Metrodata GmbH - Calibration of a type N thermocouple at 1000 °C

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 - t₀;

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
t₀	°C	nominal termperature of the calibration point

V_iX:

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.

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

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
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 %
t₀	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% (t-table 95.45%)