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Cold-junction compensation converts a reading with reference temperature $T_c$ into the equivalent reading for a chosen standard reference. Define the thermocouple reference function $F(T)=E(T,0)$, where $0$ means $0{}^{\circ }\mathrm{C}$, not absolute zero. Additivity of the definite integral givesThe final inverse function requires a suitable one-to-one calibration interval. A terminal thermometer supplies $T_c$ independently; the raw thermocouple electric potential difference supplies only the difference of the two reference-function values. In general, first converting $V_{\mathrm{raw}}$ to a temperature and then adding $T_c$ is wrong, because the thermocouple reference function need not be linear. The SCC-TC manual explicitly adds the reference-equivalent voltage before its final voltage-to-temperature conversion.^[ref]

For a stipulated model only, take $S_A-S_B=40\mu V/K$ throughout the interval. No actual material pair is assigned this constant. Because degree Celsius differences have the same numerical size as kelvin differences,In this model $F(20)=0.8\mathrm{mV}$ and $F(80)=3.2\mathrm{mV}$. Adding the $0.8\mathrm{mV}$ correction produces $3.2\mathrm{mV}$, whose inverse calibration gives $80{}^{\circ }\mathrm{C}$. Applying the zero-reference calibration directly to $2.4\mathrm{mV}$ would instead display $60{}^{\circ }\mathrm{C}$.

Now physically change only the reference temperature to $30{}^{\circ }\mathrm{C}$, leaving the measuring junction at $80{}^{\circ }\mathrm{C}$. The raw reading becomes $2.0\mathrm{mV}$; the correction becomes $F(30)=1.2\mathrm{mV}$, so the corrected total stays $3.2\mathrm{mV}$. Physically changing the reference changes the measured electric potential difference. Adding a software correction changes its interpretation and leaves the raw reading intact. If the actual reference is $30{}^{\circ }\mathrm{C}$ but the software still assumes $20{}^{\circ }\mathrm{C}$, this model displays $70{}^{\circ }\mathrm{C}$.

An actual implementation in FP-TC-120 and cFP-TC-120 Operating Instructions by National Instruments (p. 7, Cold-Junction Compensation) uses terminal-mounted temperature sensors, reports their reading as “CJ Temperature”, and enables compensation in temperature mode but not voltage mode. This makes the distinction between a raw voltage readout and a compensated temperature readout observable. The specified reference-sensor range also produces an out-of-range indication: a calculated number outside a supported range is not a validated measurement.^[ref]

The thermocouple reference junction is the connection region where the two thermoelements meet the measurement leads. In ordinary copper-lead wiring there are two material transitions, A–Cu and B–Cu, rather than a second welded A–B junction. They must have a common known temperature $T_c$ for the simple expression $E(T_h,T_c)$ to apply. An ice-water heat bath can establish a nominal $0{}^{\circ }\mathrm{C}$ reference; cold-junction compensation instead measures $T_c$ locally. The word “cold” describes the reference role and imposes no requirement that $T_c<T_h$.

Thermocouple voltage calibration relates an actual assembled sensor's electromotive force to independently established junction temperatures. It must be distinguished from selecting a nominal letter-type conversion curve. In Thermocouples Calibrations Services by National Institute of Standards and Technology (opening method description and bath-calibration table), NIST describes comparison with a maintained reference thermocouple, comparison with a standard platinum resistance thermometer in controlled heat baths, and fixed-point calibration at the freezing points of zinc, aluminum, silver and gold on the International Temperature Scale of 1990. These are independent thermal references, unlike a test that checks only a voltage-input circuit.^[ref]

For a concrete electrical check, the SCC-TC guide describes shorting the input after 30 minutes of powered operation and adjusting its offset to a zero-voltage readout. Its separate calibrator procedure requires equal connection temperatures at the calibrator and module, measures the supplied voltage, converts it to temperature, and compares with the calibrator setting. Such an injected-signal test checks the readout chain; it does not expose a real measuring junction to an independently known bath temperature.^[ref]

Useful additional checks follow from the model: log the raw voltage, the reference temperature, and the final inferred temperature separately; hold $T_h$ stable while changing $T_c$ and test whether cold-junction compensation preserves the inferred $T_h$; compare against an independent thermometer at several stable heat bath settings. Check immersion and repeatability instead of assuming a steady display establishes thermal equilibrium. These are proposed diagnostic checks, not new experimental results. The equal-temperature and polarity controls are already described under Seebeck effect.

Limits arise separately from the thermocouple reference function, sensor-wire changes, thermal contact, terminal temperature differences, and the voltage-input circuit. In particular, the SCC-TC guide warns of connector-to-module temperature gradients and voltage drops caused by the fault-detection electric current flowing through lead electrical resistance.^[ref] A fitted curve or compensation algorithm cannot make all these errors vanish. No single accuracy is assigned to every thermocouple.