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What is the working principle of a thermocouple? Apparently, it isn't the contact voltage but, well, what is it? Finally it seems to be about the thermodiffusion but there is quite a lot going on so I would like to have an explanation in one or two sentences which I can use as a basis to dive deeper while I know where it is leading to.

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Well, a decent explanation would of course still be appreciated. For example, I'm totally overwhelmed how the chemical potential, contact voltage, temperature and diffusion interact with each other or, respectively, how they contribute in the end.

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  • $\begingroup$ Seebeck and Peltier effects hyperphysics.phy-astr.gsu.edu/hbase/electric/tcoup.html $\endgroup$
    – saad
    Jul 30, 2020 at 7:06
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    $\begingroup$ The paper Thermoelectric Effects in Metals - Thermocouples provides an excellent introduction starting from the Seebeck effect in one metal and then considering metal junctions. $\endgroup$
    – Farcher
    Jul 30, 2020 at 7:50
  • $\begingroup$ @Farcher I wouldn't call it excellent but rather "reasonably good". Discarding mispells like "Thompson" instead of Thomson, he simply throws words like "diffuse" without any justification (it is absolutely not trivial that electrons would diffuse from a side to the other in a non homogeneously heated metal rod, despite what one can read on the Internet and many textbooks). He doesn't say a word on Li's positive S despite it being the best case of what he calls a "normal metal". And his discussion about the sign of S indicating whether a semiconductor is p or n doped is not quite accurate. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 30, 2020 at 8:11
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    $\begingroup$ @thermomagnetic condensed boson As a simple if not completely accurate and detail introduction I thought it merited a mention. The author did try and put some meat on the bones without the analysis being too complex. $\endgroup$
    – Farcher
    Jul 30, 2020 at 9:55
  • $\begingroup$ @Farcher I agree with you and this is why I think it deserves the mention "reasonably good" instead of "excellent" or "bad/wrong". $\endgroup$
    – untreated_paramediensis_karnik
    Jul 30, 2020 at 10:33

4 Answers 4

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Ok, I give a shot at a simple explanation.

Draw a "circuit" of the thermocouple attached to a voltmeter, like in the following picture. enter image description here

I picked $T_p$ as the probed temperature. $T_\text{ref}$ is a reference temperature, Ni stands for nickel and Ag for silver. In this particular case, the voltage read by the voltmeter is $V=S_\text{Ag}\Delta T - S_\text{Ni}\Delta T$, as long as the voltmeter's lead are of a single material (regardless of which material it is).

So a quick explanation would be that a thermocouple is a union of two materials made at a point where one seeks to probe its temperature. Thanks to the Seebeck effect, which states that a temperature difference across a material induces a voltage proportional to this temperature difference, one can arrange a simple setup where reading the voltage of the couple leads back to $T_p$ which is the goal.

The reason this works is because $T_\text{ref}$ is assumed to be known as well as the Seebeck coefficients of the two materials (in a given temperature range), hence the knowledge of $V$ yields the knowledge of $T_p$.

Responding to your comment, I will give a try that involves some physics. From Onsager theory, we have the generalized Ohm's law $\vec J_e = - \sigma \nabla \overline \mu - \sigma S \nabla T$ which tells us, amongst other things, that an electrical current can be due to both an applied voltage or a temperature difference across a given length. In the case of a thermocouple, there is no current and so $\vec J_e = \vec 0$ from which one derives the relation $d\overline \mu = - SdT$.

At any of the junctions of the materials making up the thermocouple, the conditions are isothermal and there is no current. This means that the electrochemical potential $\overline \mu$ is spatially continuous at the junctions. From this information, one gets $V = \int _{T_\text{ref}}^T (S_\text{Ag} - S_\text{Ni}) dT$ (voltage displayed by the voltmeter) which is essentially the formula I wrote above.

Now, from first principles it is in general extremely hard to explain the value of $S$ of a material. There are some formulae like Mott's one which are derived assuming a free electron model and are valid for some metals, and other formulae are valid for some semiconductors, etc. In general there is no simple explanation of the value of the Seebeck coefficient. Sometimes it is a sum of several "effects" like phonon drag for example.

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  • $\begingroup$ Thank you! I know I exactly asked this but I'm actually more interested in the theory behind it why it basically works. btw: The image isn't available(?). $\endgroup$
    – Ben
    Jul 30, 2020 at 9:46
  • $\begingroup$ I have modified my answer by adding more information. I can see the picture, isn't it still not displayed by default for you? Feel free to ask for anything if something's not clear. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 30, 2020 at 13:45
  • $\begingroup$ Thanks a lot! I think I got the concept itself but, e.g., cannot apply to the image I added above. I'm not sure how diffusion/chemical potential works at the specific material boundaries. $\endgroup$
    – Ben
    Jul 31, 2020 at 9:26
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    $\begingroup$ @Ben The electrochemical potential tells you how much energy is required to add a particle in a given position. If there is a difference in the value of the electrochemical potential across a distance (its gradient is not null), then there will be a particle's motion if it is allowed. So in the case of a contact between 2 metals, in your picture initially the electrochemical potential differs between the 2 metals, but very quickly a motion of electrons make it equal across the (isothermal) junction. The electrochemical potential is a function of temperature as you can see in your picture. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 31, 2020 at 9:49
  • $\begingroup$ Now I got, awesome. Thank you very much! Just another question based on your statement that the electrochemical potentials tells how much energy is needed to add a particle. I wonder why that is different from the work function which is the reverse process? $\endgroup$
    – Ben
    Jul 31, 2020 at 11:26
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An explanation in one or two sentences cannot provide an accurate understanding; at best it can provide a useful intuitive understanding. So: Think of electrons in a metal as a gas, where the electron (gas) density is different in different metals; and think of voltage as pressure.

1: The Ideal Gas Law applied to two metals in contact suggests that in order for electrons to move from "higher density" to "lower density" requires the addition of heat; and to move in the opposite direction causes release of heat.

2: The above principle, in its various permutations, provides an intuitive model of the Seebeck effect (generation of a voltage across the contact due to temperature differences), the Peltier effect (release or absorption of heat across the contact due to current flow), and the Thomson effect (the presence of a potential gradient in a conductor due to a temperature gradient).

The above explanation is an abbreviated version of the Drude model, which uses the idea of a free electron gas in metals. The book, "Free Electron Model of Metals", states:

Even though the approximation of lumping all interactions into the collision time of electrons sounds extremely rough at first, the model nevertheless provides a surprisingly good explanation of those properties of metals that are determined by the motion of electrons in applied electric or magnetic fields.

Electron "gas" does NOT follow the ideal gas law, because electrons are inevitably subject to the constraints of quantum mechanics. Treating electrons in metal as a gas can provide qualitatively correct understanding of thermoelectric processes, but in order to have a correct quantitative understanding, a much more sophisticated model must be used.

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  • $\begingroup$ This is wrong. The Thomson effect is a volume generation or absorption of heat in a material in which both a temperature gradient and an electric current are present. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 31, 2020 at 8:06
  • $\begingroup$ And by the way the Seebeck effect requires no two materials, i.e. no need for any contact. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 31, 2020 at 8:12
  • $\begingroup$ @Thermomagneticcondensedboson, britannica.com/science/Seebeck-effect : "Seebeck effect, production of an electromotive force (emf) and consequently an electric current in a loop of material consisting of at least two dissimilar conductors when two junctions are maintained at different temperatures." $\endgroup$
    – S. McGrew
    Jul 31, 2020 at 14:17
  • $\begingroup$ @thermomagneticcondensedboson, the Thomson effect aspect you refer to can be visualized as the consequence of moving an "electron gas" between regions held at different temperatures. If the distribution of temperature, electron density, and the shape of the conductor are kept constant as the "gas" moves, then heat is released or absorbed. The same physical process can drive a current. "The Seebeck and Peltier effects are different [aspects] of the same physical process...The Thomson effect is an extension of the Peltier–Seebeck model" en.wikipedia.org/wiki/Thermoelectric_effect. $\endgroup$
    – S. McGrew
    Jul 31, 2020 at 14:38
  • $\begingroup$ This is wrong and should not be trusted. The Seebeck effect is the appearance of a voltage between two point in a material when a temperature difference between those points exists. The fact that it was discovered for a pair of material, or that one needs a different material if one wants to be able to measure that voltage has nothing to do with the effect itself. See iue.tuwien.ac.at/phd/karamitaheri/node9.html . In fact there are ways to measure the Seebeck voltage without using a different material. $\endgroup$
    – untreated_paramediensis_karnik
    Jul 31, 2020 at 16:31
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The junction is only a connection between the two wires. The voltage is formed across the temperature gradient along the wire, as in the diagram below. Different metals produce different voltages for the same temperature gradient. If you connect the two together, you get the difference between the voltages produced by each wire. I think Aleksandr from Compare the Meerkat would agree that is "simples"👍. enter image description here

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The Seebeck effect tells us a temperature gradient across a piece of material results in a voltage gradient $V = S \Delta T$. In a thermocouple we bond two dissimilar (i.e. different Seebeck coefficients) conductive materials together at one end so that the voltage and temperature are the same at that end. At the other end (and throughout the length of the wires) the materials are not touching but they are close to each other so the temperature (but not voltage) is the same. We then have $V_1 = S_1 \Delta T$ and $V_2 = S_2 \Delta T$. We can measure $V_2 - V_1 = (S_2 - S_1)\Delta T$ so we see

$$ \Delta T = \frac{V_2 - V_1}{S_2 - S_1} $$

So by measuring the voltage difference and knowing the Seebeck coefficients we can determine the temperature difference between the two ends of the thermocouple.

This is a succinct and (in my opinion) clear explanation of how a thermocouple works. However, if you want to know how the Seebeck effect (upon which thermocouples rely) works (i.e. why $V = S \Delta T$), I would consider that to be a separate question which could be answered more clearly WITHOUT reference to thermocouples.

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