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:
V_{X} = V_{iX} + δV_{iX1} + δV_{iX2} + δV_{R} + δV_{LX} + δt_{X} / C_{X}  δt_{0X} / C_{X0}; δt_{X} = t_{X}  t_{0};

List of Quantities:
Quantity  Unit  Definition 

V_{X}  µV  emf of the thermocouple to be calibrated 
V_{iX}  µV  indication of the voltmeter 
δV_{iX1}  µV  voltage correction obtained from the calibration of the voltmeter 
δV_{iX2}  µV  oltage corrections due to the limited resolution of the voltmeter 
δV_{R}  µV  voltage correction due to contact effects of the reversing switch 
δV_{LX}  µV  voltage correction due to the compensating cables 
δt_{X}  °C  deviation of the temperature of the calibration point from the temperature of the furnace 
C_{X}  °C/µV  sensitiviy of the thermocouple for voltage at the measuring at the temperature of 1000 °C 
δt_{0X}  °C  temperature correction due to the deviation of the reference temperature of 0 °C 
C_{X0}  °C/µV  sensitiviy of the thermocouple for voltage at the measuring at the temperature of 0 °C 
t_{X}  °C  temperature of the furnace 
t_{0}  °C  nominal termperature of the calibration point 
V_{iX}: 
Type A Method of observation: Direct Number of observation: 1
Arithmetic Mean: 36248.00 µV 
δV_{iX1}: 
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).
δV_{iX2}: 
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.
δV_{R}: 
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.
δV_{LX}: 
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.
δt_{X}: 
Interim Result 
CORRECTION OF THE CALIBRATION POINT: Deviation of the temperature of the calibration point from the temperature of the furnace.
C_{X}: 
Constant Value: 0.026 °C/µV 
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.
δt_{0X}: 
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.
C_{X0}: 
Constant Value: 0.039 °C/µV 
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.
t_{X}: 
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
t_{0}: 
Constant Value: 1000.0 °C 
CALIBRATION POINT: The nominal termperature of the calibration point is 1000.0 °C.
Interim Results:
Quantity  Value 
Standard Uncertainty 

δt_{X}  0.500 °C  0.641 °C 
Uncertainty Budgets:
V_{X}: emf of the thermocouple to be calibrated
Quantity  Value 
Standard Uncertainty 
Distribution 
Sensitivity Coefficient 
Uncertainty Contribution 
Index 

V_{iX}  36248.00 µV  1.60 µV  normal  1.0  1.6 µV  0.4 % 
δV_{iX1}  0.0 µV  1.00 µV  normal  1.0  1.0 µV  0.2 % 
δV_{iX2}  0.0 µV  0.289 µV  rectangular  1.0  0.29 µV  0.0 % 
δV_{R}  0.0 µV  1.15 µV  rectangular  1.0  1.2 µV  0.2 % 
δV_{LX}  0.0 µV  2.89 µV  rectangular  1.0  2.9 µV  1.3 % 
C_{X}  0.026 °C/µV  
δt_{0X}  0.0 °C  0.0577 °C  rectangular  26  1.5 µV  0.4 % 
C_{X0}  0.039 °C/µV  
t_{X}  1000.500 °C  0.641 °C  normal  38  25 µV  97.5 % 
t_{0}  1000.0 °C  
V_{X}  36267.2 µV  25.0 µV 
Results:
Quantity  Value 
Expanded Uncertainty 
Coverage factor 
Coverage 

V_{X}  36267 µV  50 µV  2.00  95% (ttable 95.45%) 