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 
C_{S}: 
Constant Value: 0.077 °C/µV 
δV_{iS1}: 
Type B normal distribution Value: 0.0 µV Expanded Uncertainty: 2.0 µV Coverage Factor: 2.0 
δV_{iS2}: 
Type B rectangular distribution Value: 0.0 µV Halfwidth of Limits: 0.5 µV 
δV_{R}: 
Type B rectangular distribution Value: 0.0 µV Halfwidth of Limits: 2.0 µV 
C_{S0}: 
Constant Value: 0.189 °C/µV 
δt_{0S}: 
Type B rectangular distribution Value: 0.0 °C Halfwidth of Limits: 0.1 °C 
δt_{D}: 
Type B rectangular distribution Value: 0.0 °C Halfwidth of Limits: 0.3 °C 
δt_{F}: 
Type B rectangular distribution Value: 0.0 °C Halfwidth of Limits: 1 °C 
Uncertainty Budgets:
t_{X}: temperature to be measured of the furnaceQuantity  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%) 