**Definitions**

– T_{h}: Temperature of hot side (K)

– T_{c}: Temperature of cold side (K)

– ΔT: T_{h}-T_{c}

– T_{avg}: (T_{h}+T_{c})/2

**TEC1-12715**

This module is the one I ordered and has a detailed datasheet which includes some plots at Th=27°C (300K) and Th=50°C (323K). No formulas and parameters of the module are provided so these were derived from the plots using the fit option of Wolfram Alpha^{[1]}.

The Seebeck effect causes an electromotive force, U_{emf} when a temperature difference is applied to the sides of the module,

*U _{emf} = SΔT*,

Where S is the difference between Seebeck coefficients of the n and p material inside the module. Since the module contains 127 elements, S is equal to 127 times the Seebeck coefficient of a single element.

**Formula overview**

*U _{emf} = SΔT*

*I = (U-SΔT)/R*

*U = IR+SΔT*

*P = UI = U²/R-(USΔT)/R = I²R+ISΔT*

*Q*

_{C}= Q_{P}-P/2-Q_{L}*Q*

_{H}= Q_{P}+P/2-Q_{L}*Q*

_{P}= T_{avg}SI = T_{avg}S(U-SΔT)/R**References**

1. https://www.wolframalpha.com/