= Peltier current-reversal experiment
{c}
An actual institutional protocol is CTU's \i[Measurement of characteristics of a Peltier cell]. Its cooling run uses a water container, an insulating cap and a current-limited supply; both face <temperatures> are recorded every minute while <electric current> is monitored. The apparatus includes a water-cooled exchanger, <copper> blocks and brass containers. The heating run resets the water near room <temperature> before reversing polarity. The handout specifies no <thermometer> type and reports no dataset. Its modular junction geometry is shown separately from the external thermal assembly.<Measurement of characteristics of a Peltier cell by Milan Červenka and Ladislav Sieger>[pp. 3–4, Figs. 1.4–1.5; pp. 5–7, §§1.5.2–1.5.3 and Appendix]{ref}
\Image[/peltier-current-reversal-apparatus.png]
{title=<Peltier effect> apparatus and a junction's <conventional current> direction}
{description=Original explanatory schematic, not an apparatus photograph. The external water assembly follows the CTU protocol qualitatively; readout locations are schematic because sensor construction is unspecified. The inset is an idealized material pair, not a reconstruction of that cell's internal fabrication. Dashed arrows mark proposed parasitic <heat transfer> controls.}
The following is a proposed quantitative extension. Keep the physical face labels fixed throughout reversal: c denotes the observed object's side and h the exchanger side, even if their actual <temperatures> change order. Use an independently read <thermometer> at each thermal contact and log the actual signed <electric current> and terminal <electric potential difference>. Maintain reproducible contact pressure and contact layers. A sensor in water measures water <temperature>, which need not equal the face <temperature> during a transient; verify mixing and contact equilibration before using it as a face reading. Do not interchange sensor leads when reversing the supply.
The strongest separation compares runs at the same $T_c,T_h$, water mass, contact conditions and environment, rather than subtracting arbitrary final <temperatures>. One option is short initial-rate runs after resetting the whole assembly to a reproducible state. Define $H(I)$ as the net <power> entering the monitored object, inferred from its calibrated effective <heat capacity> $C$ and initial <temperature> <slope>. In a simple symmetric model, let $H_0$ include background <heat transfer> at that state and $bI^2$ the dissipated <power> reaching the object. Then
$$
H(I)=C\frac{dT_c}{dt}=H_0-aI+bI^2,\qquad a>0,
$$
where $a=\alpha T_c$ in the <thermoelectric cooling> model below. The half-difference and baseline-subtracted half-sum are
$$
H_{\rm odd}(I)=\frac{H(+I)-H(-I)}{2}=-aI,\qquad
H_{\rm even}(I)=\frac{H(+I)+H(-I)}{2}-H(0)=bI^2.
$$
The minus sign in the odd part means positive <electric current> cools the object. The even part has to subtract the zero-current baseline: otherwise <heat conduction> and ambient exchange remain mixed with <Joule heating>. Independently measured <heat capacity> is essential for converting a thermal <slope> into <watts>; include the blocks, container and water that actually equilibrate on the measurement timescale.
Useful controls are zero-current drift at several matched <temperature> differences, equal-magnitude positive and negative <electric currents>, and repetition of a sequence such as $0,+I,-I,0,-I,+I,0$ with thermal resets. A calibrated small heater on the object can test the <heat capacity> and lost-<heat> correction independently. Check <Joule heating> in supply leads and contacts, bypass <heat conduction> through supports and wiring, and ambient <convection> and <thermal radiation>. Insulation reduces a leak; it does not establish that it is zero. Measure terminal <power> at the module boundary so lead losses are not mistaken for module heating.
An odd thermal response supports a reversible current-coupled contribution, but does not by itself locate all of it at one junction: the <Thomson effect> in nonuniform leads can also be odd. Sensor offsets, unequal current magnitudes, drifting thermal contacts and different junction <temperatures> during the two runs can contaminate both parts. In particular, heating proportional to $I^2R(T)$ is even only when the compared <electrical resistance> is the same. CTU's qualitative reversal illustrates switching heating and cooling; the matched-state controls above would be needed for a coefficient measurement.
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