How thermocouples are calibrated

Thermocouple calibration is comparison: put the thermocouple and a reference thermometer at the same temperature, record what each says, and repeat across the range. The mechanics are the same as any comparison calibration. What makes thermocouples different is that the item being calibrated does not produce a temperature at all. It produces a voltage that depends on both of its ends.

The reference junction is the calibration

Every value in a thermocouple reference table is the emf against a reference junction at 0 °C. Your terminal block is not at 0 °C. So the meter reads the difference, and the reference junction's own emf has to be added back before the reading is inverted.

Concretely, on a type K with the measuring junction at 420 °C and the terminals at 23 °C, the meter reads 16.324 mV. Add the 23 °C reference junction's emf and invert, and you get 420.00 °C. Invert the raw reading as though the reference junction were already at 0 °C and you get 398.26 °C. The thermocouple is fine, the meter is fine, and the answer is 21.7 °C wrong.

How good does the reference junction have to be

Once compensation is applied properly, the sensitivity is close to one for one. Move the assumed reference-junction temperature by 1 °C, from 23 to 24 °C, and the computed junction temperature moves by 0.955 °C. There is no dilution and no averaging: an error in the reference junction transfers almost entirely into the result.

• An ice point, properly made from shaved ice and water in a Dewar, realises 0 °C to 0.01–0.05 °C. It is the reference method and it is cheap.
• A controlled reference-junction block is convenient and typically 0.1 °C or better.
• Electronic cold-junction compensation inside an indicator is often 0.5 °C or worse, because it is measuring a terminal block with a small sensor inside a box that has its own gradients.

If the thermocouple will be used with its own indicator's internal compensation, calibrate the whole system that way. A bare-wire calibration against an ice point, used with a 0.5 °C compensating indicator, hands the user an uncertainty that does not describe what they own.

Method

• Choose points across the working range, approached in ascending order and then repeated descending so hysteresis and drift within the run are visible.
• Immerse both the reference and the thermocouple to a depth that has been shown to be sufficient, by varying it rather than assuming the manufacturer's minimum. Sheath conduction is usually worse for a thermocouple than a PRT of the same diameter.
• Realise and record the reference junction. State on the certificate how it was realised and at what temperature.
• Record the emf, not a temperature, along with the reference thermometer's reading. The conversion is part of the calculation, and recording only the converted value hides which table and which reference junction were used.
• Evaluate inhomogeneity by withdrawing the thermocouple through the gradient in steps and recording how the reading moves. This is the term that will dominate the budget.
• Repeat at least three readings per point for a Type A term with real degrees of freedom.

What the certificate has to say

A thermocouple certificate that omits the reference junction is not usable. It should state the type, the reference-junction realisation and temperature, the instrument and leads included in the calibration, the immersion depth, the emf and the derived temperature at each point, the uncertainty with its coverage factor, and whether inhomogeneity was evaluated and how.

Sensitivity belongs there too, because voltage terms in the user's own budget have to be divided by it. For a type K it is 39.45 µV/°C at 0 °C and 42.35 µV/°C at 420 °C, so the same instrument specification is worth different amounts at different points in the range.

The limit of the method

Thermal cycling in a gradient changes the wire's composition along its length. After that, the emf depends on where the gradient sits, so moving the thermocouple to a different immersion depth or a different furnace invalidates the correction. You can measure inhomogeneity and you can budget it, but you cannot subtract it, and no amount of care in the calibration removes it.

Which is why, below about 600 °C where a platinum resistance thermometer will reach, a thermocouple is rarely the right instrument for precise work. Calibrating it well tells you how good it was on the day, in that geometry.