Peltier effect - a process accompanied by the appearance of a temperature difference on the two different materials by passing electric current through them. For the first time explained by academician and inventor Lenz.

## Thanks

We can not ignore gratitude USSR Academy of Sciences and academician AF Joffe for the great work on the development of thermoelectricity in the USSR and bringing research results to the public.

## Applicability

Peltier effect is used for cooling, heating can any guide through the Joule-Lenz. Hence, the phenomenon is useful:

- To create a low-voltage DC and refrigerators. With the possibility of heating power when changing polarity. In the west, so constructed road sandvichennitsy. The cold keeps the product from spoiling, reverse polarity allows to submit the product to the table hot.
- Coolers processors make a significant contribution to the overall noise performance of the system unit. If you replace them with Peltier elements, sometimes total lack of the fan. He rustles not so much the body is deprived of a powerful radiator and fixing reliable (unlike the motherboard material).

## The development of the theory of cooling

Peltier effect is not attracted attention of scientists, it seemed useless. Opened in 1834, collecting dust on academic libraries more than a century before the shelves, rather than steel to be the first significant technical solutions in this area. For example, Altenkirch (1911) stated inability to use the Peltier effect refrigeration systems, in the calculation was based on the use of pure metals, alloys and semiconductors instead.

The fallacy of the conclusions of the German scientist later confirmed, what great role for laboratory of the Academy of Sciences of semiconductors. By 1950, it established coherent theory, which allowed for a further number of years to create the first electrothermal refrigerator. With a relatively small efficiency of 20% lowers the temperature of the device at 24 degrees, which in most cases enough for domestic purposes. Years later, the temperature difference was already 60 degrees.

In physics 50s Peltier element was regarded as the chiller with Freon instead of the electron gas. It conducted in accordance with this system consideration. The main parameter - refrigerating efficiency, the ratio of the amount of heat per unit time in the intake to the power that is expended on. Modern freon air conditioners and refrigerators figure is greater than one. In 50-ies of the Peltier element was barely 20%.

## The effect from the standpoint of thermodynamics

Peltier effect is described by showing how much energy is transferred at a certain value of the electric current. Expressing it in time units are power devices, which is determined based on the needs of the refrigerator. Today popular noiseless elements Peltier coolers for processors. A small crystal plate cools and cools the radiator cooler. Peltier element serves as a heat pump, the heat from the discharging guaranteed CPU, preventing overheat.

In the formula in the figure are designated by alpha coefficients thermo emf halves (constituent parts) of the element. T - working temperature in degrees Kelvin. Each element is typically present side-Thomson effect if the current flowing through the conductor, and along the line has a gradient (directional difference) temperatures will be in addition to Joule, stand and other heat. The latter is named after Thomson. In some parts of the energy chain will be absorbed. Hence, the Thomson effect has a strong influence on the operation of the heaters and refrigerators. But it is, as already mentioned, side, unaccounted factor.

The heat transferred by Thomson effect, the temperature difference is directly proportional to the conductor ends and depends on the flowing current. The phenomenon occurs only in substances with a pronounced dependence of the coefficient of thermal emf on temperature. In some calculations Thomson effect is considered to be zero, it is close to the truth. The thermodynamic theory of the process of return and selection of heat is considered from the point of view of two heat flows:

- The heat flux, a cooling picks junction, followed by two parallel reaching processes:

- Parasitic heat by Joule-Lenz. In thermodynamics, it is taken as half the product of the square of current to the resistance. The second half falls to the hot junction.
- Heating the heat flow coming from a warm part. Is equal to the temperature difference, multiplying with the total thermal conductivity of the thermoelement branches.

- In the hot junction are reverse processes of the second step (heat is carried away to the cooled part) and similar to the first - Joule heat is released.

From the wording implies that an effective solution to maximize the efficiency of the insulation will be between the junctions. The pair used semiconductors, capable of generating a thermal electromotive force, electric current has to overcome her resistance. Expended energy is proportional to temperature difference and difference in thermal emf substances coefficients and depends on the flowing current. Are graphs of the curves, and differentiating them in order to find the extrema may receive conditions of maximum temperature difference (between a room and a refrigerator).

The figures show the results of taking the derivative operation where computed optimum currents for the resistance R and the thermocouple limit increase refrigerating effect. From these formulas it follows that the ideal machine will happen if:

- The conductivity of the same thermocouple material.
- The thermal conductivity of the same thermocouple material.
- The coefficients of thermal electromotive force equal but opposite in sign.
- The cross sections and lengths of branches of the same thermocouple.

To realize these conditions in practice difficult. In this case, the limiting factor is the ratio of the refrigerant temperature of the cold junction to a temperature difference. Recall, this is the perfect description of the machine, in reality, yet unattainable.

## How to optimize chiller Peltier

Figures are graphs variables affecting the efficiency of the Peltier elements. First, it is evident - the thermo-emf coefficient tends to zero with increasing carrier concentration. It recalls that the metals are not considered the best material for producing a thermocouple. Thermal conductivity, on the contrary, increases. In thermodynamics, it is believed that it is composed of two components:

- crystal lattice thermal conductivity.
- Electronic thermal conductivity. Said component for obvious reasons independent of the concentration of free charge carriers and causes the growth curve presented on the graph. The thermal conductivity of the crystal lattice remains practically constant.

Researchers are interested in the product of the square of the coefficient of thermal EMF on the electrical conductivity. Said value is placed in the numerator of the expression for the coefficient of performance. According extremum observed at a concentration of free carriers in the region of 10 to 19 degree units per cubic centimeter. This is three orders of magnitude less than that observed in the pure metals from which immediately follows the conclusion that the ideal material for semiconductors will Peltier elements.

The proportion of the second component have a relatively low down on the abscissa, and allowed to take the material in this interval. The electrical conductivity of insulators is too small, which explains the impossibility of their use in this context. All this allows you to establish the reason why the findings are not taken seriously Altenkirchen.

## Quantum theory applied to the Peltier element

Thermodynamics does not allow a precise calculation, but qualitatively describes the material selection process for the Peltier elements. To remedy the situation, physicists call on the quantum theory. It operates with the same values, expressed in terms of the concentration of free charge carriers, the chemical potential, the Boltzmann constant. Such theories are made is also called kinetic (or microscopic), because it is considered illusory and unknown world of minute particles. Among the signs are found:

- l - mean free path of the charge carriers. It depends on the temperature. The result is determined by the exponent of the electron scattering mechanism r (for atomic lattices is 0; ionic and temperatures below Debye - 0.5; above Debye - 1; when scattering of impurity ions - 2).
- f - Fermi distribution function (the energy levels).
- x - the reduced kinetic energy of the charge carriers.

Integrals of the Fermi functions are listed in the table, their calculation is not difficult. The equations of the microscopic theory of decision with respect to the thermo-emf coefficient and electrical conductivity, which allows you to find the coefficient of performance. These complex operations done by the BI Sideways, who established that the optimum value of the Seebeck coefficient is in the range between 150 and 400 mV / K, but depends on the degree of scattering mechanism. At first glance, it is clear that the values for metals are not observed. As a result, a group of physicists led by Joffe shown that the best material for thermocouples must satisfy a number of conditions:

- The maximum ratio of mobility to the coefficient of thermal conductivity of the crystal lattice.
- The carrier concentration according to the formula shown in the figure.

VP Zhuze indicates which substances exhibit the desired mobility. Their crystal structure is midway between the atomic and metal. The introduction of impurities in the material always reduces mobility. This explains the fact that the thermo-emf coefficient of alloys is higher than for pure materials. But the increase of the impurity r. The ideal material not existing in nature, thermo-emf coefficient must maintain a constant value equal to 172 uV / K. It is required that the concentration varies as indicated in the figure (see. of claim. 2).

Semiconductors possibility to choose different materials, where the carrier concentration is temperature dependent, and look for those where the difference is practically zero. Due to the combination of these qualities may try to find the closest to the ideal material.

## construction of refrigerators

To enhance the Peltier effect elements are combined in parallel. However, their power fold. To construct their own refrigerators need to be aware of the calculation of heat loss through the planar structure. Created special calculators, many are available online.

Is engaged in designing random disadvantageous for obvious reasons. And the good news is that the Peltier elements are significantly cheaper in recent years. Ali-express purchase products from China 60 watts for 300 rubles. Not difficult to see that during 3000 can be assembled refrigerator. And what it would maintain the temperature depends on the design requiring calculation.