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A thermocouple is a temperature-measuring device consisting of two dissimilar conductors that contact each other at one or more spots. It produces a voltage when the temperature of one of the spots differs from the reference temperature at other parts of the circuit. Thermocouples are a widely used type of temperature sensor for measurement and control, and can also convert a temperature gradient into electricity. Commercial thermocouples are inexpensive, interchangeable, are supplied with standard connectors, and can measure a wide range of temperatures. In contrast to most other methods of temperature measurement, thermocouples are self powered and require no external form of excitation. The main limitation with thermocouples is accuracy; system errors of less than one degree Celsius (°C) can be difficult to achieve.
Any junction of dissimilar metals will produce an electric potential related to temperature. Thermocouples for practical measurement of temperature are junctions of specific alloys which have a predictable and repeatable relationship between temperature and voltage. Different alloys are used for different temperature ranges. Properties such as resistance to corrosion may also be important when choosing a type of thermocouple. Where the measurement point is far from the measuring instrument, the intermediate connection can be made by extension wires which are less costly than the materials used to make the sensor. Thermocouples are usually standardized against a reference temperature of 0 degrees Celsius; practical instruments use electronic methods of cold-junction compensation to adjust for varying temperature at the instrument terminals. Electronic instruments can also compensate for the varying characteristics of the thermocouple, and so improve the precision and accuracy of measurements.
Thermocouples are widely used in science and industry; applications include temperature measurement for kilns, gas turbine exhaust, diesel engines, and other industrial processes. Thermocouples are also used in homes, offices and businesses as the temperature sensors in thermostats, and also as flame sensors in safety devices for gas-powered major appliances.
In 1821, the German–Estonian physicist Thomas Johann Seebeck discovered that when any conductor is subjected to a thermal gradient, it will generate a voltage. This is now known as the thermoelectric effect or Seebeck effect. Any attempt to measure this voltage necessarily involves connecting another conductor to the "hot" end. This additional conductor will then also experience the temperature gradient, and develop a voltage of its own which will oppose the original. Fortunately, the magnitude of the effect depends on the metal in use. Using a dissimilar metal to complete the circuit creates a circuit in which the two legs generate different voltages, leaving a small difference in voltage available for measurement. That difference increases with temperature, and is between 1 and 70 microvolts per degree Celsius (µV/°C) for standard metal combinations.
The voltage is not generated at the junction of the two metals of the thermocouple but rather along that portion of the length of the two dissimilar metals that is subjected to a temperature gradient. Because both lengths of dissimilar metals experience the same temperature gradient, the end result is a measurement of the difference in temperature between the thermocouple junction and the reference junction. As long as the junction is at a uniform temperature, it does not matter how the junction is made (it may be brazed, spot welded, crimped, etc.), however it is crucial for accuracy that the leads of the thermocouple maintain a well-defined composition. If there are variations in the composition of the wires in the thermal gradient region (due to contamination, oxidation, etc.), outside the junction, this can lead to changes in the measured voltage (see aging of thermocouples below).
Upon heating, the Seebeck effect will initially drive a current. However, provided the junctions all reach a uniform internal temperature, and provided an ideal voltmeter is used, then the thermocouple will soon reach an equilibrium where no current will flow anywhere (). As a result, the voltage gradient at any point in the circuit will be given simply by , where is the Seebeck coefficient at that point, and is the temperature gradient at that point. The total measured end-to-end voltage can be found by adding up the voltage contributions all along the wires.
This leads to a measured voltage difference independent of many details (e.g. neither the size nor the length of the conductors matter):
where and are the Seebeck coefficients of materials A and B as a function of temperature, and and are the temperatures of the two junctions. The voltages Vb and Vc are measured at the cold ends of materials A and B, respectively (see figure). The emf is not generated at the junctions, but rather in the wires leading between the hot and cold junctions (where ). Because the two wires give different voltages leading up to the junction, the resulting measured overall voltage is nonzero.
If the Seebeck coefficients are effectively constant for the measured temperature range, the above formula can be approximated as . In general this is not the case, however it is possible to completely characterize the thermocouple with a characteristic function E(T), defined as:
This function characterizes the thermocouple completely and is uniquely defined up to a constant of integration. Often the constant is chosen such that . The measured voltage can be found by consulting a precomputed table of values of the characteristic function at two places (the hot temperature and the cold temperature). In the example above, .
Thermocouple manufacturers and metrology standards organizations such as NIST provide tables of the function calculated over a range of temperatures, for particular thermocouple types (see External links section for access to these tables). These tables are computed from reference functions which are simple mathematical functions (typically piecewise polynomials) fitted to closely approximate the true characteristic function.
For typical metals used in thermocouples, the output voltage increases almost linearly with the temperature difference (ΔT) over a bounded range of temperatures. For precise measurements or measurements outside of the linear temperature range, non-linearity must be corrected. The nonlinear relationship between the measured temperature and the output voltage of a thermocouple containing a reference junction temperature Tref can be approximated by a polynomial:
The coefficients an are given for n from 0 to between 5 and 13 depending upon the metals. By definition, T(0) = Tref, but a0 may differ from Tref if accuracy is not needed for T near the reference temperature. In general, all of the polynomial coefficients change if a different Tref is chosen. In some cases better accuracy is obtained with additional non-polynomial terms.ref = 0 °C A database of voltage as a function of temperature, and coefficients for computation of temperature from voltage and vice-versa for many types of thermocouple is available online. In modern equipment the equation is usually implemented in a digital controller or stored in a look-up table; older devices use analog circuits.
Piece-wise linear approximations are an alternative to polynomial corrections.
Thermocouple voltage is sensitive to the temperature difference between two points but also to their common temperature. To measure an unknown temperature, one of the junctions—nominally called the cold junction—is maintained at a controlled reference temperature, and the other junction is at the temperature to be sensed.
Having a reference junction of controlled temperature, while useful for laboratory calibration, is not convenient for most measurement and control applications. Instead, in most cases it suffices to simply measure the cold junction temperature, using a thermally sensitive device such as a resistance thermometer, thermistor or diode that is thermally anchored to input connections at the instrument, with special care being taken to minimize any temperature gradient between terminals. The thermocouple voltage difference between the known cold junction temperature and the lookup table reference temperature can be calculated (from a temperature-to-voltage lookup table), and the appropriate correction is applied as an offset from measured voltage before looking up the measured temperature in the voltage-to-temperature lookup table.
This is known as "cold junction compensation". Some thermocouple interface integrated circuits are designed for cold junction temperature compensation for specific thermocouple types.
Because of the non-linearity of the relation between voltage and temperature difference, the compensation is applied to the measured voltage before converting to temperature.
A number of factors affect the accuracy of a thermocouple. Ideally, a thermocouple should follow a standard curve, as the thermoelectric voltage could then be interpreted as a temperature without error. For various reasons (economy, manufacturing variations, chemical changes), however, the of a real thermocouple may deviate from the expected curve, or may be sensitive to temperatures at points outside the junction (due to inhomogeneities).
Thermocouple wire is available in several different metallurgical formulations per type. Thermocouples are not merely defined by the composition: thermocouple grade thermocouple wire has been fabricated by an alloys manufacturer with deliberate care taken to match the materials' curve to a standard curve. This can involve deliberate mixing in of impurities to "dope" the alloy, compensating for uncontrolled variations in source material. As a result, manufacturers may sell "matched pairs" of two lots of wire which together reproduce the standard curve, but which will show larger errors if combined with other lots. In some cases a special grade (special limits of error) is available, that offers a closer match to a standard curve.
High-grade thermocouple wires can have a high cost per unit length, making it expensive to run them over long distances to voltage-measuring instrumentation. However, changes in metallurgy along the length of the thermocouple, such as from termination strips or changes in type of wire, will introduce another thermocouple junction which can affect measurement accuracy. To solve this problem, extension grade wires, the cheapest and lowest quality, are used to carry thermoelectric signals over a long distance between a high-grade thermocouple and a measuring instrument some distance away. While the high-grade thermocouple may be used at extreme temperatures, the extension grade wires are only intended to be used over a narrow range of temperatures (typically only −50 °C to +100 °C). In this range they are specified to have the same Seebeck coefficients as the high-grade wire, and so no erroneous voltages are introduced from variations in the temperature of the junction between the high-grade and extension wire.
In the case of platinum thermocouples, extension wire is a copper alloy, since it would be prohibitively expensive to use platinum for extension wires. The copper alloy is designed to have a similar thermoelectric behaviour as the platinum alloy, over a narrow range of temperatures.
The voltmeter must have high input impedance to prevent any significant current draw from the thermocouple, which would in turn produce an undesired resistive voltage drop across the wire and/or junction.
Thermocouples are often used at high temperatures and in reactive furnace atmospheres. In this case the practical lifetime is limited by thermocouple aging. The thermoelectric coefficients of the wires in a thermocouple that is used to measure very high temperatures may change with time, and the measurement voltage accordingly drops. The simple relationship between the temperature difference of the junctions and the measurement voltage is only correct if each wire is homogeneous (uniform in composition). As thermocouples age in a process their conductors can lose homogeneity due to chemical and metallurgical changes caused by extreme or prolonged exposure to high temperatures. If the inhomogeneous section of the thermocouple circuit is exposed to a temperature gradient, the measured voltage will differ, resulting in error.
For this reason, aged thermocouples cannot be taken out of their installed location and recalibrated in a bath or test furnace to determine error. This also explains why error can sometimes be observed when an aged thermocouple is pulled partly out of a furnace—as the sensor is pulled back, inhomogeneous sections may see exposure to increased temperature gradients from hot to cold as the inhomogeneous section now passes through the cooler refractory area, contributing significant error to the measurement. Likewise, an aged thermocouple that is pushed deeper into the furnace might sometimes provide a more accurate reading if being pushed further into the furnace causes the area of inhomogeneity to be located in an area of the furnace where it is no longer exposed to a temperature gradient.
Certain combinations of alloys have become popular as industry standards. Selection of the combination is driven by cost, availability, convenience, melting point, chemical properties, stability, and output. Different types are best suited for different applications. They are usually selected on the basis of the temperature range and sensitivity needed. Thermocouples with low sensitivities (B, R, and S types) have correspondingly lower resolutions. Other selection criteria include the chemical inertness of the thermocouple material, and whether it is magnetic or not. Standard thermocouple types are listed below with the positive electrode (assuming ) first, followed by the negative electrode.
Type E (chromel – constantan) has a high output (68 µV/°C) which makes it well suited to cryogenic use. Additionally, it is non-magnetic. Wide range is −50 °C to +740 °C and Narrow range is −110 °C to +140 °C.
Type J (iron – constantan) has a more restricted range than type K (−40 °C to +750 °C), but higher sensitivity of about 50 µV/°C. The Curie point of the iron (770 °C) causes a smooth change in the characteristic, which determines the upper temperature limit.
Type K (chromel – alumel) is the most common general purpose thermocouple with a sensitivity of approximately 41 µV/°C (chromel positive relative to alumel when the junction temperature is higher than the reference temperature). It is inexpensive, and a wide variety of probes are available in its −200 °C to +1350 °C / -330 °F to +2460 °F range. Type K was specified at a time when metallurgy was less advanced than it is today, and consequently characteristics may vary considerably between samples. One of the constituent metals, nickel, is magnetic; a characteristic of thermocouples made with magnetic material is that they undergo a deviation in output when the material reaches its Curie point; this occurs for type K thermocouples at around 350 °C.
Type K thermocouples may be used up to 1260 °C in oxidizing or inert atmospheres without rapid aging. In marginally oxidizing atmospheres (such as carbon dioxide) between 800 °C–1050 °C, the chromel wire rapidly corrodes and becomes magnetic in a phenomenon known as "green rot"; this induces a large and permanent degradation of the thermocouple, causing the thermocouple to read too low if the corroded area is exposed to thermal gradient. Another source of drift in type K thermocouples is that near 400 °C, a slow reordering in the chromel wire occurs; this is reversible and leads to hysteresis between heating and cooling.
Type M (Ni/Mo 82%/18% – Ni/Co 99.2%/0.8%, by weight) are used in vacuum furnaces for the same reasons as with type C (described below). Upper temperature is limited to 1400 °C. It is less commonly used than other types.
Type N (Nicrosil – Nisil) thermocouples are suitable for use between −270 °C and +1300 °C owing to its stability and oxidation resistance. Sensitivity is about 39 µV/°C at 900 °C, slightly lower compared to type K.
Designed at the Defence Science and Technology Organisation (DSTO) of Australia, by Noel A. Burley, type N thermocouples overcome the three principal characteristic types and causes of thermoelectric instability in the standard base-metal thermoelement materials:
The Nicrosil and Nisil thermocouple alloys show greatly enhanced thermoelectric stability relative to the other standard base-metal thermocouple alloys, because their compositions substantially reduces the thermoelectric instabilities described above. This is achieved primarily by increasing component solute concentrations (chromium and silicon) in a base of nickel above those required to cause a transition from internal to external modes of oxidation, and by selecting solutes (silicon and magnesium) that preferentially oxidize to form a diffusion-barrier, and hence oxidation-inhibiting films.
Type T (copper – constantan) thermocouples are suited for measurements in the −200 to 350 °C range. Often used as a differential measurement since only copper wire touches the probes. Since both conductors are non-magnetic, there is no Curie point and thus no abrupt change in characteristics. Type T thermocouples have a sensitivity of about 43 µV/°C. Note that copper has a much higher thermal conductivity than the alloys used in thermocouple constructions, and so it is necessary to exercise extra care with thermally anchoring type T thermocouples.
Types B, R, and S thermocouples use platinum or a platinum/rhodium alloy for each conductor. These are among the most stable thermocouples, but have lower sensitivity than other types, approximately 10 µV/°C. Type B, R, and S thermocouples are usually used only for high temperature measurements due to their high cost and low sensitivity.
Type B thermocouples (Pt/Rh 70%/30% – Pt/Rh 94%/6%, by weight) are suited for use at up to 1800 °C. Type B thermocouples produce the same output at 0 °C and 42 °C, limiting their use below about 50 °C. The emf function has a minimum around 21 °C, meaning that cold junction compensation is easily performed since the compensation voltage is essentially a constant for a reference at typical room temperatures.
Type R thermocouples (Pt/Rh 87%/13% – Pt, by weight) are used up to 1600 °C.
Type S thermocouples (Pt/Rh 90%/10% – Pt, by weight), similar to type R, are used up to 1600 °C. Before the introduction of the International Temperature Scale of 1990 (ITS-90), precision type S thermocouples were used as the practical standard thermometers for the range of 630 °C to 1064 °C, based on an interpolation between the freezing points of antimony, silver, and gold. Starting with ITS-90, platinum resistance thermometers have taken over this range as standard thermometers.
These thermocouples are well-suited for measuring extremely high temperatures. Typical uses are hydrogen and inert atmospheres as well as vacuum furnaces. They must never be used in oxidizing environments. Embrittlement may occur during usage.
(W/Re 95%/5% – W/Re 74%/26%, by weight)
(W/Re 97%/3% – W/Re 75%/25%, by weight)
(W – W/Re 74%/26%, by weight)
In these thermocouples (chromel – gold/iron alloy), the negative wire is gold with a small fraction (0.03–0.15 atom percent) of iron. The impure gold wire gives the thermocouple a high sensitivity at low temperatures (compared to other thermocouples at that temperature), whereas the chromel wire maintains the sensitivity near room temperature. It can be used for cryogenic applications (1.2–300 K and even up to 600 K). Both the sensitivity and the temperature range depend on the iron concentration. The sensitivity is typically around 15 µV/K at low temperatures, and the lowest usable temperature varies between 1.2 and 4.2 K.
Type P or Platinel II (Pd/Pt/Au 55%/31%/14% – Au/Pd 65%/35%, by weight) thermocouples give a thermoelectric voltage that mimics the type K over the range 500 °C to 1400 °C, however they are constructed purely of noble metals and so shows enhanced corrosion resistance. This combination is known as Platinel II.
Thermocouples of platinum/molybdenum alloy (Pt/Mo 95%/5% – Pt/Mo 99.9%/0.1%, by weight) are sometimes used in nuclear reactors as they show a low drift from nuclear transmutation as induced by neutron irradiation, compared to the platinum/rhodium alloy types.
Thermocouples made up of two different, high-purity noble metals can show high accuracy even when uncalibrated, as well as low levels of drift. Two combinations in use are gold–platinum and platinum–palladium. Their main limitations are the low melting points of the metals involved (1064 °C for gold and 1555 °C for palladium). These thermocouples tend to be more accurate than type S, and due to their economy and simplicity are even regarded as competitive alternatives to the platinum resistance thermometers that are normally used as standard thermometers.
The table below describes properties of several different thermocouple types. Within the tolerance columns, T represents the temperature of the hot junction, in degrees Celsius. For example, a thermocouple with a tolerance of ±0.0025×T would have a tolerance of ±2.5 °C at 1000 °C.
|Type||Temperature range °C (continuous)||Temperature range °C (short term)||Tolerance class one (°C)||Tolerance class two (°C)||IEC Color code||BS Color code||ANSI Color code|
|K||0 to +1100||−180 to +1300||±1.5 between −40 °C and 375 °C|
±0.004×T between 375 °C and 1000 °C
|±2.5 between −40 °C and 333 °C|
±0.0075×T between 333 °C and 1200 °C
|J||0 to +750 °C||−180 to +800||±1.5 between −40 °C and 375 °C|
±0.004×T between 375 °C and 750 °C
|±2.5 between −40 °C and 333 °C|
±0.0075×T between 333 °C and 750 °C
|N||0 to +1100||−270 to +1300||±1.5 between −40 °C and 375 °C|
±0.004×T between 375 °C and 1000 °C
|±2.5 between −40 °C and 333 °C|
±0.0075×T between 333 °C and 1200 °C
|R||0 to +1600||−50 to +1700||±1.0 between 0 °C and 1100 °C|
±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C
|±1.5 between 0 °C and 600 °C|
±0.0025×T between 600 °C and 1600 °C
|S||0 to +1600||−50 to +1750||±1.0 between 0 °C and 1100 °C|
±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C
|±1.5 between 0 °C and 600 °C|
±0.0025×T between 600 °C and 1600 °C
|B||+200 to +1700||0 to +1820||Not Available||±0.0025×T between 600 °C and 1700 °C||No standard; use copper wire||No standard; use copper wire||Not defined.|
|T||−185 to +300||−250 to +400||±0.5 between −40 °C and 125 °C|
±0.004×T between 125 °C and 350 °C
|±1.0 between −40 °C and 133 °C|
±0.0075×T between 133 °C and 350 °C
|E||0 to +800||−40 to +900||±1.5 between −40 °C and 375 °C|
±0.004×T between 375 °C and 800 °C
|±2.5 between −40 °C and 333 °C|
±0.0075×T between 333 °C and 900 °C
|Chromel/AuFe||−272 to +300||n/a||Reproducibility 0.2% of the voltage; each sensor needs individual calibration.|
Thermocouples are suitable for measuring over a large temperature range, up to 2300 °C. Applications include temperature measurement for kilns, gas turbine exhaust, diesel engines, other industrial processes and fog machines. They are less suitable for applications where smaller temperature differences need to be measured with high accuracy, for example the range 0–100 °C with 0.1 °C accuracy. For such applications thermistors, silicon bandgap temperature sensors and resistance temperature detectors are more suitable.
Type B, S, R and K thermocouples are used extensively in the steel and iron industries to monitor temperatures and chemistry throughout the steel making process. Disposable, immersible, type S thermocouples are regularly used in the electric arc furnace process to accurately measure the temperature of steel before tapping. The cooling curve of a small steel sample can be analyzed and used to estimate the carbon content of molten steel.
Many gas-fed heating appliances such as ovens and water heaters make use of a pilot flame to ignite the main gas burner when required. If the pilot flame goes out, unburned gas may be released, which is an explosion risk and a health hazard. To prevent this, some appliances use a thermocouple in a fail-safe circuit to sense when the pilot light is burning. The tip of the thermocouple is placed in the pilot flame, generating a voltage which operates the supply valve which feeds gas to the pilot. So long as the pilot flame remains lit, the thermocouple remains hot, and the pilot gas valve is held open. If the pilot light goes out, the thermocouple temperature falls, causing the voltage across the thermocouple to drop and the valve to close.
Some combined main burner and pilot gas valves (mainly by Honeywell) reduce the power demand to within the range of a single universal thermocouple heated by a pilot (25 mV open circuit falling by half with the coil connected to a 10–12 mV, 0.2–0.25 A source, typically) by sizing the coil to be able to hold the valve open against a light spring, but only after the initial turning-on force is provided by the user pressing and holding a knob to compress the spring during lighting of the pilot. These systems are identifiable by the 'press and hold for x minutes' in the pilot lighting instructions. (The holding current requirement of such a valve is much less than a bigger solenoid designed for pulling the valve in from a closed position would require.) Special test sets are made to confirm the valve let-go and holding currents, because an ordinary milliammeter cannot be used as it introduces more resistance than the gas valve coil. Apart from testing the open circuit voltage of the thermocouple, and the near short-circuit DC continuity through the thermocouple gas valve coil, the easiest non-specialist test is substitution of a known good gas valve.
Some systems, known as millivolt control systems, extend the thermocouple concept to both open and close the main gas valve as well. Not only does the voltage created by the pilot thermocouple activate the pilot gas valve, it is also routed through a thermostat to power the main gas valve as well. Here, a larger voltage is needed than in a pilot flame safety system described above, and a thermopile is used rather than a single thermocouple. Such a system requires no external source of electricity for its operation and thus can operate during a power failure, provided that all the other related system components allow for this. This excludes common forced air furnaces because external electrical power is required to operate the blower motor, but this feature is especially useful for un-powered convection heaters. A similar gas shut-off safety mechanism using a thermocouple is sometimes employed to ensure that the main burner ignites within a certain time period, shutting off the main burner gas supply valve should that not happen.
Out of concern about energy wasted by the standing pilot flame, designers of many newer appliances have switched to an electronically controlled pilot-less ignition, also called intermittent ignition. With no standing pilot flame, there is no risk of gas buildup should the flame go out, so these appliances do not need thermocouple-based pilot safety switches. As these designs lose the benefit of operation without a continuous source of electricity, standing pilots are still used in some appliances. The exception is later model instantaneous (aka "tankless") water heaters that use the flow of water to generate the current required to ignite the gas burner; these designs also use a thermocouple as a safety cut-off device in the event the gas fails to ignite, or if the flame is extinguished.
Thermopiles are used for measuring the intensity of incident radiation, typically visible or infrared light, which heats the hot junctions, while the cold junctions are on a heat sink. It is possible to measure radiative intensities of only a few μW/cm2 with commercially available thermopile sensors. For example, some laser power meters are based on such sensors.
The principle of operation of a thermopile sensor is distinct from that of a bolometer, as the latter relies on a change in resistance.
Thermocouples can generally be used in the testing of prototype electrical and mechanical apparatus. For example, switchgear under test for its current carrying capacity may have thermocouples installed and monitored during a heat run test, to confirm that the temperature rise at rated current does not exceed designed limits.
A thermocouple can produce current to drive some processes directly, without the need for extra circuitry and power sources. For example, the power from a thermocouple can activate a valve when a temperature difference arises. The electrical energy generated by a thermocouple is converted from the heat which must be supplied to the hot side to maintain the electric potential. A continuous transfer of heat is necessary because the current flowing through the thermocouple tends to cause the hot side to cool down and the cold side to heat up (the Peltier effect).
Thermocouples can be connected in series to form a thermopile, where all the hot junctions are exposed to a higher temperature and all the cold junctions to a lower temperature. The output is the sum of the voltages across the individual junctions, giving larger voltage and power output. In a radioisotope thermoelectric generator, the radioactive decay of transuranic elements as a heat source has been used to power spacecraft on missions too far from the Sun to use solar power.
Thermopiles heated by kerosene lamps were used to run batteryless radio receivers in isolated areas. There are commercially produced lanterns that use the heat from a candle to run several light-emitting diodes, and thermoelectrically-powered fans to improve air circulation and heat distribution in wood stoves.
The Peltier effect can be used for cooling, in the reverse process to a thermoelectric generator. Instead of generating electric power, the thermocouple consumes it, working as a heat pump.
Chemical production and petroleum refineries will usually employ computers for logging and for limit testing the many temperatures associated with a process, typically numbering in the hundreds. For such cases, a number of thermocouple leads will be brought to a common reference block (a large block of copper) containing the second thermocouple of each circuit. The temperature of the block is in turn measured by a thermistor. Simple computations are used to determine the temperature at each measured location.
A thermocouple can be used as a vacuum gauge over the range of approximately 0.001 to 1 torr absolute pressure. The temperature detected at the thermocouple junction depends on the thermal conductivity of the surrounding gas, which depends on the pressure of the gas. Thus, the potential difference measured by a thermocouple is proportional to the logarithm of pressure in low-to-medium vacuum. At higher and lower pressures, the thermal conductivity of air and other gases is essentially independent of pressure. The thermocouple was first used as a vacuum gauge by Voege in 1906.
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Thermocouple data tables: