Experimental Verification of the Kelvin Relation of Thermoelectricity in a Magnetic Field

The Seebeck coefficient ($S$) for a particular orientation of a bismuth single crystal at 78°K changes by by 40% when a transverse magnetic field ($B$) of 10 000 Oe is reversed in direction ("Umkehreffekt"). The Peltier coefficient (II) also changes by the same proportion, but the field direction which gives the larger Seebeck effect, gives the smaller Peltier effect. This is a verification of the modified Kelvin relation, $\Pi \mathrm{}\left(B\right)=TS(-B)\mathrm{}$.