Thomson/Joule Power Compensation and the Measurement of the Thomson Coefficient

The energy transported by the electric current that circulates a thermoelectric element (TE) varies with position due to the Joule and Thomson effects. The Thomson effect may enhance or compensate the Joule effect. A method for measuring the Thomson coefficient of a TE is presented. This method is based on the total compensation of the Joule and Thomson effects. The electric current then flows without delivering power to the TE or absorbing power from it. For a TE, the global Thomson/Joule compensation ratio Φ¯T/J is defined as the ratio of the power absorbed by the current due to the Thomson effect and the power delivered by the current to the TE due to the Joule effect. It can be expressed as Φ¯T/J=I0/I, where I is the electric current and I0 is the zero-power current, a quantity that is proportional to the average Thomson coefficient. When I=I0, the Thomson effect exactly compensates the Joule effect and the net power delivered by the current to the TE is zero. Since the power delivered by the current is related to the temperature distribution, temperature measurements for currents around I0 can be used as the basis for a measurement technique of the Thomson coefficient. With varying current, the difference between the temperature at the center of the TE and the mean temperature between its extremes reverses its sign at the zero-power current, I=I0. This observation suggests the possibility of measuring the Thomson coefficient, but a quantitative analysis is needed. With calculations using the constant transport coefficients model for Bi2Te0.94Se0.063  and Bi0.25Sb0.752Te3, it is theoretically shown that a null temperature detector with a sensitivity of the order of 1 mK allows for the accurate determination of the Thomson coefficient.