Thermocouples, their characteristic temperatures, and simple approximation of the emf vs. T

• The characteristic temperature of a thermocouple is a new tool for the analysis of its emf as a function of temperature.
• It allows one to recognize the temperature intervals where approximation is simple and accurate.
• The equation for the emf approximation is derived from the contact theory of thermoelectricity.
• Quadratic polynomial is shown to be the optimal empirical formula for the approximation with accuracy to 0.5 °C.

Calibration of the temperature and heat flux sensors for chip calorimetry is more effective if it is based on the optimal approximation of thermocouple's emf against temperature. Contact theory of thermoelectricity provides us with the formula for the approximation, but implies the characteristic temperature of a thermocouple constant ΘVΘV. This assumption turned out to be incorrect in common practical use, what did makes the main problem for the approximation of the emf. At the same time, the theory explains that the rate of increase for the emf with temperature is not greater than T2. Three-point tests with the reference tables of type E and S thermocouples and many-point test with experimental data did not reveal evident preference of one procedure of approximation over the others. In considering all circumstances of the approximation, the 2nd-order polynomial is concluded to be the best way to approximate the emf of a thermocouple for practical use. Approximation of the characteristic temperature of type E thermocouple with square polynomial 277.01 − 0.63453T + 0.00044352T2 results in the accuracy of ±0.5 K over the temperature range from 0 to 1000 °C.

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