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 + dtS + CS × (dViS1 + dViS2 + dVR) - CS / CS0 × dt0S + dtD + dtF

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.
dtS	°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
dViS1	µV	voltage correction obtained from the calibration of the voltmeter
dViS2	µV	voltage correction due to the limited resolution of the voltmeter
dVR	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
dt0S	°C	temperature correction due to the deviation of the reference temperature from 0 °C
dtD	°C	change of the values of the reference thermometers since their last calibration due to drift
dtF	°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: 1000.5000 °C Pooled Standard Deviation: 0.10 °C Standard Uncertainty: 0.1000 °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.

dtS:	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

dViS1:

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)

dViS2:

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.

dVR:	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.

dt0S:

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.

dtD:	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.

dtF:	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:
t_X: temperature to be measured of the furnace

Quantity	Value	Standard Uncertainty	Distribution	Sensitivity Coefficient	Uncertainty Contribution	Index
tS	1000.5000 °C	0.1000 °C	normal	1.0	0.10 °C	2.4 %
dtS	0.0 °C	0.1500 °C	normal	1.0	0.15 °C	5.5 %
CS	0.077 °C/µV
dViS1	0.0 µV	1.000 µV	normal	0.077	0.077 °C	1.4 %
dViS2	0.0 µV	0.2887 µV	rectangular	0.077	0.022 °C	0.1 %
dVR	0.0 µV	1.155 µV	rectangular	0.077	0.089 °C	1.9 %
CS0	0.189 °C/µV
dt0S	0.0 °C	0.05774 °C	rectangular	-0.41	-0.024 °C	0.1 %
dtD	0.0 °C	0.1732 °C	rectangular	1.0	0.17 °C	7.3 %
dtF	0.0 °C	0.5774 °C	rectangular	1.0	0.58 °C	81.2 %
tX	1000.5000 °C	0.6409 °C

Results:

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