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The Seebeck coefficient $S(T)$ quantifies the thermoelectric voltage response per small temperature difference at zero electric current. Use $S=-dV/dT$ along a homogeneous material, with voltage understood through electrochemical potential. Its units are volts per kelvin, commonly $\mu V/K$. The word thermopower is also used, despite this being a voltage response rather than power; some authors use that word for $|S|$, so check their convention. ^[ref].

For the A-minus-B terminal order in the Seebeck effect experiment,Thus a small temperature difference around $T_0$ gives $V_{AB}\approx [S_A(T_0)-S_B(T_0)]\Delta T$. The finite-interval ratio $V_{AB}/\Delta T$ is an average of the coefficient difference, not necessarily its value at either endpoint. Ordinary two-material measurements determine a relative Seebeck coefficient: to recover $S_A$ from the measured difference, add a separately known $S_B$. Neither the choice of a zero for voltage nor the use of a familiar reference material makes $S_B$ identically zero.

A concrete research example is Martin and colleagues' 2021 certification experiment. They measured small temperature differences and voltages on six silicon–germanium specimens at 13 base temperatures between $295$ and $900\mathrm{K}$. At each setting they acquired 40 voltage-and-temperature-difference pairs and used linear regression with a free intercept, so a constant voltage offset did not become part of the slope. Platinum voltage leads required a reference-material correction; their terminal order gave $S_{\mathrm{measured}}=S_{\mathrm{Pt}}-S_{\mathrm{specimen}}$, hence $S_{\mathrm{specimen}}=S_{\mathrm{Pt}}-S_{\mathrm{measured}}$. This is an actual measurement protocol, unlike the toy plot above. ^[ref].

Microscopically, a temperature gradient changes charge carrier transport until an opposing electrical response balances it at zero net electric current. In the usual simple semiconductor picture, Electrons and electron holes give opposite Seebeck coefficient signs, and their contributions are weighted by their electrical conductivities. The Seebeck coefficient is a transport property: density of states alone does not determine it, since carrier motion and scattering also matter. Its usefulness extends beyond temperature sensing to diagnosing which carriers transport electric charge. ^[ref].

The Seebeck effect is the generation of a thermoelectric electromotive force by a temperature difference. In a thermocouple, two different homogeneous electrical conductors A and B connect a measuring junction at $T_h$ to two reference connections at a common $T_c$. With negligible electric current, the measured terminal voltage is determined by the difference of their Seebeck coefficients. A hot junction alone does not specify the reading: the reference temperature, the second material, and the terminal order matter.

For a motivating experiment, join one end of A to one end of B, insulating the wires elsewhere. Connect their free ends to identical meter leads at reference temperature $T_c$, for example in an ice-water heat bath. A meter with input electrical resistance much larger than the thermocouple's electrical resistance approximates an open circuit, meaning $I\approx 0$. Keep the measuring junction in a separately controlled heat bath at $T_h$ and wait for stable junction temperatures. Both reference connections must share $T_c$; identical leads with identical endpoint temperatures have cancelling thermoelectric contributions, allowing the meter to be elsewhere. ^[ref].

Define the reading as $V_{AB}=V_A-V_B$, with the positive input on the A reference terminal and the negative input on B. Use the Seebeck coefficient convention in which the voltage change along a homogeneous wire at zero electric current is $dV=-S(T)dT$. Following the path from A at $T_c$ to the common junction at $T_h$, then back along B to $T_c$, givesThis formula assumes homogeneous materials whose Seebeck coefficients depend only on the local temperature, and no additional uncompensated lead contributions. Here voltage is the electrical transport voltage associated with electrochemical potential, rather than a direct measurement of an isolated equilibrium contact electric potential.

Start with $T_h=T_c$, then increase $T_h$ while holding $T_c$ fixed and record $V_{AB}$ at each stable setting. In the ideal model the equal-temperature reading is zero. If $S_A-S_B>0$ throughout the interval, A reads positive when $T_h>T_c$. Exchanging meter inputs reverses the reading; exchanging the two junction temperatures reverses the oriented integral. Repeating the run with identical homogeneous materials gives zero because $S_A=S_B$. These controls test the stated model; a nonzero experimental baseline should be measured rather than silently removed by assuming it is zero.

For an explicitly toy linear example, stipulate constant Seebeck coefficients $S_A=25\mu V/K$ and $S_B=-15\mu V/K$. Choose reference temperature $T_c=20{}^{\circ }\mathrm{C}$ and measuring-junction temperature $T_h=70{}^{\circ }\mathrm{C}$. A temperature difference has the same numerical size in kelvins and on the degree Celsius scale, soSwapping the inputs gives $-2.00\mathrm{mV}$. Bringing both junction regions to the same temperature gives zero. With temperature-dependent Seebeck coefficients, shifting both junction temperatures equally while keeping their difference fixed can change the reading. No actual material pair is claimed to have the stipulated coefficients over this interval.

Real thermocouples need a calibrated voltage-versus-temperature relation: the constant-Seebeck coefficient approximation is useful only where the coefficient difference changes little. Wire inhomogeneity can make the result depend on where the temperature gradient lies, and reference connections at unequal or unknown temperatures introduce errors. An electronic reference correction uses a measured reference temperature in place of an ice bath. ^[ref]. Burns and colleagues provide the standardized reference functions for common letter-designated thermocouple types; the toy line above is not a replacement for them. ^[ref].

The historical experiment used a different detector. In his 1821–1823 investigations, Seebeck found that a closed electrical circuit of two dissimilar materials with junctions at different temperatures deflected a compass needle. The modern explanation is that thermoelectric electromotive force drives an electric current, whose magnetic field deflects the needle. The open-circuit experiment above detects voltage while drawing negligible electric current. The striking connection is that a thermal imbalance can become an electrical signal and then a magnetic response. ^[ref].

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.