Calibration of a type N thermocouple at 1000 °C: Furnace temperature

In the N-type thermocouple calibration at 1000 °C the temperature of the furnace is determined by two R-type thermocouples placed the same distance above and below the thermocouple two be calibated. The tempearture at the location of the hot junction of the thermocouple to be calibrated is given as the mean of the temperatures of the hot junction of the two reference thermocouples.

Model Equation:

tX = tS + δtS + CS × (δViS1 + δViS2 + δVR) - CS / CS0 × δt0S + δtD + δtF

List of Quantities:

Quantity Unit Definition
tX °C temperature to be measured of the furnace
tS °C temperature of the reference thermometer in terms of voltage with cold junction at 0 °C. The function is given in the calibration certificate.
δtS °C correction of the temperature of the reference thermocouples due to their calibration
CS °C/µV sensitivities of the reference thermocouples for voltage at the measuring temperature of 1000 °C
δViS1 µV voltage correction obtained from the calibration of the voltmeter
δViS2 µV voltage correction due to the limited resolution of the voltmeter
δVR µV voltage correction due to contact effects of the reversing switch
CS0 °C/µV sensitivities of the reference thermocouples for voltage at the reference temperature of 0 °C
δt0S °C temperature correction due to the deviation of the reference temperature from 0 °C
δtD °C change of the values of the reference thermometers since their last calibration due to drift
δtF °C temperature correction due to non-uniformity of the temperature of the furnace

tS: Type A
Method of observation: Direct
Number of observation: 1
No. Observation
1 1000.5 °C

Arithmetic Mean: 1000.500 °C
Pooled Standard Deviation: 0.10 °C
Standard Deviation of the Mean: 0.100 °C
Pooled Degrees of Freedom: 9

MEASUREMENTS: The indications of the voltmeter are precalculated to reduce the effects of temperature drift in the thermal source and parasitic thermal voltages (see EAL-R2-S1:S5.15). The readings are combined to one observation only, which is the temperature of the furnace at the location of the thermocouple to be cailbrated. In order to evaluate the uncertainty of measurement associated with the observation, a series of ten measurements has been previously undertaken at the same temperature of operation. It gave a pooled estimate of standard deviation for the temperature of the furnace.

δtS: Type B normal distribution
Value: 0.0 °C
Expanded Uncertainty: 0.3 °C
Coverage Factor: 2
REFERENCE STANDARDS: The reference thermocouples are supplied with calibration certificates that relate the temperature at their hot junction with their cold junction at 0 °C to the voltage across their wires. The expanded uncertainty of measurement at 1000 °C is U=0,3 °C (coverage factor k=2 )

CS: Constant
Value: 0.077 °C/µV
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables

δViS1: Type B normal distribution
Value: 0.0 µV
Expanded Uncertainty: 2.0 µV
Coverage Factor: 2.0
CALIBRATION OF THE VOLTMETER: The voltmeter has been calibrated. Corrections to the measured voltages are made to all results. The calibration certificate gives a constant expanded uncertainty of measurement for voltages smaller than 50 mV of U=2 µV (coverage factor k=2)

δViS2: Type B rectangular distribution
Value: 0.0 µV
Halfwidth of Limits: 0.5 µV
RESOLUTION OF THE VOLTMETER: A 4½ digit microvoltmeter has been used in its 10 mV range resulting in resolution limits of ±0,5 µV at each indication.

δVR: Type B rectangular distribution
Value: 0.0 µV
Halfwidth of Limits: 2.0 µV
PARASITIC VOLTAGES: Residual parasitic offset voltages due to the switch contacts have been estimated to be zero within ±2 µV.

CS0: Constant
Value: 0.189 °C/µV
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.

δt0S: Type B rectangular distribution
Value: 0.0 °C
Halfwidth of Limits: 0.1 °C
REFERENCE TEMPERATURE: The temperature of the reference point of each thermocouple is known to be 0 °C within ±0,1 °C.

δtD: Type B rectangular distribution
Value: 0.0 °C
Halfwidth of Limits: 0.3 °C
DRIFT OF THE REFERENCE STANDARDS: From previous calibrations the drift of the reference standards are estimated to be zero within the limits ±0,3 °C.

δtF: Type B rectangular distribution
Value: 0.0 °C
Halfwidth of Limits: 1 °C
TEMPERATURE GRADIENTS: The temperature gradients inside the furnace have been measured. At 1000 °C deviations from non-uniformity of temperature in the region of measurement are within ±1 °C.

Uncertainty Budgets:

tX: temperature to be measured of the furnace
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
tS 1000.500 °C 0.100 °C normal 1.0 0.10 °C 2.4 %
δtS 0.0 °C 0.150 °C normal 1.0 0.15 °C 5.5 %
CS 0.077 °C/µV          
δViS1 0.0 µV 1.00 µV normal 0.077 0.077 °C 1.4 %
δViS2 0.0 µV 0.289 µV rectangular 0.077 0.022 °C 0.1 %
δVR 0.0 µV 1.15 µV rectangular 0.077 0.089 °C 1.9 %
CS0 0.189 °C/µV          
δt0S 0.0 °C 0.0577 °C rectangular -0.41 -0.024 °C 0.1 %
δtD 0.0 °C 0.173 °C rectangular 1.0 0.17 °C 7.3 %
δtF 0.0 °C 0.577 °C rectangular 1.0 0.58 °C 81.2 %
tX 1000.500 °C 0.641 °C

Results:

Quantity Value Expanded
Uncertainty
Coverage
factor
Coverage
tX 1000.5 °C 1.3 °C 2.00 95% (t-table 95.45%)

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