A type N thermocouple is calibrated by comparison with two reference thermocouples of type R in a horizontal furnace at a temperature of 1000 °C. The emfs generated by the thermocouples are measured with a digital voltmeter through a selector/reversing switch. All thermocouples have their reference junctions at 0 °C. The thermocouple to be calibrated is connected to the reference point using compensating cables.

Model Equation:

VX = ViX + dViX1 + dViX2 + dVR + dVLX + dtX / CX - dt0X / CX0; dtX = tX - t0;

List of Quantities:

Quantity	Unit	Definition
VX	µV	emf of the thermocouple to be calibrated
ViX	µV	indication of the voltmeter
dViX1	µV	voltage correction obtained from the calibration of the voltmeter
dViX2	µV	oltage corrections due to the limited resolution of the voltmeter
dVR	µV	voltage correction due to contact effects of the reversing switch
dVLX	µV	voltage correction due to the compensating cables
dtX	°C	deviation of the temperature of the calibration point from the temperature of the furnace
CX	°C/µV	sensitiviy of the thermocouple for voltage at the measuring at the temperature of 1000 °C
dt0X	°C	temperature correction due to the deviation of the reference temperature of 0 °C
CX0	°C/µV	sensitiviy of the thermocouple for voltage at the measuring at the temperature of 0 °C
tX	°C	temperature of the furnace
t0	°C	nominal termperature of the calibration point

ViX:	Type A Method of observation: Direct Number of observation: 1 No. Observation 1 36248 µV Arithmetic Mean: 36248.000 µV Pooled Standard Deviation: 1.6 µV Standard Uncertainty: 1.600 µV 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 voltage 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 voltage of the thermocouple.

dViX1:

Type B normal distribution Value: 0.0 µV Expanded Uncertainty: 2 µV Coverage Factor: 2

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).

dViX2:

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 mV 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.

dVLX:

Type B rectangular distribution Value: 0.0 µV Halfwidth of Limits: 5 µV

COMPENSATING CABLES: The compensating cables have been investigated in the range 0 °C to 40 °C. From this the voltage differences between the cables and the thermocouple wires are estimated to be within ±5 µV.

dtX:	Interim Result

CORRECTION OF THE CALIBRATION POINT: Deviation of the temperature of the calibration point from the temperature of the furnace.

CX:	Constant Value: 0.026 °C/µV

VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.

dt0X:

Type B rectangular distribution Value: 0.0 °C Halfwidth of Limits: 0.1 °C

REFERENCE TEMPERATURES: The temperature of the reference point of each thermocouple is known to be 0 °C within ±0,1 °C.

CX0:	Constant Value: 0.039 °C/µV

VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.

tX:	Type B normal distribution Value: 1000.5 °C Expanded Uncertainty: 0.641 °C Coverage Factor: 1.0

TEMPERATURE OF THE FURNACE: The temperature of the furnace is evaluated in a second analysis named temperature

t0:	Constant Value: 1000.0 °C

CALIBRATION POINT: The nominal termperature of the calibration point is 1000.0 °C.

Uncertainty Budgets:
V_X: emf of the thermocouple to be calibrated

Quantity	Value	Standard Uncertainty	Distribution	Sensitivity Coefficient	Uncertainty Contribution	Index
ViX	36248.000 µV	1.600 µV	normal	1.0	1.6 µV	0.4 %
dViX1	0.0 µV	1.000 µV	normal	1.0	1.0 µV	0.2 %
dViX2	0.0 µV	0.2887 µV	rectangular	1.0	0.29 µV	0.0 %
dVR	0.0 µV	1.155 µV	rectangular	1.0	1.2 µV	0.2 %
dVLX	0.0 µV	2.887 µV	rectangular	1.0	2.9 µV	1.3 %
dtX	0.5000 °C	0.6410 °C
CX	0.026 °C/µV
dt0X	0.0 °C	0.05774 °C	rectangular	-26	-1.5 µV	0.4 %
CX0	0.039 °C/µV
tX	1000.5000 °C	0.6410 °C	normal	38	25 µV	97.5 %
t0	1000.0 °C
VX	36267.23 µV	24.97 µV

Results:

Quantity	Value	Expanded Uncertainty	Coverage factor	Coverage
VX	36267 µV	50 µV	2.00	95% (t-table 95.45%)