Editing Thermocouple (section)

==Principle of operation==

In 1821, the [[Germany|German]] physicist [[Thomas Johann Seebeck]] discovered that a magnetic needle held near a circuit made up of two dissimilar metals got deflected when one of the dissimilar metal junctions was heated. At the time, Seebeck referred to this consequence as thermo-magnetism. The magnetic field he observed was later shown to be due to thermo-electric current. In practical use, the voltage generated at a single junction of two different types of wire is what is of interest as this can be used to measure temperature at very high and low temperatures. The magnitude of the voltage depends on the types of wire being used. Generally, the voltage is in the microvolt range and care must be taken to obtain a usable measurement. Although very little current flows, power can be generated by a single thermocouple junction. Power generation using multiple thermocouples, as in a [[thermopile]], is common.

[[File:Thermocouple circuit Ktype including voltmeter temperature.svg|thumb|upright=1.7|[[Thermocouple#Type K|Type K]] thermocouple ([[chromel]]–[[alumel]]) in the standard thermocouple measurement configuration. The measured voltage <math>\scriptstyle V</math> can be used to calculate temperature <math>\scriptstyle T_\mathrm{sense}</math>, provided that temperature <math>\scriptstyle T_\mathrm{ref}</math> is known.]]

The standard configuration of a thermocouple is shown in the figure. The dissimilar conductors contact at the measuring (aka hot) junction and at the reference (aka cold) junction. The thermocouple is connected to the electrical system at its reference junction. The figure shows the measuring junction on the left, the reference junction in the middle and represents the rest of the electrical system as a voltage meter on the right.

The temperature ''T''<sub>sense</sub> is obtained via 
a characteristic function ''E''(''T'') for the type of thermocouple which requires inputs: measured voltage ''V'' and reference junction temperature ''T''<sub>ref</sub>. The solution to the equation ''E''(''T''<sub>sense</sub>) = ''V'' + ''E''(''T''<sub>ref</sub>) yields ''T''<sub>sense</sub>. Sometimes these details are hidden inside a device that packages the reference junction block (with ''T''<sub>ref</sub> thermometer), voltmeter, and equation solver.

===Seebeck effect===

{{main article|Seebeck effect}}

The Seebeck effect refers to the development of an [[electromotive force]] across two points of an electrically conducting material when there is a temperature difference between those two points.
Under open-circuit conditions where there is no internal current flow, the [[gradient]] of voltage (<math>\scriptstyle \boldsymbol \nabla V</math>) is directly proportional to the gradient in temperature (<math>\scriptstyle \boldsymbol \nabla T</math>):
:<math>\boldsymbol \nabla V  =  -S(T) \boldsymbol \nabla T,</math>
where <math>S(T)</math> is a temperature-dependent [[material property]] known as the [[Seebeck coefficient]].

The standard measurement configuration shown in the figure shows four temperature regions and thus four voltage contributions:
# Change from <math>\scriptstyle T_\mathrm{meter}</math> to <math>\scriptstyle T_\mathrm{ref}</math>, in the lower copper wire.
# Change from <math>\scriptstyle T_\mathrm{ref}</math> to <math>\scriptstyle T_\mathrm{sense}</math>, in the alumel wire.
# Change from <math>\scriptstyle T_\mathrm{sense}</math> to <math>\scriptstyle T_\mathrm{ref}</math>, in the chromel wire.
# Change from <math>\scriptstyle T_\mathrm{ref}</math> to <math>\scriptstyle T_\mathrm{meter}</math>, in the upper copper wire.

The first and fourth contributions cancel out exactly, because these regions involve the same temperature change and an identical material.
As a result, <math>\scriptstyle T_\mathrm{meter}</math> does not influence the measured voltage.
The second and third contributions do not cancel, as they involve different materials.

The measured voltage turns out to be
:<math>V = \int_{T_\mathrm{ref}}^{T_\mathrm{sense}} \left( S_{+}(T) - S_{-}(T) \right) \, dT,</math>
where <math>\scriptstyle S_{+}</math> and <math>\scriptstyle S_{-}</math> are the [[Seebeck coefficient]]s of the conductors attached to the positive and negative terminals of the voltmeter, respectively (chromel and alumel in the figure).

===Characteristic function===

The thermocouple's behaviour is captured by a '''characteristic function''' <math>\scriptstyle E(T)</math>, which needs only to be consulted at two arguments:
:<math>V = E(T_\mathrm{sense}) - E(T_\mathrm{ref}).</math>
In terms of the Seebeck coefficients, the characteristic function is defined by
:<math>E(T) = \int^T S_{+}(T') - S_{-}(T') dT' + \mathrm{const} </math>
The [[constant of integration]] in this [[indefinite integral]] has no significance, but is conventionally chosen such that <math>\scriptstyle E(0\,{}^{\circ}{\rm C}) = 0</math>.

Thermocouple manufacturers and metrology standards organizations such as [[NIST]] provide tables of the function <math>\scriptstyle E(T)</math> that have been measured and interpolated over a range of temperatures, for particular thermocouple types (see ''External links'' section for access to these tables).

===Reference junction===

[[File:Cold Junction Compensation with Thermistor to measure the junction temperature..jpg|thumb|right|Reference junction block inside a Fluke CNX t3000 temperature meter. Two white wires connect to a [[thermistor]] (embedded in white thermal compound) to measure the reference junctions' temperature.]]

To obtain the desired measurement of <math>\scriptstyle T_\mathrm{sense}</math>, it is not sufficient to just measure <math>\scriptstyle V</math>.
The temperature at the reference junctions <math>\scriptstyle T_\mathrm{ref}</math> must also be known.
Two strategies are often used here:
* "Ice bath": The reference junction block is maintained at a known temperature as it is immersed in a semi-frozen bath of distilled water at atmospheric pressure. The precise temperature of the melting point [[phase transition]] acts as a natural [[thermostat]], fixing <math>\scriptstyle T_\mathrm{ref}</math> to 0&nbsp;°C. 
* Reference junction sensor (known as "{{visible anchor|cold junction compensation}}"): The reference junction block is allowed to vary in temperature, but the temperature is measured at this block using a separate temperature sensor. This secondary measurement is used to compensate for temperature variation at the junction block. The thermocouple junction is often exposed to extreme environments, while the reference junction is often mounted near the instrument's location.  [[Silicon bandgap temperature sensor|Semiconductor thermometer]] devices are often used in modern thermocouple instruments.

In both cases the value <math>\scriptstyle V + E(T_\mathrm{ref})</math> is calculated, then the function <math>\scriptstyle E(T)</math> is [[root-finding algorithm|searched]] for a matching value. The argument where this match occurs is the value of <math>\scriptstyle T_\mathrm{sense}</math>:
:<math>E(T_\mathrm{sense}) = V + E(T_\mathrm{ref})</math>.