Basic principles of thermocouples
Since the early 1900s, thermocouples have provided critical temperaturemeasurements, especially at very high temperature. For many industrial and processcritical applications, both T/Cs and RTDs (resistor temperature detectors) have become "gold standards" for temperature measurement. Although RTDs have better accuracy and repeatability, the relative advantages of thermocouples include:

Larger measurement range

Shorter response times

Lower cost

Better durability

Self powered (no excitation signal required)

No selfheating effect
Making highaccuracy temperature measurements with thermocouples can, however, be tricky. You can optimize measurement accuracy through solid circuit design and calibration, but understanding how thermocouples work helps before you design circuits or use thermometers.
Thomas Seebeck
(17701831) 
How thermocouples work
When a voltage source is applied across a piece of metal wire, electrons flow from the positive terminal to the negative terminal, and some energy is lost heating up the metal wire. The Seebeck effect, discovered in 1821 by Thomas Johann Seebeck, is a reverse phenomenon. When a temperature gradient is applied across a metal wire, an electric potential is created. This is the physical basis of thermocouple.
(Eq.1)
Where ?V is the gradient of voltage, ?T is the gradient of temperature, and S(T) is the Seebeck coefficient. This coefficient is dependent on the material, and it also varies as a function of temperature. The voltage across two different temperature points on a wire equals the integration of the Seebeckcoefficient function over the temperature range.
(Eq.2)
For example, T_{1}, T_{2}, and T_{3} in Figure 1 represent temperatures at different locations on a piece of metal wire. T_{1} (blue) represents the coldest point and T3 (red) the hottest point. The voltage across points T_{2} and T_{1} is
(Eq. 3)
Similarly, the voltage across points T_{3} and T_{1} is
(Eq. 4)
Because of the additive property of definite integral, V_{31} also equals
(Eq. 5)
Keep this situation in mind when we discuss thermocouple voltagetotemperature conversion.
Figure 1. Voltages are created on a conductive wire by temperature gradient and the Seebeck effect.
Thermocouples consist of two dissimilar materials, usually metal wires with different Seebeck coefficients, S(T). Why are two materials essential when a temperature difference in a single material produces a voltage difference? Assume that the metal wire in Figure 2 is made of a material "A." If a voltmeter with probe wires that are also made of material A, the voltmeter will theoretically not detect any voltage.
Figure 2. Voltage measurement connection when the probes and wires are made of same material shows no potential difference.
The reason is that when the probes are connected to the ends of the wire, they act as the extension of the metal wire. The ends of this long wire that connects to the inputs of the voltmeter are at the same temperature (T_{M}). If the ends of a wire are at the same temperature, no voltage will develop across the wire.
To prove this mathematically, we calculate the voltage accumulated across the whole wire loop starting from the positive terminal of the voltmeter to the negative terminal.
(Eq.6)
Using the additive property of integral, the above equation becomes:
(Eq.7)
When the lower bound and upper bound of the integral limits are the same, the result of the integral is V = 0.
If the probe material is made of material B as shown in Figure 3, then:
(Eq.8)
Simplifying the integral, we get:
(Eq.9)
Eq. 9 shows the measuring voltage is equal to the integral of the difference of the Seebeck coefficient functions of the two material types. This is the reason why thermocouples are made with two dissimilar types of metal.
Figure 3. Voltage measurement connection but with the probes and wires are made of different materials shows the physical reality of the Seebeck effect.
From the circuit of Fig. 3 and Eq. 9, assuming S_{A}(T), S_{B}(T), and the measured voltage are known, we still can't calculate the temperature at the hot junction (T_{H}) unless we know the temperature at the cold junction (T_{C}). In the early days of thermocouples, an ice bath corresponding to 0°C was used as a reference temperature (hence the term cold junction) because this method is low cost, very easily accessible, and the temperature selfregulated. The equivalent circuit is shown in Figure 4.
Figure 4. Thermocouples need a reference temperature, shown here at 0°C, for calculating the unknown temperature T_{H}.
Although we know the reference temperature for the circuit in Fig. 4, it's not practical to solve the integral equation for T_{H}. Standard reference tables are available for all common types of thermocouples, so you can look up the temperature for corresponding voltage output. But, it's important to keep in mind that all of the standard thermocouple reference tables were tabulated with a 0°C reference temperature.
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