Question 15.2: Suppose the thermocouple in Figure 15–21 is measuring 200°C ...
Suppose the thermocouple in Figure 15–21 is measuring 200°C in an industrial oven. The circuit board is in an area where the ambient temperature can vary from 15°C to 35°C. Using Table 15–2 for a type- T (copper/constantan) thermocouple, determine the voltage across the circuit input terminals at the ambient temperature extremes. What is the maximum percent error in the voltage at the circuit input terminals?
| TABLE 15–2 • Type-T thermocouple voltage. | |
| TEMPERATURE (°C) | OUTPUT (mV) |
| -200 | -5.603 |
| -100 | -3.378 |
| 0 | 0.000 |
| +100 | 4.277 |
| +200 | 9.286 |
| +300 | 14.860 |
| +400 | 20.869 |
From Table 15–2 , you know that the measuring thermocouple is producing 9.286 mV. To determine the voltage that the unwanted thermocouple is creating at 15°C, you must interpolate from the table. Since 15°C is 15% of 100°C, a linear interpolation gives the following voltage:
0.15(4.277 mV) = 0.642 mV
Since 35°C is 35% of 100°C, the voltage is
0.35(4.277 mV) = 1.497 mV
The voltage across the circuit input terminals at 15°C is
9.286 mV – 0.642 mV = 8.644 mV
The voltage across the circuit input terminals at 35°C is
9.286 mV – 1.497 mV = 7.789 mV
The maximum percent error in the voltage at the circuit input terminals is
\left(\frac{9.286 ~\mathrm{mV}-7.789 ~\mathrm{mV}}{9.286~ \mathrm{mV}}\right) 100 \%=16.1 \%
You can never be sure how much it is off because you have no control over the ambient temperature. Also, the linear interpolation may or may not be accurate depending on the linearity of the temperature characteristic of the unwanted thermocouple.
P R A C T I C E EXERCISE
In the case of the circuit in Figure 15–21 , if the temperature being measured goes up to 300°C, what is the maximum percent error in the voltage across the circuit input terminals?