Thermocouple polynomials

Table 2.1 Thermocouple polynomial coefficients. All polynomials are from reference [6] with the exception of types R and B, which were determined by...

Thermocouples Voltage to temperature conversion. For selected values of voltage, the conversion may be obtained by consulting tables or graphs. For a systematic conversion of data by a computer, power series polynomials may be used, such as exemplified by a nested 5th order polynomial ... 

It is important to understand that the tables and polynomials are based on the assumption that the cold junction of the thermocouple pair is at zero degrees Celsius. In the laboratory, the cold junction is generally at room temperature or slightly above (the temperature at the screw terminals where the thermocouple wires and lead-wires join), hence a correction factor is needed. The law of successive potentials (Figure 2.6) may be stated as The sum of the EMF s from the two thermocouples is equal to the EMF of a single thermocouple spanning the entire temperature range ... 

A polynomial was fit to the calibration curve for the thermocouple by means of a minimization of the maximum deviation technique using the Nelder Mead sequential simplex minimization algorithm method.( 5,6, 7) The coefficients of this polynomial are stored in the analysis program and are used to convert thermocouple voltages to temperature values. Y values are converted to dH(t,T)/dt, the heat flow into and out of the sample in mcal/sec. The operator selects a baseline for the analysis by entering the temperatures of the beginning and end points of the baseline. A plot is produced of the raw data with the operator selected baseline shown as illustrated in Figure A. 

The system is designed to collect up to six channels of analog information, as a function of time, from each thermobalance. Nominal collection rate is one data set logged alternately from each instrument every 5 sec for a per instrument rate of six sets per min. Data acquired from the two thermobalances is converted to actual units, such as temperature in °C. and so on. and stored in two arrays of 100 data sets, with one array being assigned to each instrument The conversion of the thermocouple EMF into temperature is based on two polynomials, one for the PtRhlO%-Pt system and the other for NiCr-Ni and stored in the data acquisition program. When the two arrays are filled, they are automatically recorded on tape. 

The first set of tables below lists, for each thermocouple type, the emf as a function of temperature on the International Temperature Scale of 1990 (ITS-90). The coefficients in the equation used to generate the table are also given. The second set of tables gives the inverse relationships, i.e., the coefficients in the polynomial equation which expresses the temperature as a function of thermocouple emf. The accuracy of these equations is also stated. 

Type B Thermocouples Coefficients (c.) of Polynomials for the Computation of Temperatures... 

Type J Thermocouples Coefficients (c.) of Polynomials for the Computation of Temperatures in °C as a Function of the Thermocouple emf in Various Temperature and emf Ranges... 

Thermocouples are a widely used application of the Seebeck effect, and they are the main means of temperature monitoring and regulation for measurements of temperatures above about 150 °C (Figure 15.13). This is because the potential generated in the circuit is easily measured, and metal thermocouples capable of operating up to temperatures of almost 2000 °C are available. In practice, one junction is maintained at 0 °C. The voltage generated by a thermocouple is related to the temperature difference between the junctions by a polynomial function, such as... 

Finally, a polynomial of fifth order was applied to state a relation between the potential difference and the temperature difference. For example, a temperature difference AT of 10 °C resulted in a potential difference of 4 x 10 " V. In turn, if a potential difference of 4 x 10 " V with the yam-based thermocouple airings... 

This approach ignores the uncertainty related to the potentiometer. To derive a more precise value, the sensitivity of the thermocouple should be taken into consideration either with the high-order polynomial or by deriving a lower-order polynomial in the vicinity of the temperature of interest. For a Type J thermocouple in the range of 0-1000 C, a second-order polynomial accounts for 99.994% of the variance in the data (i.e. = 0.99994) ... 

Derive a second-order polynomial expression relating the temperature and emf for a Type K thermocouple from 0 " C to 1000 C. 

In practice, the Seebeck electromotive force is related to the temperature difference by a polynomial equation, where the polynomial coefficients (i.e., c , c, Cj, C3, etc.) are empirical constants determined by experiment and that characterize the thermocouple selected. 

Thermocouple type Polynomial equation with NIST coefficients and electromotive force in volts... 

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