eFunda: Theory of Thermocouples
engineering fundamentals Thermocouples: Theory
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Thermoelectric Effect

The basis of thermocouples was established by Thomas Johann Seebeck in 1821 when he discovered that a conductor generates a voltage when subjected to a temperature gradient. To measure this voltage, one must use a second conductor material which generates a different voltage under the same temperature gradient. Otherwise, if the same material was used for the measurement, the voltage generated by the measuring conductor would simply cancel that of the first conductor. The voltage difference generated by the two materials can then be measured and related to the corresponding temperature gradient. It is thus clear that, based on Seebeck's principle, thermocouples can only measure temperature differences and need a known reference temperature to yield the abolute readings.

There are three major effects involved in a thermocouple circuit: the Seebeck, Peltier, and Thomson effects.

The Seebeck effect describes the voltage or electromotive force (EMF) induced by the temperature difference (gradient) along the wire. The change in material EMF with respect to a change in temperature is called the Seebeck coefficient or thermoelectric sensitivity. This coefficient is usually a nonlinear function of temperature.

Peltier effect describes the temperature difference generated by EMF and is the reverse of Seebeck effect. Finally, the Thomson effect relates the reversible thermal gradient and EMF in a homogeneous conductor.

Thermocouple Circuit

A typical thermocouple circuit can be illustrated as follows:

Typical Thermocouple Circuit

Suppose that the Seebeck coefficients of two dissimilar metallic materials, metal A and metal B, and the lead wires are SA, SB, and SLead respectively. All three Seebeck coefficients are functions of temperature. The voltage output Vout measured at the gage (see schematic above) is,

where TRef is the temperature at the reference point, TTip is the temperature at the probe tip. Note that mathematically the voltage induced by the temperature and/or material mismatch of the lead wires cancels, whereas in reality the lead wires will introduce noise into the circuit.

If the Seebeck coefficient functions of the two thermocouple wire materials are pre-calibrated and the reference temperature TRef is known (usually set by a 0°C ice bath), the temperature at the probe tip becomes the only unknown and can be directly related to the voltage readout.

If the Seebeck coefficients are nearly constant across the targeted temperature range, the integral in the above equation can be simplified, allowing one to solve directly for the temperature at the probe tip,

In practice, vendors will provide calibration functions for their products. These functions are usually high order polynomials and are calibrated with respect to a certain reference temperature, e.g., 0 °C (32 °F). Suppose that the coefficients of the calibration polynomials are a0, a1, a2, ..., an. The temperature at the probe tip can then be related to the voltage output as,

Note that the above formula is effective only if the reference temperature TRef in the experiment is kept the same as the reference temperature specified on the data sheet. Furthermore, these coefficients are unit sensitive. Make sure to use the vendor-specified temperature unit (i.e. Celsius/centigrade, Fahrenheit, or Kelvin) when plugging in numbers.

Again, a thermocouple is a relative not absolute temperature sensor. In other words, a thermocouple requires a reference of known temperature which is provided by ice water in the above illustration. While ice water is an easy to obtain and well known reference, it is not practical out side of a laboratory. Thus, common commercialized thermocouples often includes another temperature sensor, such as thermistor, to provide the reading of the reference (room/surrounding) temperature.

Thermoelectric Sensitivity

The Seebeck coefficients (thermoelectric sensitivities) of some common materials at 0 °C (32 °F) are listed in the following table.

Material Seebeck
Coeff.
*
  Material Seebeck
Coeff.
*
  Material Seebeck
Coeff.
*
Bismuth -72   Aluminum 3.5   Tungsten 7.5
Constantan -35   Lead 4.0   Iron 19
Nickel -15   Tantalum 4.5   Nichrome 25
Potassium -9.0   Rhodium 6.0   Antimony 47
Sodium -2.0   Copper 6.5   Germanium 300
Platinum 0   Gold 6.5   Silicon 440
Mercury 0.60   Silver 6.5   Tellurium 500
Carbon 3.0   Cadmium 7.5   Selenium 900
*: Units are µV/°C; all data provided at a temperature of 0 °C (32 °F)

 
The above table also reveals some possible wire pairings. For instance, iron or copper can be put on the positive terminal while constantan can be used for the negative terminal of a thermocouple circuit (Type J and T).
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