Calibration of a type N thermocouple at 1000 °C

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 + δViX1 + δViX2 + δVR + δVLX + δtX / CX - δt0X / CX0;

δtX = tX - t0;

List of Quantities:

Quantity Unit Definition
VX µV emf of the thermocouple to be calibrated
ViX µV indication of the voltmeter
δViX1 µV voltage correction obtained from the calibration of the voltmeter
δViX2 µV oltage corrections due to the limited resolution of the voltmeter
δVR µV voltage correction due to contact effects of the reversing switch
δVLX µV voltage correction due to the compensating cables
δtX °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
δt0X °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: 36248.00 µV
Pooled Standard Deviation: 1.6 µV
Standard Deviation of the Mean: 1.60 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.

δViX1: 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).

δViX2: 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.

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.

δVLX: 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.

δtX: 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.

δt0X: 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.

Interim Results:

Quantity Value Standard
Uncertainty
δtX 0.500 °C 0.641 °C

Uncertainty Budgets:

VX: emf of the thermocouple to be calibrated
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
ViX 36248.00 µV 1.60 µV normal 1.0 1.6 µV 0.4 %
δViX1 0.0 µV 1.00 µV normal 1.0 1.0 µV 0.2 %
δViX2 0.0 µV 0.289 µV rectangular 1.0 0.29 µV 0.0 %
δVR 0.0 µV 1.15 µV rectangular 1.0 1.2 µV 0.2 %
δVLX 0.0 µV 2.89 µV rectangular 1.0 2.9 µV 1.3 %
CX 0.026 °C/µV          
δt0X 0.0 °C 0.0577 °C rectangular -26 -1.5 µV 0.4 %
CX0 0.039 °C/µV          
tX 1000.500 °C 0.641 °C normal 38 25 µV 97.5 %
t0 1000.0 °C          
VX 36267.2 µV 25.0 µV

Results:

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

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