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A reference-junction temperature sweep tests a thermocouple measurement system by varying its connection-region temperature while holding the thermocouple measuring junction at an independently known, stable temperature. The intended invariant is the inferred measuring-junction temperature after cold-junction compensation; the raw electric potential difference is expected to change.

Let $F(T)=E(T,0)$ be the thermocouple reference function, $T_h$ the fixed measuring-junction temperature, $T_j$ the actual terminal temperature and $T_s$ the reference-sensor reading. In an ideal matched readout,If $T_s=T_j$, the sum inside the inverse function stays equal to $F(T_h)$ throughout the sweep. This tests the thermal reference and the compensation calculation together; it does not require the raw signal to be constant.

A primary design verification by Mike Beckman and Luis Chioye places the ADS1118 board and reference connections in a temperature-controlled environment, while the other end of the thermocouple remains in a stable bath. Its Figure17 keeps the USB interface outside that environment. The companion experiment instead varies the measuring-junction bath while holding the reference region near ambient temperature. These are different tests of the measurement chain.^[ref]

For an original linear model only, stipulate $F(T)=ST$ with $S=40\mu V/K$ and a fixed measuring junction at $80{}^{\circ }\mathrm{C}$. Raising the reference from $20$ to $35{}^{\circ }\mathrm{C}$ changes the raw signal from $2.4$ to $1.8\mathrm{mV}$. The appropriate reference correction changes from $0.8$ to $1.4\mathrm{mV}$, leaving the corrected sum at $3.2\mathrm{mV}$. No actual thermocouple material is assigned this constant coefficient.

If the reference sensor reads $33{}^{\circ }\mathrm{C}$ while the terminals are actually at $35{}^{\circ }\mathrm{C}$, the same model reports $78{}^{\circ }\mathrm{C}$. For a nonlinear reference function, first-order expansion givesprovided $F^{\prime }(T_h)\ne 0$. A reference-sensor temperature error therefore need not transfer one-for-one to the final temperature at every operating point.

Log the raw readout, reference-sensor reading, independent bath temperature and inferred temperature separately. Plateau measurements test steady behaviour; deliberate ramps can expose cold-junction thermal coupling and finite settling time. Reversing sweep direction can help distinguish reproducible offsets from lag. Maintaining a stable bath and adequate immersion remains necessary: a drift in the measuring junction would otherwise be confounded with reference compensation error.

A thermocouple uses two different electrical conductors and the Seebeck effect to infer a measuring-junction temperature from a voltage and a known reference temperature. The reference material and the reference temperature are distinct choices: B specifies the comparison Seebeck coefficient, while $T_c$ specifies the lower limit of the integral. The two-material experiment in Seebeck effect gives the geometry, sign convention, and calibration limitations.

The useful measurement is a pair: the raw terminal electric potential difference and the thermocouple reference junction temperature. For the A-positive terminal order and homogeneous-wire assumptions of Seebeck effect, write the open-circuit electromotive force asHere $T_h$ is the thermocouple measuring junction temperature and $T_c$ is the common temperature of the reference connections. The subscript $h$ names the measuring end; it need not be hotter. A voltmeter senses the complete connected thermoelectric path through the wires and its leads, in the electrochemical potential convention already described under Seebeck effect. It does not measure an absolute temperature, the individual Seebeck coefficient of A, or an isolated contact electric potential.

The thermocouple measuring junction joins A and B at the location whose temperature is to be inferred. Its own temperature is what the electrical measurement estimates. To infer a surrounding object's temperature, the junction must approach thermal equilibrium with that object: insufficient immersion, heat conduction along the wires, or a changing environment can keep the junction at another temperature. A stable electrical display alone does not establish that this thermal condition holds. The two-heat bath procedure and terminal-reversal controls under Seebeck effect provide the starting experiment; the practical issue here is the reference and conversion chain.

A thermopile absorber converts incident electromagnetic radiation into heat near the thermocouple measuring junctions. Electrically separate junctions can share its temperature through thermal contact. The reference support provides a path for heat transfer and a comparison temperature; “cold” denotes this reference role, even if it is warmer than the absorber.

Distinguish incident power from absorbed power. A window, the illuminated area, and the absorption of the coating determine their relation. A detector's measured voltage sensitivity can depend on where a small illuminated spot lies.^[ref] The model in thermopile thermal response takes absorbed power as its input, so an optical calibration is a separate step.

Use the A-positive terminal order of Seebeck effect for each thermocouple. Its thermocouple measuring junction has temperature $T_{h,i}$ and its reference connections have temperature $T_{c,i}$. Define the difference of Seebeck coefficients as ${\alpha }_i(T)=S_{A,i}(T)-S_{B,i}(T)$. Connect the B reference end of one thermocouple to the A reference end of the next at a common local temperature, so the terminal electric potential differences add:The first A reference terminal is the positive meter input; the final B reference terminal is the negative input. Following this connected path and adding the individual Seebeck effect integrals proves the result. Matched meter leads with common endpoint temperatures cancel as in an isothermal terminal block. The manufacturer's sum formula also allows unequal individual contributions.^[ref]

If all pairs share $T_h,T_c$ and the same nearly constant difference $\alpha$ of Seebeck coefficients throughout that temperature interval, thenThis $\alpha$ is the pair's relative Seebeck coefficient, not either material's individual coefficient or a universal device constant. As an original constructed example, choose $N=20$, $\alpha =40\mu \mathrm{V}{\mathrm{K}}^{-1}$ and $\Delta T=5\mathrm{K}$. Each thermocouple contributes $0.20\mathrm{mV}$ andReversing the meter connections changes the sign. Exchanging $T_h$ and $T_c$ reverses the integrals and hence the electromotive force; this reversible sign response does not make a detector with heat conduction a reversible thermodynamic process. Reversing the wiring of one pair instead gives $(N-2)\alpha \Delta T$, because one contribution is subtracted rather than added. For this example the result is $3.6\mathrm{mV}$, and at equal junction temperatures every contribution vanishes.

The open-circuit condition matters. If the array's total electrical resistance is $R_{\mathrm{pile}}$ and the meter input has electrical resistance $R_m$, the elementary voltage divider model gives $V_m=V_{\mathrm{oc}}{R}_m/(R_m+R_{\mathrm{pile}})$. Thus $R_m\gg R_{\mathrm{pile}}$ is needed to suppress voltmeter loading. Appreciable electric current also permits Joule heating and the thermoelectric heat transfer to disturb the assumed junction temperatures.