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The voltage generated by thermocouples is very small. They are in the order of milivolts. In the application of thermocouples to measure temperature, it is often required to convert the milivolts signals of thermocouples to temperature values. To aid this conversion, several milivolts voltages for the different types of thermocouples are tabulated against known standard temperatures. With these thermocouple reference tables, it is then easy to determine any given temperature for known milivolts values.

Thermocouple reference tables are based on a reference junction of 0 degree C. If the reference junction is not at 0 degree C, then a correction factor must be applied.

**Calculating Temperature from Voltage (reference junction = 0 degree C)**

The steps involved are:

- Select the correct reference table for the thermocouple type in use. e.g. J,S,T etc

- Locate the milivolt reading in the body of the table, and read from the margins the temperature value.

a straight line approximation (or interpolation) can be made between two values.

From the little sketch above, suppose we are given the milivolts reading of a particular type of thermocouple to be

**V**and_{H}**V**and the corresponding temperatures are_{L}**T**and_{H}**T**, the temperature T_{L}_{M}corresponding to the measured voltage,**V**is given by:_{M}**(V**

_{M}- V_{L})/(V_{H}- V_{L}) = (T_{M}– T_{L})/(T_{H}- T_{L})
This simplifies to:

**T**

_{M}= T_{L}+ [(V_{M}– V_{L})/(V_{H}– V_{L})](T_{H}– T_{L})Where:

**V**is the measured voltage

_{M}**V**is the higher voltage read from the table

_{H}**V**is the lower voltage read from the table

_{L}**T**is the calculated temperature

_{M}**T**is the higher temperature read from the table (corresponding to

_{H}**VH**)

**T**is the lower temperature read from the table (corresponding to

_{L}**VL**)

The values of

**V**and_{H}, V_{L}, T_{H}**T**are read from the thermocouple reference tables. Interpolation is then done using the formula above to determine the more precise temperature._{L}**Milivolts to Temperature Calculations For Thermocouples**

To calculate milivolts values, we use the thermoelectric voltage in milivolts for type J thermocouple reference table shown below:

**Problem A**

A voltage of 14.82mV is measured with a type J thermocouple with a 0 degree C reference temperature. Find the temperature of the sensing junction.

**Solution**

From the reference table for J-type thermocouples above, it is found that V

_{M}= 14.82mV is between V_{L}= 14.67mV and V_{H}= 14.94mV(**the red box and red arrows**) These voltages have corresponding temperatures of T_{L}= 270^{0}C and T_{H}= 275^{0}C.Using our interpolation formula, we determine the temperature to be:

**T**

_{M}= T_{L}+ [(V_{M}– V_{L})/(V_{H}– V_{L})](T_{H}– T_{L})
T

_{M}= 270 + [(14.82 – 14.67)/(14.94 – 14.67)](275 – 270) = 272.8^{0}C**Calculating Temperature From Voltage If Reference Junction Temperature Is Greater Than Zero**:

- Select the correct reference table for the thermocouple type in use, i.e. J,S,T etc.

- Locate the milivolt reading for the reference junction in the body of the table, and read from the margins the temperature value.

- Add this milivolt reading to that measured by the instrument.

**Problem B**

A voltage of 3.444 mV is measured with a type J thermocouple with a 25 degree C reference temperature. Find the temperature of the sensing junction.

**Solution**:

The voltage of the reference junction at 25 degree C, from the J-type reference table is 1.277mV(

**the blue box and blue arrow**).

The measured voltage needs to be corrected such that the actual sensing voltage is the sum of the two:

1.277 + 3.444 = 4.721mV

From the J-type thermocouple reference table above, V

_{M}= 4.721mV is between V_{H}= 4.726mV and V_{L}= 4.672mV corresponding to T_{H}= 90^{0}C and T_{L}= 89^{0}C (**the green box and green arrows**).
T

_{M}= 89 + [(4.721 – 4.672)/(4.726 – 4.672)](90 – 89) = 89.907^{0}C