# Z TcThm TcTh

Summing up, there are three different considerations in optimizing the efficiency of a thermocouple:

1. Choice of appropriate materials in order to maximize Z.

2. Choice of the best geometry in order to minimize AR.

3. Choice of the proper value of the load resistance relative to the internal resistance of the device, that is, selection of the best value for m.

Equation 5.23 shows that for Z ^to, n* = -"4-^TT ■ (5.31)

Maximum n* is obtained by using m = to. Having an infinite m means that there is infinitely more resistance in the load than in the thermocouple. In other words, the couple must have zero resistance, which can only be achieved by the use of superconductors. Superconductors, unfortunately, have inherently zero Seebeck coefficients. Consequently, n* = 1 cannot be achieved even theoretically. Indeed, with present-day technology, it is difficult to achieve Zs in excess of 0.004 K-1. This explains why thermocouples have substantially less efficiency than thermomechanical engines.

Figure 5.9 plots n* versus TH (for TC = 300K), using two different values of Z, in each case for optimum m. From this graph one can see that thermocouples created with existing technology can achieve (theoretically) some 30% of the Carnot efficiency. Compare this with the General Electric combined cycle "H" system that attains 60% overall efficiency. The temperature of the first-stage nozzle outlet is 1430 C. Assume a final output temperature of 300 C. The Carnot efficiency of a machine working between these two temperatures is 66%. Thus, the GE system realizes 90% of the Carnot efficiency.