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I wish I knew how to calibrate a thermocouple!
You have several ways that apply to all thermocouple types, but the right way for you depends on your conditions. However, you always need a calibration furnace. So let’s go through the options.
If you have a lab with the thermocouple and voltmeter in the same ambient temperature, you can use a compensating cable. Put your sensor in the calibration furnace and set the furnace to increase and decrease the temperature. As the voltmeter measures the millivolts, you can find the temperature using a reference table.
Usually, the factory lab calibrates your sensor using a cold junction for higher accuracy. It uses zero degrees Celsius as a reference point because the reference tables base their values on that point. This should give you an accurate millivolt value.
Comparative calibration + external reference junction
Here you have a second thermocouple connected to an external reference junction. Thus, you can compare your sensor output with the reference sensor. Both will start at zero degrees Celsius again.
You can connect the sensor directly to a digital calibrator, which will compensate for the ambient temperature. You can also find calibrators that work with the calibration furnace to increase and decrease the temperature and collect all the data automatically.
This video will tell you more about thermocouple calibration: