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Every material has its own Seebeck Coefficient
Seebeck Coefficient means a voltage produced by applying difference temperature at two end of material.
S: Seebeck Coefficient
∆V: thermoelectric voltage
∆T: difference temperature

Let join two kind of Conductor, at Junction end has temperature T2 bigger than Tail end temperature T1
By difference of Temperature T1 and T2, Conductor1 has Seebeck Voltage of Vab = Va - Vb
Conductor2 is Vcb = Vc - Vb
Voltage produced at Tail end is:
Vac = Vab - Vcb = (Va-Vb) - (Vc-Vb) =Va-Vc
What if Conductor1 and Conductor2 are same type? They will have same Seebeck coefficient, then same Seebeck Voltage. Therefore Vac = Vcb, Vac = Vab – Vcb = 0
To build up a Thermocouple, Conductor1 and Conductor2 have to be two different materials; Tail end can produce a voltage then.
So, how to calculate T2?
The temperature vs voltage relationship is given by:
S12: Seebeck coefficient of the thermocouple
S1: Seebeck coefficient of Conductor1
S2: Seebeck coefficient of Conductor2

Voltage of Tail end can be expressed as:
Vac = Va-Vc = S12(T2 – T1)
T2 = Vac/S12 + T1
Information of Vac, S12, T1 can be known, therefore T2 is also found out by upper equation.
T1, also called as reference temperature, is put on Ice bath to become 0oC, therefore:
T2 = Vac/S12
 In industry, Ice Bath is an integrated circuit called Cold Junction compensator; in fact the cold junction compensator produces a voltage equal to the thermocouple voltage between 0°C and ambient temperature T2
Most control module already integrated Cold Junction compensator, user just declares kind of using thermocouple, it will automatically calculated compensation voltage.
For example: Yokogawa AST143, Siemens thermocouple module EM 231
There are many kind of Thermocouple
Type R, S and B thermocouples use Pt-base thermoelements and they can operate at temperatures up to 1700°C; however they are more expensive and their voltage output is lower than type K and type N thermocouples, which use Ni-base thermoelements. However, Ni base thermocouples can operate at lower temperatures than the Pt-base ones.
Voltage vs Temperature relationship for letter-designated thermocouples

Approximate composition for thermoelements of letter-designated thermocouples

 Seebeck coefficient is temperature dependent. Again, module in industry used for calculating temperature from Thermocouple already integrated this characteristic. Additional details on the voltage-temperature relationships for letter designated thermocouple can be found at

Type K Seebeck coefficient vs Temperature

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