In a lossless thermocouple (R = 0 and A = 0), = TC/AT, which is the Carnot efficiency, ^Ccarnot, of the heat pump. See Problem 5.34. For our example &Ccarnot = 4.63. The actual thermocouple does not come anywhere close to this value.
Figure 5.14 shows how the power, PC, pumped from the cold source varies with the current. If I < 0 (not shown in the figure), the heat is being pumped into the cold source. At I = 0 (also not shown), there is no Peltier effect and heat still flows into the cold side by conduction. As I increases, some Peltier pumping starts to counteract this heat conduction, and, eventually (in a properly designed device), heat will actually begin flowing from the cold side to the hot side. This amount of heat will initially increase as I increases, but eventually Joule losses will begin to generate so much heat that the Peltier pumping is overwhelmed. Further increases in I will result in a reduction of the heat extracted from the cold side.
It is easy to calculate what current causes maximum heat pumping: dPf = aTc - RI = 0 (5.77)
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