Documenting Instanity

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Just in case anybody else without the forethought to click on the page edit button was interested in the story about the kids from Utah who came up with a "better car air conditioning system" I can offer a couple of things. Their link, on the day of their post, to the original story seems lost.... sorry. The description of the Peltier effect link, before someone decided they would like a visit from extremely serious looking guys with funky ear pieces read:

The '''Peltier-Seebeck effect''', or '''thermoelectric effect''', is the direct conversion of heat differentials to electric [[voltage]] and vice versa. Related effects are the '''Thomson effect''' and [[Joule heating]]. The Peltier, Seebeck, and Thomson effects are reversible; Joule heating is not, and cannot be, under the [[laws of thermodynamics]].

==Seebeck effect==
The '''Seebeck effect''' is the conversion of [[heat]] differences directly into [[electricity]].

This effect was first discovered, accidentally, by the [[Estonia]]n physicist [[Thomas Johann Seebeck]] in [[1821]], who found that a voltage existed between two ends of a [[metal]] bar when a temperature gradient $\backslash nabla\; T$ existed in the bar.

He also discovered that a [[compass]] needle would be deflected when a closed loop was formed of two metals with a temperature difference between the junctions. This is because the metals respond differently to the heat difference, which creates a current loop, which produces a [[magnetic field]].

A [[voltage]], the thermoelectric [[Electromotive force|EMF]], is created in the presence of a [[temperature]] difference between two different metals or [[semiconductor]]s. This usually causes a continuous current to flow in the conductors. The voltage created is on the order of several μV per [[kelvin]] (or degree [[Celsius]]) of difference.

In the circuit:

[[Image:Seebeck_effect_circuit_2.png]]

(which can be in several different configurations and be governed by the same equations), the voltage developed can be derived from:

:$V\; =\; \backslash int\_\{T\_1\}^\{T\_2\}\; \backslash left(\; S\_B(T)\; -\; S\_A(T)\; \backslash right)\; \backslash ,\; dT$

''S_A'' and ''S_B'' are the [[Seebeck coefficient]]s (also called ''thermoelectric power'' or ''thermopower'') of the metals A and B, and ''T₁'' and ''T₂'' are the temperatures of the two junctions. The Seebeck coefficients are non-linear, and depend on the conductors' absolute temperature, material, and molecular structure. If the Seebeck coefficients are effectively constant for the measured temperature range, the above formula can be approximated as:

:$V\; =\; (S\_B\; -\; S\_A)\; \backslash cdot\; (T\_2\; -\; T\_1)$

Thus, a [[thermocouple]] works by measuring the difference in potential caused by the dissimilar wires. It can be used to measure a temperature difference directly, or to measure an absolute temperature, by setting one end to a known temperature. Several thermocouples in series are called a thermopile.

This is also the principle at work behind [[thermal diode]]s and [[thermoelectric generator]]s (such as [[radioisotope thermoelectric generator]]s or RTGs) which are used for creating power from heat differentials.

The Seebeck effect is due to two effects: ''charge carrier diffusion'' and ''phonon drag''.

=== Thermopower ===
If the temperature difference between the two nodes is small,

:$T\_2\; =\; T\_1\; +\; \backslash Delta\; T\; \backslash ,$

and a voltage Δ''V'' is seen at the terminals, then the [[thermopower]] of the entire thermocouple is defined as:

:$S\_\{AB\}\; =\; S\_B-S\_A\; =\; \backslash lim\_\{\backslash Delta\; T\; \backslash to\; 0\}\; \{\backslash Delta\; V\; \backslash over\; \backslash Delta\; T\}$

This can also be written in relation to the electric field ''E'' and the temperature gradient
$\backslash nabla\; T$, by the equation

:$S\; =\; \{E\; \backslash over\; \backslash left\; |\; \backslash nabla\; T\; \backslash right\; |\}$

[[Superconductor]]s have zero thermopower, and can be used to make thermocouples. This allows a direct measurement of the thermopower of the other material, since it is the thermopower of the entire thermocouple as well.

In [[semiconductor]]s the sign of the thermopower is used to decide whether the charge carriers are electrons or holes.

=== Charge carrier diffusion ===
Charge carriers in the materials (electrons in metals, electrons and holes in semiconductors, ions in ionic conductors) will diffuse when one end of a conductor is at a different temperature than the other. Hot carriers diffuse from the hot end to the cold end, since there is a lower density of hot carriers at the cold end of the conductor. Cold carriers diffuse from the cold end to the hot end for the same reason.

If the conductor were left to reach [[equilibrium]], this process would result in heat being distributed evenly throughout the conductor (see [[heat transfer]]). The movement of heat (in the form of hot charge carriers) from one end to the other is called a [[heat current]]. As charge carriers are moving, it is also an [[electrical current]].

In a system where both ends are kept at a constant temperature relative to each other (a constant heat current flows from one end to the other), there is a constant diffusion of carriers. If the rate of diffusion of hot and cold carriers were equal, there would be no net change in charge. However, the diffusing charges are [[scattering|scattered]] by impurities, imperfections, and lattice vibrations ([[phonon]]s). If the scattering is energy dependent, the hot and cold carriers will diffuse at different rates. This creates a higher density of carriers at one end of the material, and the distance between the positive and negative charges produces a potential difference; an electrostatic voltage.

This electric field, however, opposes the uneven scattering of carriers, and an equilibrium is reached where the net number of carriers diffusing in one direction is canceled by the net number of carriers moving in the opposite direction from the electrostatic field. This means the thermopower of a material depends greatly on impurities, imperfections, and structural changes (which often vary themselves with temperature and electric field), and the thermopower of a material is a collection of many different effects.

=== Phonon drag ===
[[Phonon]]s are not always in local thermal equilibrium; they move along the thermal gradient. They lose momentum by interacting with electrons (or other carriers) and imperfections in the crystal. If the phonon-electron interaction is predominant, the phonons will tend to push the electrons to one end of the material, losing momentum in the process. This contributes to the already present thermoelectric field. This contribution is most important in the temperature region where phonon-electron scattering is predominant. This happens for

:$T\; \backslash approx\; \{1\; \backslash over\; 5\}\; \backslash theta\_D$

where ''θ_D'' is the [[Peter Debye|Debye]] temperature. At lower temperatures there are less phonons available for drag, and at higher temperatures they tend to lose momentum in phonon-phonon scattering instead of phonon-electron scattering.

This region of the thermopower versus temperature function is highly variable under a magnetic field.

==Peltier effect==
The '''Peltier effect''' is the reverse of the Seebeck effect; a creation of a heat difference from an electric voltage.

It occurs when a current is passed through two dissimilar metals or [[semiconductor]]s (n-type and p-type) that are connected to each other at two junctions ([[Peltier junction]]s). The current drives a transfer of heat from one junction to the other: one junction cools off while the other heats up. This effect was observed 13 years after Seebeck's initial discovery in 1834 by [[Jean Charles Athanase Peltier|Jean Peltier]].

[[Image:Peltier_effect_circuit.png]]

When a current ''I'' is made to flow through the circuit, heat is evolved at the upper junction (at T₂), and absorbed at the lower junction (at T₁). The Peltier heat absorbed by the lower junction per unit time, $\backslash dot\{Q\}$ is equal to

:$\backslash dot\{Q\}\; =\; \backslash Pi\_\{AB\}\; I\; =\; \backslash left(\; \backslash Pi\_B\; -\; \backslash Pi\_A\; \backslash right)\; I$

Where Π is the Peltier coefficient Π_''AB'' of the entire thermocouple, and Π_''A'' and Π_''B'' are the coefficients of each material. P-type silicon typically has a positive Peltier coefficient (though not above ~550 K), and n-type silicon is typically negative.

The conductors are attempting to return to the electron equilibrium that existed before the current was applied by absorbing energy at one connector and releasing it at the other. The individual couples can be connected in series to enhance the effect.

The direction of heat transfer is controlled by the polarity of the current, reversing the polarity will change the direction of transfer and thus the sign of the heat absorbed/evolved.

A '''Peltier cooler'''/heater or thermoelectric [[heat pump]] is a solid-state active heat pump which transfers heat from one side of the device to the other. Peltier coolers are also called ''Thermo Electric Converter''s (TEC).

==Thomson effect==
'''Thomson effect''', named for [[William Thomson, 1st Baron Kelvin]], describes the heating or cooling of a current-carrying conductor with a temperature gradient.

Any current-carrying conductor, with a temperature difference between two points,
will either absorb or emit heat, depending on the material.

If a current density ''J'' is passed through a homogeneous conductor, heat production per unit volume is

:$q\; =\; \backslash rho\; J^2\; -\; \backslash mu\; J\; dT/dx\; \backslash ,$

where

''ρ'' is the [[resistivity]] of the material

''dT''/''dx'' is the temperature gradient along the wire

''μ'' is the Thompson coefficient.

The first term ''ρ J'' is simply the [[Joule heating]], which is not reversible.

The second term is the Thomson heat, which changes sign when ''J'' changes directions.

The Peltier and Seebeck coefficients are related by the Thomson relation

:$\backslash Pi\; =\; S\; \backslash cdot\; T$

which predicted the Thomson effect before it was actually formalized. It can also be written

:$\backslash mu\; =\; T\; dS/dT\; \backslash ,$

where ''T'' is the absolute temperature of the metal.

In metals such as [[zinc]] and [[copper]], which have a hotter end at a higher potential and a cooler end at a lower potential, when current moves from the hotter end to the colder end, it is moving from a high to a low potential, so there is an evolution of energy. When it moves from the colder to the hotter end, there is an energy absorption. This is called the '''positive Thomson effect'''.

In metals such as [[cobalt]], [[nickel]], and [[iron]], which have a cooler end at a higher potential and a hotter end at a lower potential, when current moves from the hotter end to the colder end, it is moving from a low to a high potential, there is an absorption of energy. When it moves from the colder to the hotter end, there is an energy evolution. This is called the '''negative Thomson effect'''.

In [[lead]], there is zero Thomson effect.

The Seebeck effect is actually a combination of the Peltier and Thomson effects.

==See also==
*[[Thermoelectricity]]
*[[Joule's law]]
*[[Heat transfer]]
*[[Thermoelectric cooling]]
*[[Pyroelectric effect]] - the creation of an electric field in a crystal after uniform heating

==Patents==

* {{US patent|2510397}} - [[Clarence Hansell|Clarence W. Hansell]] - "''Heat-to-electrical energy converter''".
* {{US patent|2881384}} - [[Lyndon Durant|Lyndon A. Durant]] - "''Thermal electric alternator''"
* {{US patent|2915652}} - [[George Hatsopoulos|G. N. Hatsopoulos]] - "''Conversion of thermal energy into electrical energy''".
* {{US patent|3175105}} - [[John Creedon| John E. Creedon]] - "''Conversion of heat to electricity''"

==External links==

=== General ===
*[http://www.nanothermel.org/public_main.htm Thermoelectricity, including equations and applications]
*[http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_2/backbone/r2_3_3.html General]
*[http://www.insa-lyon.fr/Laboratoires/GEMPPM/TEP/index.htm Has an explanation of carrier diffusion and phonon drag components of thermopower]

=== Semiconductors ===
*[http://www.coolworksinc.com/about_thermoelectric_technology.htm A brief explanation]
*[http://www.electronics-cooling.com/Resources/EC_Articles/SEP96/sep96_04.htm An introduction to thermoelectric coolers]
*[http://www.its.caltech.edu/~jsnyder/thermoelectrics/science_page.htm The science and materials of thermoelectrics]

=== Metals ===
*[http://www.uni-konstanz.de/physik/Jaeckle/papers/thermopower/thermopower.html The origin of the thermoelectric potential]

=== Related ===
*[http://www.peltier-info.com/info.html Directory of Peltier device information]
*[http://www.trnmag.com/Stories/2001/121901/Chips_turn_more_heat_to_power_121901.html A news article on the increases in thermal diode efficiency]
*[http://www.sii.co.jp/info/eg/thermic_main.html A wristwatch powered by thermocouples, using the heat difference between the human body and its surroundings]

[[Category:Thermodynamics]]
[[Category:HVAC]]
[[Category:Electricity]]

[[fr:Effet Peltier]]
[[ja:ペルチエ効果]]
[[nl:Peltier-effect]]
[[pl:Efekt Peltiera]]
[[pt:Força eletromotriz de Peltier]]

good luck to the Department of Treasury folks in their tracking exercise :-)

posted by mailgeek @ 12:51 AM