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I’ve been reading about the thermoelectric effect and Peltier cells, but one thing the sources seem to gloss over is where the cooling or heating actually occurs. They all seem to say “at the junction of the two materials”. What I’m wondering is, if one where to prevent any heat transfer between the materials (say an infinitely thin, infinitely electrically conductive, perfect thermal insulator placed in-between), where would heating/cooling occur?

EntropyDestroyer
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2 Answers2

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enter image description here Taken from: https://sciencestruck.com/seebeck-effect-with-applications

In the diagram above, you can see that heat does not actually travel between junction materials. Heat does not flow from junction material A to junction material B resulting in A being colder than B.

Instead, each individual junction material sits in a temperature gradient. In other words, A has a different temperature on each end, and B also has a different temperature on each end. It's not the temperature difference between junction materials that matters. It's the temperature difference within the same junction material.

So that was the Seebeck effect where you apply a temperature gradient to produce current. The Peltier effect is just in reverse. So you apply current to produce a temperature gradient.

Therefore, since your electrically conductive, thermally conductive material still allows current to flow between junction materials, and since the temperature gradient is within each junction metal rather than between junction metals, the thermal insulation does nothing and the system still works like normal.

DKNguyen
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  • This answer seems to address the Seebeck effect, where a temperature gradient already exists, whereas the question is about the inverse effect—the Peltier effect—where the temperature gradient is created. – Chemomechanics Jul 02 '21 at 14:59
  • @Chemomechanics My understanding is that they are the same effect, just in the reverse it has a different name. – DKNguyen Jul 02 '21 at 15:13
  • Agreed. But in one, the temperature gradient is applied, and in the other, it spontaneously arises. The question is about the details of the latter, no? But maybe I'm misreading it. – Chemomechanics Jul 02 '21 at 15:19
  • @Chemomechanics I don't think you're misreading. I guess I just thought it was easier to explain things from the reverse end and from there it would be obvious what would happen if reversed. I have added a parapgraph to make it more explicit. – DKNguyen Jul 02 '21 at 18:37
  • @Chemomechanics Yes, that's correct, I was asking about the Peltier effect. I don't quite understand why we see a temperature gradient though. I was under the impression that the electrons had to jump to a different energy level for cooling/heating to occur, so why would this happen along the length of the material? In practice of course it would look like this due to heat transfer (at steady state), but I'm more interested in the transient response, where the cooling/heating should happen much quicker than heat transfer. – EntropyDestroyer Jul 02 '21 at 20:41
  • @EntropyDestroyer Charge carriers also carry entropy, which is the extensive conjugate parameter of heat transfer. By forcing charge carriers to flow through an electric field, one conveniently forces heat flow as well, which generates a temperature gradient. This entire process is thermodynamically spontaneous because it minimizes the relevant potential: the electrochemical potential. – Chemomechanics Jul 02 '21 at 20:55
  • The Seebeck effect is not the reverse of the Peltier effect, to be pedantic. The Seebeck effect is just a charge carrier redistribution due to an applied thermal gradient, establishing a voltage between points at different temperature. This voltage can be used to, but is absolutely not obliged, create a current by using the TE material in a closed electrical circuit. The Peltier effect is an interface heat generation/absorption when an electrical current passes at the interface of two materials differing in their Seebeck coefficient. – untreated_paramediensis_karnik Jul 04 '21 at 17:57
  • @AccidentalBismuthTransform So what you are saying is that same mechanism, but the pedantic part comes in where Seebeck effect always produces a voltage which may or may not push a current, whereas Peltier absolutely does require current to be flowing (voltage alone is not enough for Peltier)? Sort of like how a generator can produce voltage with no current at open circuit but to make a motor spin you really do need current input? – DKNguyen Jul 04 '21 at 18:02
  • The Peltier effect is not a thermal gradient. It is a heat generation. It can, but need not, create a thermal gradient around it. This would depend on the properties of the surrounding materials around the interface, etc. Both the Peltier effects and Seebeck effects are a manifestation of the same "effect", called thermoelectricity, which is a sort of interference (not in the optical sense), between heat transfer processes and electrical processes. – untreated_paramediensis_karnik Jul 04 '21 at 18:04
  • I'll probably have to make some notes or something, because this stuff is usually completely messed up in the literature, and poorly explained in textbooks. Maybe that's because usually it isn't written by physicists, but I don't know (nor do I want to know). – untreated_paramediensis_karnik Jul 04 '21 at 18:04
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    Yes @DKNguyen , your latest comment is correct. – untreated_paramediensis_karnik Jul 04 '21 at 18:06
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Your title question is broader and has a different answer than what you ask in the body of your text.

Regarding the body of your text:

In a Peltier cell, the n and p materials make contact usually with copper or gold. In that case, n and p materials (semiconductors) have "high" Seebeck coefficient, of the order of $400$ µV/K, while metals (copper/gold) have at least an order of magnitude smaller Seebeck coefficient. What happens at the interface metal/semiconductor, is a heat generated, proportional to the difference in the Seebeck coefficients of the two interfaced materials. This heat is called the Peltier heat, and has a magnitude worth $(S_\text{A}-S_\text{B})TI$. This heat is generated right at the interface, it is not a volume-generated heat. The only ways to prevent this Peltier heat to generate is to either remove the current ($I=0$), pick two different materials which happen to possess the same Seebeck coefficient, or reach absolute zero temperature (of course impossible in practice, unlike the previous two).

Regarding thermoelectricity in general, to be short, there are several different possible volume-heat generations (Thomson and Bridgman heats to name the two most famous), these heats occur at every single point inside the thermoelectric materials. Some of them require a thermal gradient to exist, others require an anisotropy in the Seebeck coefficient (amongst other prerequisites), some of them require a position-dependent doping to occur, etc.

untreated_paramediensis_karnik
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  • Thanks for this answer! You mention that this is poorly explained in the literature; do you know of any books that explain it properly? – EntropyDestroyer Jul 04 '21 at 18:50
  • Hmm maybe not a single book. There is the paper by Domenicali https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.26.237 where the different effects (manifestations) are correctly described, and he covers the Bridgman effect too, which is very often forgotten. I have found a useful. If I remember well, Nye's textbook "Physical Properties of Crystals" also covered thermoelectricity quite well even though the main topic isn't thermoelectricity. There was another old textbook I could find only in archive.org that described it well, too. – untreated_paramediensis_karnik Jul 04 '21 at 19:04
  • (I forgot the name... but could search for it in case you really ask for it). Then, a more recent textbook although I don't remember to have found it particularly good or enough detailed, is the one by Goupil, called "Continuum Theory of Thermoelectric Elements", but it's probably not too bad.

    Then there are the "classics", which are related to thermoelectricty and which give insights... the original 1931 papers by Onsager who got him a Nobel prize, and the textbook "Non equilibrium thermodynamics" by de Groot and Mazur. These stuffs are NOT easy to go through!

     – untreated_paramediensis_karnik Jul 04 '21 at 19:06