= Solution
A <thermocouple> uses \b[two materials with different <Seebeck coefficients>]. With their junctions at different <temperatures>, the net <open-circuit voltage> is
$$
V_{\rm oc}=\int_{T_c}^{T_h}(\alpha_p-\alpha_n)\,dT
\simeq(\alpha_p-\alpha_n)\Delta T.
$$
Using p-type and n-type legs makes the two contributions add. Many pairs can be connected electrically in series to add <voltage> while remaining thermally in parallel between the same hot and cold plates. A single homogeneous wire does not provide this same complete-circuit <voltage> when its return lead has the same <thermopower>.
The reciprocal <Peltier effect> transports heat when <electric current> passes through a junction. The Kelvin relation $\Pi=\alpha T$ connects the heat carried per unit charge to the <Seebeck coefficient>. The same combination of large <thermopower>, high <electrical conductivity> and low <thermal conductivity> gives a favorable dimensionless figure of merit
$$
ZT=\frac{\alpha^2\sigma T}{\kappa}.
$$
Thus materials useful for a generator are also useful for a cooler when <electric current> is driven in the appropriate direction. <Joule heating> and thermal leakage oppose cooling; device geometry, contact resistance and operating <temperature> must still be appropriate. Reversibility of the thermoelectric coupling does not make either device lossless.
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