2949:( … I dipped into boiling water one end of such an arc for about half a minute, then I took it out and without giving it time to cool, resumed the experiment with the two glasses of cool water; and at this point that the frog in the bath convulsed; and this even two, three, four times, repeating the experiment; until, cooled – by such dips more or less long and repeated, or by a longer exposure to the air – the end of the iron dipped earlier into the hot water, this arc returned completely incapable of exciting convulsions of the animal.)
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transfer from the hot reservoir to the cold reservoir would need to be prevented by a specifically matching voltage difference maintained by the electric reservoirs, and the electric current would need to be zero. For a steady state, there must be at least some heat transfer or some non-zero electric
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The thermoelectric effects lie beyond the scope of equilibrium thermodynamics. They necessarily involve continuing flows of energy. At least, they involve three bodies or thermodynamic subsystems, arranged in a particular way, along with a special arrangement of the surroundings. The three bodies are
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In practice, thermoelectric effects are essentially unobservable for a localized hot or cold spot in a single homogeneous conducting material, since the overall emfs from the increasing and decreasing temperature gradients will perfectly cancel out. Attaching an electrode to the hotspot in an attempt
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is the
Thomson coefficient. The Thomson effect is a manifestation of the direction of flow of electrical carriers with respect to a temperature gradient within a conductor. These absorb energy (heat) flowing in a direction opposite to a thermal gradient, increasing their potential energy, and, when
1177:
in magnetic induction): if a simple thermoelectric circuit is closed, then the
Seebeck effect will drive a current, which in turn (by the Peltier effect) will always transfer heat from the hot to the cold junction. The close relationship between Peltier and Seebeck effects can be seen in the direct
2904:
In 1794, Volta found that if a temperature difference existed between the ends of an iron rod, then it could excite spasms of a frog's leg. His apparatus consisted of two glasses of water. Dipped in each glass was a wire that was connected to one or the other hind leg of a frog. An iron rod was
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functions similarly to a thermocouple but involves an unknown material instead of an unknown temperature: a metallic probe of known composition is kept at a constant known temperature and held in contact with the unknown sample that is locally heated to the probe temperature, thereby providing an
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If the
Thomson coefficient of a material is measured over a wide temperature range, it can be integrated using the Thomson relations to determine the absolute values for the Peltier and Seebeck coefficients. This needs to be done only for one material, since the other values can be determined by
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The
Thomson coefficient is unique among the three main thermoelectric coefficients because it is the only one directly measurable for individual materials. The Peltier and Seebeck coefficients can only be easily determined for pairs of materials; hence, it is difficult to find values of absolute
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article for more details) the voltage measured at the loose ends of the wires is directly dependent on the unknown temperature, and yet totally independent of other details such as the exact geometry of the wires. This direct relationship allows the thermocouple arrangement to be used as a
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1276:
For certain materials, the
Seebeck coefficient is not constant in temperature, and so a spatial gradient in temperature can result in a gradient in the Seebeck coefficient. If a current is driven through this gradient, then a continuous version of the Peltier effect will occur. This
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that develops across two points of an electrically conducting material when there is a temperature difference between them. The emf is called the
Seebeck emf (or thermo/thermal/thermoelectric emf). The ratio between the emf and temperature difference is the Seebeck coefficient. A
740:
to measure the locally shifted voltage will only partly succeed: it means another temperature gradient will appear inside of the electrode, and so the overall emf will depend on the difference in
Seebeck coefficients between the electrode and the conductor it is attached to.
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the two different metals and their junction region. The junction region is an inhomogeneous body, assumed to be stable, not suffering amalgamation by diffusion of matter. The surroundings are arranged to maintain two temperature reservoirs and two electric reservoirs.
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Often, more than one of the above effects is involved in the operation of a real thermoelectric device. The
Seebeck effect, Peltier effect, and Thomson effect can be gathered together in a consistent and rigorous way, described here; this also includes the effects of
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726:
The
Seebeck coefficients generally vary as function of temperature and depend strongly on the composition of the conductor. For ordinary materials at room temperature, the Seebeck coefficient may range in value from −100 μV/K to +1,000 μV/K (see
1260:) that varies with the square of current, the thermoelectric heating effect is linear in current (at least for small currents) but requires a cold sink to replenish with heat energy. This rapid reversing heating and cooling effect is used by many modern
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measures the difference in potential across a hot and cold end for two dissimilar materials. This potential difference is proportional to the temperature difference between the hot and cold ends. First discovered in 1794 by
Italian scientist
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measuring pairwise Seebeck coefficients in thermocouples containing the reference material and then adding back the absolute Seebeck coefficient of the reference material. For more details on absolute Seebeck coefficient determination, see
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In 1854, Lord Kelvin found relationships between the three coefficients, implying that the Thomson, Peltier, and Seebeck effects are different manifestations of one effect (uniquely characterized by the Seebeck coefficient).
971:, who discovered it in 1834. When a current is made to flow through a junction between two conductors, A and B, heat may be generated or removed at the junction. The Peltier heat generated at the junction per unit time is
2595:(It's undoubtedly necessary to distinguish henceforth this new class of electrical circuits by an indicative name; and as such I propose the expression "thermo-electric circuits" or perhaps "thermelectric circuits" … )
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involves multiple junctions in series, through which a current is driven. Some of the junctions lose heat due to the Peltier effect, while others gain heat. Thermoelectric heat pumps exploit this phenomenon, as do
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are like a thermocouple/thermopile but instead draw some current from the generated voltage in order to extract power from heat differentials. They are optimized differently from thermocouples, using high quality
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bent into a bow and one end was heated in boiling water. When the ends of the iron bow were dipped into the two glasses, a thermoelectric current passed through the frog's legs and caused them to twitch. See:
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Prunet, G.; Pawula, F.; Fleury, G.; Cloutet, E.; Robinson, A.J.; Hadziioannou, G.; Pakdel, A. (2021). "A review on conductive polymers and their hybrids for flexible and wearable thermoelectric applications".
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is a refrigerator that is compact and has no circulating fluid or moving parts. Such refrigerators are useful in applications where their advantages outweigh the disadvantage of their very low efficiency.
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321:, measure temperature or change the temperature of objects. Because the direction of heating and cooling is affected by the applied voltage, thermoelectric devices can be used as temperature controllers.
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2273:, and it is worth noting that this second Thomson relation is only guaranteed for a time-reversal symmetric material; if the material is placed in a magnetic field or is itself magnetically ordered (
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is the electric current (from A to B). The total heat generated is not determined by the Peltier effect alone, as it may also be influenced by Joule heating and thermal-gradient effects (see below).
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The Peltier coefficients represent how much heat is carried per unit charge. Since charge current must be continuous across a junction, the associated heat flow will develop a discontinuity if
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1268:(PCR). PCR requires the cyclic heating and cooling of samples to specified temperatures. The inclusion of many thermocouples in a small space enables many samples to be amplified in parallel.
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involve two wires, each of a different material, that are electrically joined in a region of unknown temperature. The loose ends are measured in an open-circuit state (without any current,
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To describe the Peltier and Thomson effects, we must consider the flow of energy. If temperature and charge change with time, the full thermoelectric equation for the energy accumulation,
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336:(the Seebeck coefficient varies with temperature). The Seebeck and Peltier effects are different manifestations of the same physical process; textbooks may refer to this process as the
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cannot be uniquely distinguished. This is more complicated than the often considered thermodynamic processes, in which just two respectively homogeneous subsystems are connected.
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current. The two modes of energy transfer, as heat and by electric current, can be distinguished when there are three distinct bodies and a distinct arrangement of surroundings.
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flowing in the same direction as a thermal gradient, they liberate heat, decreasing their potential energy. The Thomson coefficient is related to the Seebeck coefficient as
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needle would be deflected by a closed loop formed by two different metals joined in two places, with an applied temperature difference between the joints. Danish physicist
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There is a generalized second Thomson relation relating anisotropic Peltier and Seebeck coefficients with reversed magnetic field and magnetic order. See, for example,
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2585:"Il faudra sans doute désormais distinguer cette nouvelle classes de circuits électriques par une dénomination significative; et comme telle je propose l'expression de
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in a thermopile arrangement, to maximize the extracted power. Though not particularly efficient, these generators have the advantage of not having any moving parts.
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Thermoelectric coolers are trivially reversible, in that they can be used as heaters by simply reversing the current. Unlike ordinary resistive electrical heating (
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2366:– a thermoelectric phenomenon when a sample allowing electrical conduction in a magnetic field and a temperature gradient normal (perpendicular) to each other
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This relation expresses a subtle and fundamental connection between the Peltier and Seebeck effects. It was not satisfactorily proven until the advent of the
1953:{\displaystyle -{\dot {q}}_{\text{ext}}=\nabla \cdot (\kappa \nabla T)+\mathbf {J} \cdot \left(\sigma ^{-1}\mathbf {J} \right)-T\mathbf {J} \cdot \nabla S.}
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in the material to diffuse from the hot side to the cold side. This is due to charge carrier particles having higher mean velocities (and thus
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As the "figure of merit" approaches infinity, the Peltier–Seebeck effect can drive a heat engine or refrigerator at closer and closer to the
306:. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it,
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is the Seebeck coefficient. This relationship is easily shown given that the Thomson effect is a continuous version of the Peltier effect.
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1285:(William Thomson). It describes the heating or cooling of a current-carrying conductor with a temperature gradient. If a current density
2947:" … tuffava nell'acqua bollente un capo di tal arco per qualche mezzo minuto, … inetto de tutto ad eccitare le convulsioni dell'animale."
2939:(New memoir on animal electricity, divided into three letters, addressed to Abbot Antonio Maria Vassalli … First letter), pp. 197–206;
967:: the presence of heating or cooling at an electrified junction of two different conductors. The effect is named after French physicist
390:) at higher temperatures, leading them to migrate on average towards the colder side, in the process carrying heat across the material.
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and ordinary heat conduction. As stated above, the Seebeck effect generates an electromotive force, leading to the current equation
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are formed from many thermocouples in series, zig-zagging back and forth between hot and cold. This multiplies the voltage output.
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If the material is not in a steady state, a complete description needs to include dynamic effects such as relating to electrical
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Depending on the material properties and nature of the charge carriers (whether they are positive holes in a bulk material or
2936:"Nuova memoria sull'elettricità animale, divisa in tre lettere, dirette al Signor Abate Anton Maria Vassalli … Lettera Prima"
2911:"Nuova memoria sull'elettricità animale del Sig. Don Alessandro Volta … in alcune lettere al Sig. Ab. Anton Maria Vassalli …"
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This article is about the thermoelectric effect as a physical phenomenon. For applications of the thermoelectric effect, see
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are different. The Peltier effect can be considered as the back-action counterpart to the Seebeck effect (analogous to the
2913:[New memoir on animal electricity from Don Alessandro Volta … in some letters to Abbot Antonio Maria Vassalli …].
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2378:– the creation of an electric polarization in a crystal after heating/cooling, an effect distinct from thermoelectricity
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1688:{\displaystyle {\dot {e}}=\nabla \cdot (\kappa \nabla T)-\nabla \cdot (V+\Pi )\mathbf {J} +{\dot {q}}_{\text{ext}},}
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are often combined in series as they have opposite directions for heat transport, as specified by the sign of their
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Goupil, Christophe; Ouerdane, Henni; Zabrocki, Knud; Seifert, Wolfgang; Hinsche, Nicki F.; Müller, Eckhard (2016).
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are nonlinearly temperature dependent and different for the two materials, the open-circuit condition means that
1474:). This equation, however, neglects Joule heating and ordinary thermal conductivity (see full equations below).
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is passed through a homogeneous conductor, the Thomson effect predicts a heat production rate per unit volume.
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1833:. Using these facts and the second Thomson relation (see below), the heat equation can be simplified to
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material, is not generally termed a thermoelectric effect. The Peltier–Seebeck and Thomson effects are
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If the material has reached a steady state, the charge and temperature distributions are stable, so
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2384:- the production of electrical power from a galvanic cell with electrodes at different temperatures
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Jack, P.M. (2003). "Physical Space as a Quaternion Structure I: Maxwell Equations. A Brief Note".
2011:
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The voltage in this case does not refer to electric potential but rather the "voltmeter" voltage
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Any device that works at the Carnot efficiency is thermodynamically reversible, a consequence of
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625:. In general, the Seebeck effect is described locally by the creation of an electromotive field
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curves of the two materials, and of the reference temperature at the measured loose wire ends.
508:(EMF) and leads to measurable currents or voltages in the same way as any other EMF. The local
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being an indirect consequence, and so coined the more accurate term "thermoelectricity".
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noted that the temperature difference was in fact driving an electric current, with the
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of negative charge), heat can be carried in either direction with respect to voltage.
352:). The Thomson effect is an extension of the Peltier–Seebeck model and is credited to
324:
The term "thermoelectric effect" encompasses three separately identified effects: the
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2281:, etc.), then the second Thomson relation does not take the simple form shown here.
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A thermoelectric circuit composed of materials of different Seebeck coefficients (p-
2933:… . (in Italian) Florence (Firenze), (Italy): Guglielmo Piatti. vol. 2, part 1.
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2395:- production of electrical power from thermal energy using the photovoltaic effect
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straightforward uncalibrated thermometer, provided knowledge of the difference in
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2697:
2431:
2372:– thermoelectric phenomenon affecting current in a conductor in a magnetic field
2034:
907:
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Thomson, William (1851). "On a mechanical theory of thermo-electric currents".
2603:[Notice of new electro-magnetic experiments of Mr. Seebeck in Berlin].
2601:"Notiz von neuen electrisch-magnetischen Versuchen des Herrn Seebeck in Berlin"
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The middle term is the Joule heating, and the last term includes both Peltier (
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Direct conversion of temperature differences to electric voltage and vice versa
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Annali di Chimica e Storia Naturale (Annals of Chemistry and Natural History)
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340:(the separation derives from the independent discoveries by French physicist
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1725:, and the second term shows the energy carried by currents. The third term,
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1548:{\displaystyle \mathbf {J} =\sigma (-{\boldsymbol {\nabla }}V-S\nabla T).}
568:{\displaystyle \mathbf {J} =\sigma (-\nabla V+\mathbf {E} _{\text{emf}}),}
2571:"Nouvelles expériences de M. Seebeck sur les actions électro-magnetiques"
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But in the case of continuous variation in the media, heat transfer and
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For an imagined, but not actually possible, thermodynamic equilibrium,
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2573:[New experiments by Mr. Seebeck on electro-magnetic actions].
2522:
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Disalvo, F. J. (1999). "Thermoelectric Cooling and Power Generation".
2008:
in thermal gradient) effects. Combined with the Seebeck equation for
1361:{\displaystyle {\dot {q}}=-{\mathcal {K}}\mathbf {J} \cdot \nabla T,}
2714:[New experiments on the heat effects of electric currents].
700:(also known as thermopower), a property of the local material, and
362:, the heat that is generated whenever a current is passed through a
2827:"On the dynamical theory of heat. Part V. Thermo-electric currents"
2284:
Now, using the second relation, the first Thomson relation becomes
939:
928:
489:
Seebeck observed what he called "thermomagnetic effect" wherein a
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2712:"Nouvelles expériences sur la caloricité des courants électrique"
904:. This can help distinguish between different metals and alloys.
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307:
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from one side to the other, creating a temperature difference.
1033:{\displaystyle {\dot {Q}}=(\Pi _{\text{A}}-\Pi _{\text{B}})I,}
40:
1761:, is the heat added from an external source (if applicable).
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Seebeck or Peltier coefficients for an individual material.
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3125:
A news article on the increases in thermal diode efficiency
2137:{\displaystyle {\mathcal {K}}\equiv {\frac {d\Pi }{dT}}-S,}
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approximate measurement of the unknown Seebeck coefficient
328:(temperature differences causes electromotive forces), the
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Collezione dell'Opere del Cavaliere Conte Alessandro Volta
959:
When an electric current is passed through a circuit of a
2543:
Continuum Theory and Modeling of Thermoelectric Elements
1096:
are the Peltier coefficients of conductors A and B, and
448:. If the load resistor at the bottom is replaced with a
332:(thermocouples create temperature differences), and the
3051:
Semiconductor Thermoelements and Thermoelectric Cooling
3018:
Besançon, Robert M. (1985). Besançon, Robert M. (ed.).
2736:"4. On a Mechanical Theory of Thermo-Electric Currents"
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3114:"2.3.3 Thermoelectric Effects: General Consideration"
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667:{\displaystyle \mathbf {E} _{\text{emf}}=-S\nabla T,}
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1463:{\displaystyle {\mathcal {K}}=T{\tfrac {dS}{dT}}}
1264:, laboratory devices used to amplify DNA by the
774:). Although the materials' Seebeck coefficients
2414:"The Peltier Effect and Thermoelectric Cooling"
2831:Transactions of the Royal Society of Edinburgh
504:The Seebeck effect is a classic example of an
3078:Proceedings of the Royal Society of Edinburgh
2741:Proceedings of the Royal Society of Edinburgh
444:and n-doped semiconductors), configured as a
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1281:was predicted and later observed in 1851 by
955:Video from thermal camera of peltier element
1826:{\displaystyle \nabla \cdot \mathbf {J} =0}
1237:The Peltier effect can be used to create a
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131:Learn how and when to remove this message
2929:Reprinted in: Volta, Alessandro (1816)
3026:(3rd ed.). Van Nostrand Reinhold.
2897:
2867:Thermoelectrics Handbook: Macro to Nano
2405:
1754:{\displaystyle {\dot {q}}_{\text{ext}}}
1178:connection between their coefficients:
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2966:Thermoelectrics Handbook:Macro to Nano
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2539:"Thermodynamics and thermoelectricity"
1471:
1208:
478:, it is named after the Russian born,
2545:. New York: Wiley-VCH. pp. 2–3.
2078:Heat transfer physics § Electron
1484:Heat transfer physics § Electron
1249:Other heat pump applications such as
245:Radioisotope thermoelectric generator
7:
3106:International Thermoelectric Society
933:The Seebeck circuit configured as a
69:adding citations to reliable sources
825:{\displaystyle \nabla V=-S\nabla T}
378:At the atomic scale, a temperature
250:Automotive thermoelectric generator
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1393:is the temperature gradient, and
1253:may also use Peltier heat pumps.
2803:Leon van Dommelen (2002-02-01).
2747:. Cambridge Univ. Press: 91–98.
2716:Annales de Chimie et de Physique
2210:is the Peltier coefficient, and
2016:
1934:
1918:
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1223:devices found in refrigerators.
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370:, whereas Joule heating is not.
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2775:CRC Handbook of Thermoelectrics
2541:. In Goupil, Christophe (ed.).
2233:The second Thomson relation is
1166:{\displaystyle \Pi _{\text{B}}}
1139:{\displaystyle \Pi _{\text{A}}}
1089:{\displaystyle \Pi _{\text{B}}}
1062:{\displaystyle \Pi _{\text{A}}}
832:everywhere. Therefore (see the
731:article for more information).
432:made from iron and copper wires
56:needs additional citations for
2183:{\displaystyle {\mathcal {K}}}
2086:The first Thomson relation is
1885:
1873:
1652:
1640:
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1410:{\displaystyle {\mathcal {K}}}
1021:
995:
767:{\displaystyle \mathbf {J} =0}
559:
532:
1:
2945:From (Volta, 1794), p. 139:
2805:"A.11 Thermoelectric effects"
2166:is the absolute temperature,
1723:Fourier's heat conduction law
1478:Full thermoelectric equations
969:Jean Charles Athanase Peltier
723:is the temperature gradient.
486:who rediscovered it in 1821.
342:Jean Charles Athanase Peltier
2773:Rowe, David Michael (1994).
2514:10.1016/j.mtphys.2021.100402
2450:10.1126/science.285.5428.703
2190:is the Thomson coefficient,
2074:Onsager reciprocal relations
2023:{\displaystyle \mathbf {J} }
1792:{\displaystyle {\dot {e}}=0}
1300:{\displaystyle \mathbf {J} }
499:generation of magnetic field
368:thermodynamically reversible
294:is the direct conversion of
3022:The Encyclopedia of Physics
2587:circuits thermo-électriques
317:This effect can be used to
3166:
2909:Volta, Alessandro (1794).
2577:. 2nd series (in French).
2477:"THERMOELECTRIC PHENOMENA"
2071:
1985:at junction) and Thomson (
1579:{\displaystyle {\dot {e}}}
1481:
1230:
29:
3112:Föll, Helmut (Oct 2019).
3090:10.1017/S0370164600027310
3084:(published 1857): 91–98.
3032:10.1007/978-1-4615-6902-2
2865:Rowe, D. M., ed. (2010).
2843:10.1017/S0080456800032014
2825:Thomson, William (1857).
2753:10.1017/S0370164600027310
2733:Thomson, William (1857).
2669:{\displaystyle V=-\mu /e}
1266:polymerase chain reaction
914:Thermoelectric generators
466:electromotive force (emf)
2964:Rowe, D.M., ed. (2006).
2625:10.1002/andp.18230730410
2464:classical thermodynamics
2260:{\displaystyle \Pi =TS.}
2001:{\displaystyle \nabla S}
1978:{\displaystyle \nabla S}
1721:. The first term is the
1386:{\displaystyle \nabla T}
919:thermoelectric materials
716:{\displaystyle \nabla T}
446:thermoelectric generator
298:differences to electric
240:Thermoelectric generator
220:Thermoelectric materials
32:Thermoelectric materials
2502:Materials Today Physics
1710:{\displaystyle \kappa }
1241:. Notably, the Peltier
1200:{\displaystyle \Pi =TS}
614:{\displaystyle \sigma }
80:"Thermoelectric effect"
2690:
2670:
2332:
2261:
2224:
2204:
2184:
2160:
2138:
2024:
2002:
1979:
1954:
1827:
1793:
1755:
1711:
1689:
1580:
1549:
1464:
1411:
1387:
1362:
1301:
1233:Thermoelectric cooling
1221:thermoelectric cooling
1201:
1167:
1140:
1110:
1090:
1063:
1034:
956:
937:
898:
881:Thermoelectric sorting
871:
851:
826:
788:
768:
717:
690:
668:
615:
591:
569:
457:
433:
338:Peltier–Seebeck effect
235:Thermoelectric cooling
36:Thermoelectric cooling
3120:. University of Kiel.
2978:10.1201/9781420038903
2691:
2671:
2333:
2262:
2225:
2205:
2185:
2161:
2139:
2025:
2003:
1980:
1955:
1828:
1794:
1756:
1712:
1690:
1581:
1550:
1465:
1412:
1388:
1363:
1302:
1243:thermoelectric cooler
1202:
1168:
1141:
1111:
1091:
1064:
1035:
954:
935:thermoelectric cooler
932:
899:
872:
852:
827:
789:
769:
718:
691:
669:
616:
592:
570:
495:Hans Christian Ørsted
484:Thomas Johann Seebeck
439:
424:
350:Thomas Johann Seebeck
302:and vice versa via a
292:thermoelectric effect
168:Thermoelectric effect
146:Thermoelectric effect
3118:Electronic Materials
3049:Ioffe, A.F. (1957).
2970:Taylor & Francis
2689:{\displaystyle \mu }
2680:
2643:
2418:ffden-2.phys.uaf.edu
2370:Ettingshausen effect
2359:Barocaloric material
2290:
2239:
2214:
2203:{\displaystyle \Pi }
2194:
2170:
2150:
2092:
2012:
1989:
1966:
1839:
1803:
1768:
1729:
1719:thermal conductivity
1701:
1592:
1561:
1499:
1422:
1397:
1374:
1313:
1289:
1182:
1150:
1123:
1100:
1073:
1046:
977:
888:
861:
841:
798:
778:
750:
704:
680:
631:
605:
581:
518:
411:Seebeck coefficients
319:generate electricity
197:Ettingshausen effect
65:improve this article
2617:1823AnP....73..430O
2583:From pp. 199–200:
2382:Thermogalvanic cell
2347:Seebeck coefficient
729:Seebeck coefficient
698:Seebeck coefficient
506:electromotive force
189:Seebeck coefficient
3140:Physical phenomena
2807:. eng.famu.fsu.edu
2686:
2666:
2605:Annalen der Physik
2393:Thermophotovoltaic
2328:
2326:
2257:
2220:
2200:
2180:
2156:
2134:
2062:thermodynamic work
2020:
1998:
1975:
1950:
1823:
1789:
1751:
1707:
1685:
1576:
1545:
1460:
1458:
1407:
1383:
1358:
1297:
1214:A typical Peltier
1197:
1163:
1136:
1106:
1086:
1059:
1030:
957:
938:
894:
867:
847:
822:
784:
764:
713:
686:
664:
611:
587:
565:
458:
434:
3150:Thermoelectricity
3145:Energy conversion
2575:Annales de chimie
2444:(5428): 703–706.
2432:Carnot efficiency
2325:
2279:antiferromagnetic
2271:Onsager relations
2223:{\displaystyle S}
2159:{\displaystyle T}
2123:
2068:Thomson relations
1861:
1855:
1780:
1748:
1742:
1679:
1673:
1604:
1573:
1457:
1325:
1160:
1133:
1109:{\displaystyle I}
1083:
1056:
1018:
1005:
989:
952:
897:{\displaystyle S}
870:{\displaystyle T}
850:{\displaystyle S}
787:{\displaystyle S}
689:{\displaystyle S}
643:
590:{\displaystyle V}
556:
288:
287:
141:
140:
133:
115:
16:(Redirected from
3157:
3121:
3093:
3072:
3045:
3025:
3014:
3012:
2999:
2950:
2922:
2902:
2885:
2884:
2861:
2855:
2854:
2822:
2816:
2815:
2813:
2812:
2800:
2789:
2788:
2770:
2764:
2763:
2761:
2759:
2738:
2730:
2724:
2723:
2710:Peltier (1834).
2707:
2701:
2695:
2693:
2692:
2687:
2675:
2673:
2672:
2667:
2662:
2637:
2631:
2628:
2599:Oersted (1823).
2591:thermélectriques
2582:
2563:
2557:
2556:
2534:
2528:
2527:
2525:
2496:
2490:
2489:
2487:
2486:
2481:
2473:
2467:
2461:
2428:
2422:
2421:
2410:
2337:
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2324:
2316:
2308:
2299:
2298:
2266:
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2258:
2229:
2227:
2226:
2221:
2209:
2207:
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2201:
2189:
2187:
2186:
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2179:
2178:
2165:
2163:
2162:
2157:
2143:
2141:
2140:
2135:
2124:
2122:
2114:
2106:
2101:
2100:
2029:
2027:
2026:
2021:
2019:
2007:
2005:
2004:
1999:
1984:
1982:
1981:
1976:
1959:
1957:
1956:
1951:
1937:
1926:
1922:
1921:
1916:
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1895:
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1416:
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1405:
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1389:
1384:
1367:
1365:
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1359:
1345:
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1339:
1327:
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1318:
1306:
1304:
1303:
1298:
1296:
1206:
1204:
1203:
1198:
1172:
1170:
1169:
1164:
1162:
1161:
1158:
1145:
1143:
1142:
1137:
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1115:
1113:
1112:
1107:
1095:
1093:
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1087:
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1084:
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1068:
1066:
1065:
1060:
1058:
1057:
1054:
1039:
1037:
1036:
1031:
1020:
1019:
1016:
1007:
1006:
1003:
991:
990:
982:
953:
903:
901:
900:
895:
876:
874:
873:
868:
856:
854:
853:
848:
831:
829:
828:
823:
793:
791:
790:
785:
773:
771:
770:
765:
757:
722:
720:
719:
714:
695:
693:
692:
687:
673:
671:
670:
665:
645:
644:
641:
639:
620:
618:
617:
612:
596:
594:
593:
588:
574:
572:
571:
566:
558:
557:
554:
552:
525:
491:magnetic compass
476:Alessandro Volta
280:
273:
266:
191:
184:
179:
174:
155:
143:
136:
129:
125:
122:
116:
114:
73:
49:
41:
21:
3165:
3164:
3160:
3159:
3158:
3156:
3155:
3154:
3130:
3129:
3111:
3101:
3096:
3075:
3061:
3048:
3042:
3017:
3010:math-ph/0307038
3002:
2988:
2963:
2959:
2957:Further reading
2954:
2953:
2908:
2903:
2899:
2894:
2889:
2888:
2881:
2864:
2862:
2858:
2824:
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2767:
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2732:
2731:
2727:
2709:
2708:
2704:
2678:
2677:
2641:
2640:
2638:
2634:
2598:
2569:Œrsted (1823).
2568:
2564:
2560:
2553:
2536:
2535:
2531:
2498:
2497:
2493:
2484:
2482:
2479:
2475:
2474:
2470:
2435:
2429:
2425:
2412:
2411:
2407:
2402:
2376:Pyroelectricity
2355:
2317:
2309:
2288:
2287:
2237:
2236:
2212:
2211:
2192:
2191:
2168:
2167:
2148:
2147:
2115:
2107:
2090:
2089:
2080:
2070:
2010:
2009:
1987:
1986:
1964:
1963:
1904:
1903:
1899:
1845:
1837:
1836:
1801:
1800:
1766:
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1732:
1727:
1726:
1699:
1698:
1663:
1590:
1589:
1559:
1558:
1497:
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1449:
1441:
1420:
1419:
1395:
1394:
1372:
1371:
1311:
1310:
1287:
1286:
1274:
1262:thermal cyclers
1235:
1229:
1180:
1179:
1153:
1148:
1147:
1126:
1121:
1120:
1098:
1097:
1076:
1071:
1070:
1049:
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1011:
998:
975:
974:
940:
927:
886:
885:
859:
858:
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838:
796:
795:
776:
775:
748:
747:
737:
702:
701:
678:
677:
634:
629:
628:
603:
602:
579:
578:
547:
516:
515:
510:current density
419:
384:charge carriers
376:
284:
255:
254:
215:
207:
206:
187:
182:
177:
172:
163:
137:
126:
120:
117:
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62:
50:
39:
28:
23:
22:
15:
12:
11:
5:
3163:
3161:
3153:
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3147:
3142:
3132:
3131:
3128:
3127:
3122:
3109:
3100:
3099:External links
3097:
3095:
3094:
3073:
3059:
3053:. Infosearch.
3046:
3040:
3015:
3000:
2986:
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2944:
2943:
2927:
2917:(in Italian).
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2765:
2725:
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2630:
2629:
2611:(4): 430–432.
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1321:
1295:
1279:Thomson effect
1273:
1272:Thomson effect
1270:
1231:Main article:
1228:
1225:
1196:
1193:
1190:
1187:
1156:
1129:
1105:
1079:
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1010:
1001:
997:
994:
988:
985:
965:Peltier effect
926:
925:Peltier effect
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893:
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846:
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803:
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524:
462:Seebeck effect
426:Seebeck effect
418:
417:Seebeck effect
415:
399:Semiconductors
388:kinetic energy
375:
372:
334:Thomson effect
330:Peltier effect
326:Seebeck effect
286:
285:
283:
282:
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183:Thomson effect
180:
178:Peltier effect
175:
173:Seebeck effect
164:
161:
160:
157:
156:
148:
147:
139:
138:
53:
51:
44:
26:
24:
18:Seebeck effect
14:
13:
10:
9:
6:
4:
3:
2:
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3098:
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3062:
3060:0-85086-039-3
3056:
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3041:0-442-25778-3
3037:
3033:
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2987:0-8493-2264-2
2983:
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2882:
2880:9781420038903
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2776:
2769:
2766:
2754:
2750:
2746:
2742:
2737:
2729:
2726:
2721:
2718:(in French).
2717:
2713:
2706:
2703:
2699:
2683:
2663:
2659:
2655:
2652:
2649:
2646:
2636:
2633:
2626:
2622:
2618:
2614:
2610:
2607:(in German).
2606:
2602:
2597:
2594:
2590:
2589:ou peut-être
2586:
2580:
2576:
2572:
2567:
2566:
2562:
2559:
2554:
2552:9783527413379
2548:
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2368:
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2364:Nernst effect
2362:
2360:
2357:
2356:
2352:
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2338:
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2313:
2310:
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2275:ferromagnetic
2272:
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2044:
2043:heat capacity
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121:November 2019
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82: –
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54:This article
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735:Applications
725:
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623:conductivity
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214:Applications
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63:Please help
58:verification
55:
2941:see p. 202.
2925:see p. 139.
2837:: 123–171.
2698:Fermi level
2035:capacitance
1283:Lord Kelvin
908:Thermopiles
354:Lord Kelvin
312:transferred
296:temperature
3134:Categories
2921:: 132–144.
2811:2022-11-23
2784:0849301467
2758:7 February
2722:: 371–386.
2581:: 199–201.
2523:2262/98609
2508:: 100402.
2485:2024-08-13
2400:References
2388:Thermopile
2072:See also:
2039:inductance
1482:See also:
482:physicist
430:thermopile
364:conductive
348:physicist
230:Thermopile
162:Principles
91:newspapers
3069:600476276
2871:CRC Press
2851:120018011
2684:μ
2656:μ
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2243:Π
2198:Π
2126:−
2112:Π
2103:≡
1993:∇
1970:∇
1942:∇
1939:⋅
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1239:heat pump
1216:heat pump
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450:voltmeter
395:electrons
2996:70217582
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3005:arXiv
2892:Notes
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3055:ISBN
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2992:OCLC
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2875:ISBN
2779:ISBN
2760:2022
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