Act[ m

where m = a/1 + Z < T >, as before, and TC/AT is, as stated, the Carnot efficiency of the refrigerator.

Applying this to our example,

m = y/l + Z <T> ^ y 1 + 0.00288 xi-^-j = 1.374 (5.87)

To obtain this coefficient of performance, one must use a current of aAT 0.055 x (338 - 278)

Table 5.8 compares two batteries of identical thermocouples, both pumping 100 W of heat from 258 K to 323 K. One battery is adjusted to pump this heat with a minimum number of cells—that is, it operates with current that maximizes PC. The other battery operates with the current that maximizes the coefficient of performance. The substantially larger

Table 5.8 Thermocouples Operated at Maximum PC and at Optimum PC = 100 W

Point of Number PE PH

Max Pc 100 540 640 18.5%

efficiency of the second battery comes at a cost of the larger number of cells required.

Commonly, the characteristics of thermocouples used as heat pumps are displayed in graphs like the one in Figure 5.15, which corresponds to the unit in our example and is roughly similar to the Tellurex CZ1-1.0-127-1.27 unit—a battery consisting of 127 cells in series. This explains the large value of a—each cell has an a of 0.055/127 = 0.000433 V/K. For an example of how to use such graphs, see Problem 5.33.

5.11.2 Design Based on Given Semiconductors

If semiconducting materials have been selected, but the exact dimensions of the thermocouples have not yet been determined, then although the values of a, p, and A are known, those of R and A are not. Presumably, the dimensions of the arms of the thermocouple will be optimized,

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