Thomson relations
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 determined for pairs of materials; hence, no direct methods exist for determining absolute Seebeck or Peltier coefficients for an individual material. In 1854, Lord Kelvin found relationships between the three coefficients, implying that only one could be considered unique. The first Thomson relation is
where T is the absolute temperature, μ is the Thomson coefficient and S is the Seebeck coefficient. The second Thomson relation is
where Π is the Peltier coefficient. It predicted the Thomson effect before it was formalized.
Figure of merit
The figure of merit Z for thermoelectric devices is defined as
where σ is the electrical conductivity, κ is the thermal conductivity, and S is the Seebeck coefficient. The dimensionless figure of merit ZT is formed by multiplying Z with the average temperature.
A greater ZT indicates a greater thermodynamic efficiency, subject to certain provisions, particularly that the two materials in the couple have similar Z. ZT is therefore a method for comparing the potential efficiency of devices using different materials. Values of 1 are considered good; values in the 3–4 range are essential for thermoelectrics to compete with mechanical devices in efficiency. To date, the best reported ZT values are in the 3–4 range. Currently this goal of high ZT values is referred to as: "high-figure-of-merit". Much of the research in thermoelectric materials has focused on increasing S and reducing κ by manipulating the nanostructure of the materials.
Device efficiency
The efficiency of a thermoelectric device for electricity generation is given by η, defined as
The maximum efficiency ηmax is defined as
where
TH
is the temperature at the hot junction and TC
is the temperature at the surface being cooled.
is
the modified dimensionless figure of merit, which takes into
consideration the thermoelectric capacity of both thermoelectric
materials being used in the device and is defined as
where
ρ
is the electrical resistivity,
is
the average temperature between the hot and cold surfaces and the
subscripts n and p denote properties related to the n- and p-type
semiconducting thermoelectric materials, respectively. Since
thermoelectric devices are heat engines, their efficiency is limited
by the Carnot
efficiency, hence the TH
and TC
terms in
.
Regardless, the coefficient
of performance of current commercial thermoelectric refrigerators
ranges from 0.3 to 0.6, one-sixth the value of traditional
vapor-compression refrigerators.[9]
[edit] Applications
See also: Thermoelectric materials
[edit] Seebeck effect
Main article: Thermoelectric generator
The Seebeck effect is used in the thermoelectric generator, which functions like a heat engine, but is less bulky, has no moving parts, and is typically more expensive and less efficient. These have a use in power plants for converting waste heat into additional power (a form of energy recycling), and in automobiles as automotive thermoelectric generators (ATGs) for increasing fuel efficiency. Space probes often use radioisotope thermoelectric generators with the same mechanism but using radioisotopes to generate the required heat difference.
[edit] Peltier effect
Main article: Thermoelectric cooling
The Peltier effect can be used to create a refrigerator which 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.
[edit] Temperature measurement
Thermocouples and thermopiles are devices that use the Seebeck effect to measure the temperature difference between two objects, one connected to a voltmeter and the other to the probe. The temperature of the voltmeter, and hence that of the material being measured by the probe, can be measured separately using cold junction compensation techniques.[citation needed]
[edit] See also