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## Conversion of ZT of a Thermoelectric to Refrigeration COP

The tool uses the following formula for the ZT to COP (refrigeration) conversion:

$$x_c$$

_{\text{R}}=\frac{T_{\text{c}}}{T_{\text{h}} – T_{\text{c}}} \frac{\sqrt{1 + ZT_{\text{m}}} – T_{\text{h}}/T_{\text{c}}}{\sqrt{1 + ZT_{\text{m}}} + 1}

$$\theta (x,t)=\frac{T(x,t)-T_{\text{initial}}}{T_h-T_{\text{initial}}}$$

where $$T_{c}$$ and $$T_{h}$$ are the cold and hot side temperatures of the thermoelectric, respectively (both in absolute temperatures!). The “T” in “ZT” is assumed to be the arithmetic average of the cold and hot temperatures.

The CDF tool follows.