consisted of pure platinum. This thermocouple, which is also known as the Le Chatelier thermocouple , is still the most common precious metal thermocouple in its composition and is standardized as type S.

In the first half of the 20th century, mainly thermocouples made of base metals found their way into practice. Numerous pairings have been researched in order to generate the most stable, linear and high thermal voltage possible. In the second half of the 20th century, the platinum-rhodium thermocouples were further developed, whereby the rhodium content of both legs was varied in order to find the ideal alloy for different operating conditions.

Further thermocouples have also been developed in order to achieve higher accuracies and to expand the temperature range. The latter was achieved primarily through the development of the tungsten - rhenium thermocouples, which were first used in 1962 to measure the hydrogen temperature in a nuclear reactor . With this thermocouple, it was possible for the first time to measure temperatures above 2,000 ° C in a touch-like manner. The W-Re thermocouples became famous in 1963 when NASA announced that they would be used to measure the temperature on the heat shield of the Apollo spacecraft in order to measure its temperature when it re-entered the earth's atmosphere, with temperatures of 2,300 ° C occurring. With further modifications to the W-Re thermocouples, it was possible in 1967 to exceed 3,000 ° C.

Comparison of different thermocouples

The following table gives characteristic data (largely from) and the identification of different types of thermocouples.

Due to the expected drift, it is recommended to maintain an upper operating temperature that is dependent on the wire diameter. For types K, J, N, E, T, a continuous service life of 10,000 h in clean air is expected, for the precious metal types R, S, B of 2,000 h. With the information in brackets, a shortened service life of 250 h or 50 h is expected.

In the information on the limit deviation , the Celsius temperature of the measuring point stands for . Of the two pieces of information, the larger of the two applies, namely the amount. For example, a thermocouple with the specification “1.5 ° C or 0.004 × ” can measure the temperature at 1000 ° C with a deviation of up to –4 ° C or up to +4 ° C. The guaranteed limit deviations only apply to thermowires marked as belonging together in the delivery condition. ${\ displaystyle t}$ ${\ displaystyle | t |}$

Type	materials	can be used up to ... ° C	defined from ... to ... ° C	Limit deviation in class 1	Limit deviation in class 2
K	NiCr-Ni	750 - 1100 (850 - 1200)	−270 to +1300	1.5 ° C or 0.004 × in −40 to 1000 ° C ${\ displaystyle \| t \|}$	2.5 ° C or 0.0075 × in −40 to 1200 ° C ${\ displaystyle \| t \|}$
J	Fe-CuNi	400-600 (500-750)	−210 to +1200	1.5 ° C or 0.004 × in −40 to 750 ° C ${\ displaystyle \| t \|}$	2.5 ° C or 0.0075 × in −40 to 750 ° C ${\ displaystyle \| t \|}$
N	NiCrSi-NiSi	850 - 1200 (900 - 1250)	−270 to +1300	1.5 ° C or 0.004 × in −40 to 1000 ° C ${\ displaystyle \| t \|}$	2.5 ° C or 0.0075 × in −40 to 1200 ° C ${\ displaystyle \| t \|}$
E.	NiCr-CuNi	440-690 (480-800)	−270 to +1000	1.5 ° C or 0.004 × in −40 to 800 ° C ${\ displaystyle \| t \|}$	2.5 ° C or 0.0075 × in −40 to 900 ° C ${\ displaystyle \| t \|}$
T	Cu-CuNi	200-300 (250-350)	−270 to +400	0.5 ° C or 0.004 × in −40 to 350 ° C ${\ displaystyle \| t \|}$	1 ° C or 0.0075 × in −40 to 350 ° C ${\ displaystyle \| t \|}$
R.	Pt13Rh-Pt	1400 (1600)	−50 to +1768	1 ° C in 0 to 1100 ° C or 1 ° C + 0.003 × ( −1100 ° C) in 1100 to 1600 ° C ${\ displaystyle t}$	1.5 ° C or 0.0025 × in 0 to 1600 ° C ${\ displaystyle t}$
S.	Pt10Rh-Pt	1400 (1600)	−50 to +1768	1 ° C in 0 to 1100 ° C or 1 ° C + 0.003 × ( −1100 ° C) in 1100 to 1600 ° C ${\ displaystyle t}$	1.5 ° C or 0.0025 × in 0 to 1600 ° C ${\ displaystyle t}$
B.	Pt30Rh-Pt6Rh	1500 (1700)	0 to +1820	- - -	1.5 ° C or 0.0025 × in 600 to 1700 ° C ${\ displaystyle t}$
C.	W5Re-W26Re		0 to 2315	- - -	0.01 × in 426 to 2315 ° C ${\ displaystyle t}$
A.	W5Re-W20Re		0 to 2500	- - -	0.01 × in 1000 to 2500 ° C ${\ displaystyle t}$
	AuFe-NiCr	−272 - +300	not available	0.2% of the voltage is reproducible; each sensor has to be calibrated individually.

For the measurement of low temperatures, with types T, E, K, N, limit deviations can also be guaranteed down to −200 ° C in class 3 when using selected material.

The order states of NiCr-Ni thermocouples

In the case of NiCr-Ni thermocouples, different states of order appear, which are caused by the temperature and cooling rate of the NiCr alloy. In this context, one speaks of the K-state (ordered state) and the U-state (disordered state). In both states, the thermocouple generates a reproducible thermal voltage, but the deviations from one another can be up to 5 K. The NiCr alloy has a face-centered cubic crystal lattice . In the K state, chromium atoms form the corners and the nickel atoms are in the center of the surfaces. This state always occurs at temperatures above 600 ° C. If the thermocouple is allowed to cool down at a rate of more than 100 K / h in the range of 600 ... 400 ° C, "disturbances" result in the crystal lattice, ie. H. Nickel atoms at the corners of the structure and chromium atoms in the center. This arrangement is called the U-state. At higher cooling rates, the atoms do not have time to break out of the ordered state. Since temperature is a very sluggish quantity in metrological practice, NiCr-Ni thermocouples usually cool down too slowly, and the K state is established below 600 ° C. This effect can be minimized by adding silicon to the extent that it is negligible in terms of measurement technology. This has been implemented with the thermocouple type N, NiCrSi-NiSi, but it is only slowly finding its way into metrological practice.

Efficiency

The voltage generated depends on the temperature difference and the Seebeck coefficient : ${\ displaystyle U _ {\ mathrm {th}}}$ ${\ displaystyle \ Delta T = T _ {\ mathrm {h}} -T _ {\ mathrm {l}}}$ ${\ displaystyle \ alpha}$

{\ displaystyle U _ {\ mathrm {th}} = \ alpha \, \ Delta T}

The dimensionless ratio (Engl. Figure of merit ) determines the efficiency . grows quadratically with and linearly with the mean absolute use temperature. The greater the electrical conductivity and the smaller the specific thermal conductivity , the greater it is: ${\ displaystyle ZT}$ ${\ displaystyle \ eta}$ ${\ displaystyle ZT}$ ${\ displaystyle \ alpha}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ lambda}$

{\ displaystyle ZT = {\ frac {\ alpha ^ {2} \, T \, \ sigma} {\ lambda}}}

And the following applies to the efficiency:

{\ displaystyle \ eta = {\ frac {{\ sqrt {1 + ZT}} - 1} {{\ sqrt {1 + ZT}} + T _ {\ mathrm {l}} / T _ {\ mathrm {h}} }} \, \ eta _ {\ mathrm {carnot}}}

With

{\ displaystyle \ eta _ {\ mathrm {carnot}} = {\ frac {T _ {\ mathrm {h}} -T _ {\ mathrm {l}}} {T _ {\ mathrm {h}}}}}

Ideally, it is infinite and the maximum efficiency. ${\ displaystyle ZT}$ ${\ displaystyle \ eta _ {\ mathrm {carnot}}}$

Example: With an operating temperature of , an ambient temperature of and a figure of merit , the efficiency of the Carnot efficiency is , in total, a maximum . With it increases to the Carnot efficiency so overall . In use, efficiencies have so far hardly been greater than achieved. ${\ displaystyle T _ {\ mathrm {h}} = 500 \; \ mathrm {K}}$ ${\ displaystyle T _ {\ mathrm {l}} = 300 \; \ mathrm {K}}$ ${\ displaystyle ZT = 1}$ ${\ displaystyle 20 \, \%}$ ${\ displaystyle 40 \, \%}$ ${\ displaystyle 8 \, \%}$ ${\ displaystyle ZT = 2}$ ${\ displaystyle 30 \, \%}$ ${\ displaystyle 12 \, \%}$ ${\ displaystyle 5 \, \%}$

In metals, the electrical conductivity correlates with the thermal conductivity, since the contributions from electrons dominate in both. According to the Wiedemann-Franz estimate , the reciprocal of , the Lorenz number , is included . depends only on the Seebeck coefficient. For metals it is significantly smaller than and therefore significantly smaller than . In semiconductors, the phononic and electronic components and thus the two conductivities can be decoupled. Highly doped semiconductors and quantum well nanostructures achieve ZT values of up to . ${\ displaystyle T \ sigma / \ lambda}$ ${\ displaystyle 2 {,} 5 \ cdot 10 ^ {- 8} \; \ mathrm {V ^ {2} / K ^ {2}}}$ ${\ displaystyle ZT}$ ${\ displaystyle 100 \, \ mu {\ text {V}} / {\ text {K}}}$ ${\ displaystyle ZT}$ ${\ displaystyle 0 {,} 4}$ ${\ displaystyle 1 {,} 5}$ ${\ displaystyle 2 {,} 6}$

Applications

Temperature measurement

This data acquisition device can measure up to 60 thermal voltages

An open slot for the data acquisition device with 20 connected thermocouples

Temperature difference

With a measuring circuit - as in the picture above in the basics - three different material combinations arise through transitions to copper conductors: A → B, B → Cu, Cu → A. At the same temperature at both connection terminals, the copper potential drops out of the calculation, and what remains at this point is the potential difference of the combination B → A. The connection terminals thus take on the function of the comparison point. The reference junction can be relocated to a more distant location by means of so-called extension cables or compensating cables , e.g. B. in industrial plants up to the control room. These extension cables are made of identical thermal materials and the compensating cables are made of cheaper materials that have the same thermoelectric properties as the thermocouple itself over a limited temperature range.

Temperature instead of temperature difference

Since only a temperature difference can be determined with the aid of a thermocouple, a cold junction compensation (CJC) is necessary to measure the temperature . In the simplest case, the temperature at the transition point (the reference junction temperature) must be known; The temperature difference for the measured thermal voltage is read off in a table; this is added to the reference junction temperature. This procedure can only be used if a linear approximation is permissible.

For many measurement purposes, the relationship between thermal voltage and temperature difference is not sufficiently linear. Before using the table, note the reference temperature from which the table is calculated (0 mV mostly at 0 ° C). If there is a difference between the reference junction and reference temperature, the measured voltage must be corrected before using the table by the table value of the voltage that corresponds to the reference junction temperature . In the case of a curved characteristic curve, the following rule applies to include the comparison point:

The addition of partial voltages correctly leads to the total voltage. The addition of the associated table values of the partial temperatures does not lead to the total temperature!

The thermal voltage can be processed by a suitable amplifier in order to be able to distribute it resiliently. Commercially available measuring transducers amplify, also take into account the (variable) reference junction temperature and linearize the output signal and temperature at a specified reference junction temperature (temperature-linear instead of voltage-linear output signal).

Inclusion of the reference junction temperature

Closed circuit for measurement with two elements made of metals A and B.

Cold junction compensation in one measuring device. A temperature sensor that measures the temperature at the transfer point is embedded in the white heat-conducting compound between the two metal contacts (sensor connection)

To include the reference junction temperature in the measurement, a second thermocouple of the same type can be connected in series with opposite polarity to the thermocouple. If its temperature is kept stable at a known value (e.g. in ice water for 0 ° C or in a cold junction thermostat for 50 ° C), then this temperature becomes the stable cold junction temperature.

A circuit with two thermocouples initially contains two metal junctions (measuring and reference junction), whose thermal voltages in the circuit are directed in opposite directions. There are also two more transitions when a voltmeter is connected. At the same temperature at both transition points, two identical thermal voltages arise, which cancel each other out; the temperature of the transition points is irrelevant here.

As an alternative to the second thermocouple, a compensation circuit with a temperature sensor is used, which supplies a voltage as high as that from a thermocouple. For example, it generates as much voltage in the range of 0 to 50 ° C as a thermocouple of the required type at a temperature difference of 20 ° C. This corrects it to a fixed reference junction temperature of 20 ° C.

Integrated circuits to support the temperature measurement with thermocouples not only serve as amplifiers for the measured voltage, but they also compensate the reference junction temperature in terms of circuitry - provided they have the same temperature as the connection / reference junction. This method is often used in digital multimeters that are equipped with a thermocouple to measure temperature.

In addition to the analog-technical inclusion of the comparison point, there is also the digital-technical one. The thermal voltage is measured and the variable reference junction temperature at the terminal point is also determined with a thermistor such as a Pt100. The digitized measured value of the thermal voltage, which represents a temperature difference, is corrected mathematically. This so-called internal temperature compensation is provided by many modern evaluation units such as programmable logic controllers or compact controllers, for example. It is important that the thermocouples are connected to the evaluation unit directly or via the mentioned extension cables or compensating cables . If other materials are used, the reference junction does not arise on the field device and incorrect measurements result. The evaluation units usually have the characteristics of the thermocouples defined in the DIN EN 60584-1 standard (see table above). The characteristic curve must be selected on the field device according to the thermocouple used.

Aging of thermocouples

Thermocouples are often used at high temperatures and in reactive furnace atmospheres. Here the service life is limited in practice by aging. The thermoelectric coefficients of the wires in the area of the higher temperature change over time and with them the thermal voltage. Both a decrease and an increase in the thermal voltage are observed, depending on the type of thermocouple and the operating temperature. It is important here that the simple consideration of the temperature differences between the connection points only applies if the wires are otherwise homogeneous. However, this is precisely not the case with an aged thermocouple. The properties of the metals in the area of the temperature gradient are decisive for the development of the thermal voltage . Therefore, if a permanently installed, aged thermocouple is pulled out of the furnace a little, the metal, which has aged at a high temperature inside the furnace, comes into the entire range of the temperature gradient, and the measurement error increases considerably. Conversely, if an aged thermocouple is pushed deeper into the furnace, it will display again accurately.

Radiation measurement

The series connection of several thermocouples results in a thermo chain ( thermopile ). The thermoelectric voltage multiplies with the number of thermocouples. Thermal chains are used in sensitive infrared detectors and laser power meters. The temperature difference is measured along a heat conductor (disc, cone) by attaching the connection points of the thermocouples alternately closer or further away from the absorption surface. In the case of sensitive structures, the thermocouples themselves form the heat conductor.

Monitoring of combustion systems

Thermal fuse with thermocouple, lead with contact and magnetic switch

In gas stoves and gas water heaters , thermocouples are used to monitor the burning flame. The thermocouple heated by the flame supplies the electrical current required to keep a fuel valve open electromagnetically. If the flame goes out, the thermocouple cools down, the solenoid valve closes and the further fuel supply is interrupted. The method has the advantage that it does not require any auxiliary energy. The disadvantage of this system is that it reacts very slowly and therefore a certain amount of gas can flow out.

In heating systems, this thermal fuse has been replaced by ignition fuses due to its inertia , which monitor the ionization of the flame and its conductivity. They react faster, but require an auxiliary power source .

On the right of the picture you can see the usual thermocouple of such a thermal fuse. When hot, it supplies around 30 ... 40 mV voltage and a current of several amperes, with which a special solenoid valve ( electromagnet with, for example, 16 milliohm coil resistance), which was previously opened manually by pressing a button, can be kept open. When it cools down, the magnet position drops again within 30 seconds (audible click) and the valve closes.

Thermoelectric generator

Principle structure of a thermoelectric generator (same structure as Peltier element )

The direct conversion of heat into electrical energy is possible with a "thermoelectric generator" ( thermovoltaics ). Instead of metals, semiconductor materials are used here, similar to the Peltier element , which significantly increases the efficiency compared to metallic thermocouples. The efficiency of thermoelectric generators is around 17%, a fraction of the Carnot efficiency . In terms of simple construction, reliability and service life, however, they are superior to all other methods.

Common materials are Bi ₂ Te ₃ , lead telluride PbTe, SiGe, BiSb or FeSi ₂ with achievable efficiencies between three and eight percent. In order to obtain sufficiently high voltages, several elements mounted between the cold and the warm side are electrically connected in series.

Petroleum lamps, petroleum gas burners or charcoal grills equipped with thermoelectric generators are used as electrical energy sources for low power in remote areas, for example to operate a radio receiver.

Thermoelectric generators are also used in radionuclide batteries , for example for space probes (e.g. because the distance from the sun is too great ) or in remote measuring probes, when solar cells cannot be used to generate energy. The radioactive decay of artificially produced radioisotopes generates the heat required for operation.

literature

Daniel Jänsch (Ed.): Thermoelectrics. An opportunity for the automotive industry. expert-Verlag, Renningen 2009, ISBN 978-3-8169-2877-5 ( Haus der Technik textbook ).

Web links

Commons : Thermocouples - collection of images, videos and audio files

Individual evidence

↑ ^a ^b ^c ^d ^e ^f DIN EN 60584-1: 2014-07: Thermocouples - Part 1: Thermal voltages and limit deviations (IEC 60584-1: 2013)
↑ ^a ^b ^c VDI / VDE guideline 3511 sheet 2: Technical temperature measurements - contact thermometer , 1996
↑ Frank Bernhard (Ed.): Technical Temperature Measurement Volume III: Physical and Metrological Basics , Springer, 2004, p. 765
↑ DIN EN 60617-8: 1997, No. 08-06-01 and -02
↑ Database of the National Institute of Standards and Technology (NIST)
↑ Data sheet of the NiCr alloy
↑ DIN EN 62460: 2009-05 Temperature - tables of the electromotive force (EMF) for combinations of pure element thermocouples (IEC 62460: 2008)
^ Franz X. Eder: Working methods of thermodynamics: Volume 1: Temperature measurement. Springer, 1981, p. 252 ff
↑ ^a ^b László von Körtvélyessy: Thermoelement-Praxis , Vulkan, 1998
↑ ^a ^b DIN EN 60584-3: 2008-08: Thermocouples - Part 3: Extension cables and compensating cables - Limit deviations and labeling system (IEC 60584-3: 2007)
↑ http ://www. Temperaturblog.de/2011/09/15/der-k-effekt-von-typ-k-thermoelemente/
↑ Matthias Nau: Electrical temperature measurement with thermocouples and resistance thermometers . JUMO, Fulda 2007, ISBN 978-3-935742-06-1 ( full text [PDF; 4.5 MB ]).
↑ Archived copy ( Memento from May 11, 2014 in the Internet Archive )
^ Marius Beul: Alternative power generation (2) . In: elektor . October 2008, p. 8–9 ( elektor.de ).

[D584-1] ↑ ^a ^b ^c ^d ^e ^f DIN EN 60584-1: 2014-07: Thermocouples - Part 1: Thermal voltages and limit deviations (IEC 60584-1: 2013)

[V11-2-2] VDI / VDE guideline 3511 sheet 2: Technical temperature measurements - contact thermometer , 1996

[3] Frank Bernhard (Ed.): Technical Temperature Measurement Volume III: Physical and Metrological Basics , Springer, 2004, p. 765

[4] DIN EN 60617-8: 1997, No. 08-06-01 and -02

[5] Database of the National Institute of Standards and Technology (NIST)

[6] Data sheet of the NiCr alloy

[7] DIN EN 62460: 2009-05 Temperature - tables of the electromotive force (EMF) for combinations of pure element thermocouples (IEC 62460: 2008)

[8] Franz X. Eder: Working methods of thermodynamics: Volume 1: Temperature measurement. Springer, 1981, p. 252 ff

[vK-9] László von Körtvélyessy: Thermoelement-Praxis , Vulkan, 1998

[D584-3-10] DIN EN 60584-3: 2008-08: Thermocouples - Part 3: Extension cables and compensating cables - Limit deviations and labeling system (IEC 60584-3: 2007)

[11] ttp ://www. Temperaturblog.de/2011/09/15/der-k-effekt-von-typ-k-thermoelemente/

[12] Matthias Nau: Electrical temperature measurement with thermocouples and resistance thermometers . JUMO, Fulda 2007, ISBN 978-3-935742-06-1 ( full text [PDF; 4.5 MB ]).

[13] Archived copy ( Memento from May 11, 2014 in the Internet Archive )

[14] Marius Beul: Alternative power generation (2) . In: elektor . October 2008, p. 8–9 ( elektor.de ).