Calibration of a type N thermocouple at 1000 °C: Furnace temperature
In the Ntype thermocouple calibration at 1000 °C the temperature of the furnace is determined by two Rtype 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:
t_{X} = t_{S} + δt_{S} + C_{S} × (δV_{iS1} + δV_{iS2} + δV_{R})  C_{S} / C_{S0} × δt_{0S} + δt_{D} + δt_{F}

List of Quantities:
Quantity  Unit  Definition 

t_{X}  °C  temperature to be measured of the furnace 
t_{S}  °C  temperature of the reference thermometer in terms of voltage with cold junction at 0 °C. The function is given in the calibration certificate. 
δt_{S}  °C  correction of the temperature of the reference thermocouples due to their calibration 
C_{S}  °C/µV  sensitivities of the reference thermocouples for voltage at the measuring temperature of 1000 °C 
δV_{iS1}  µV  voltage correction obtained from the calibration of the voltmeter 
δV_{iS2}  µV  voltage correction due to the limited resolution of the voltmeter 
δV_{R}  µV  voltage correction due to contact effects of the reversing switch 
C_{S0}  °C/µV  sensitivities of the reference thermocouples for voltage at the reference temperature of 0 °C 
δt_{0S}  °C  temperature correction due to the deviation of the reference temperature from 0 °C 
δt_{D}  °C  change of the values of the reference thermometers since their last calibration due to drift 
δt_{F}  °C  temperature correction due to nonuniformity of the temperature of the furnace 
t_{S}: 
Type A Method of observation: Direct Number of observation: 1
Arithmetic Mean: 1000.500 °C 
δt_{S}: 
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 )
C_{S}: 
Constant Value: 0.077 °C/µV 
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables
δV_{iS1}: 
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)
δV_{iS2}: 
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.
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.
C_{S0}: 
Constant Value: 0.189 °C/µV 
VOLTAGE SENSITIVITIES: The voltage sensitivities of the thermocouples have been taken from reference tables.
δt_{0S}: 
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.
δt_{D}: 
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.
δt_{F}: 
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 nonuniformity 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 

t_{S}  1000.500 °C  0.100 °C  normal  1.0  0.10 °C  2.4 % 
δt_{S}  0.0 °C  0.150 °C  normal  1.0  0.15 °C  5.5 % 
C_{S}  0.077 °C/µV  
δV_{iS1}  0.0 µV  1.00 µV  normal  0.077  0.077 °C  1.4 % 
δV_{iS2}  0.0 µV  0.289 µV  rectangular  0.077  0.022 °C  0.1 % 
δV_{R}  0.0 µV  1.15 µV  rectangular  0.077  0.089 °C  1.9 % 
C_{S0}  0.189 °C/µV  
δt_{0S}  0.0 °C  0.0577 °C  rectangular  0.41  0.024 °C  0.1 % 
δt_{D}  0.0 °C  0.173 °C  rectangular  1.0  0.17 °C  7.3 % 
δt_{F}  0.0 °C  0.577 °C  rectangular  1.0  0.58 °C  81.2 % 
t_{X}  1000.500 °C  0.641 °C 
Results:
Quantity  Value 
Expanded Uncertainty 
Coverage factor 
Coverage 

t_{X}  1000.5 °C  1.3 °C  2.00  95% (ttable 95.45%) 