Practical Examples: Thermocouple Table Use and Error Analysis
Let’s look at some simple examples to ascertain how to use thermocouple tables. We will look at the Type-J Thermocouple Tables (Table 8.6 in Figliola & Beasley on Page 308).
Example 1. The Type-J Iron-Constantan thermocouple (Tx), connected in a setup shown in Figure 1, is to be exposed to a temperature of approximately -53 oC to 185oC. Tconn and Tmeter are both at approximately 70 oC. So that we can select the appropriate meter and scale, what is the voltage we anticipate?
The solution is to first understand that the setup shown is exactly the setup that the table was built for, so this is an easy calculation. There are two entries to consider:
We might, therefore, choose an instrument and scale capable of measuring ±10mv.
Example 2. The second example discards the ice reference junction and connects the Type-J thermocouple directly to the instrument. This time we are more careful and use a thermometer to record the temperature of the instrument face where the thermocouple is attached. We read 39 oC ± 1 oC. In our testing, we read a value of 3.456±0.002 mv at the meter, and we want to know what the unknown temperature Tx is.
The answer is found by realizing that the meter is creating a virtual thermocouple junction at 39 oC which reduces the voltage readout, and we may compute that offset as
Eoff = Ea + (Tref-Ta)/aref
More simply, since the temperature is 39oC, we may look in the table and find that the thermocouple is creating the equivalent of Eoff = 2.006mv offset to the reading for Tx. If the configuration were as shown in Figure 1, the reading would then be
E = Eact + Eoff = 3.456mv + 2.006mv = 5.462mv
The thermocouple table can be quickly scanned and the temperature Tx is found to be between 103 oC and 104 oC. We linearly interpolate and find that it is
T = 103 + (5.462-5.432)*1 oC/(5.487-5.432) = 103 + 0.03/0.055 = 103.545 oC
Unfortunately, we do not know the resolution of this measurement. We do know that the measurement is a function of the voltmeter’s accuracy and that of the thermometer. We can write that
Tx = T1 +(1/ax)(E-E1) = T1 +(1/ax)( Eact +Ea + aref (Tref-Ta) -E1)
Tx = T1 + (Eact +Ea + a ref(Tref-Ta) -E1) /ax
The “variables” in this equation may be written as Tx = F(Tref, Eact) and applying the RSS method we can write that the error of the measurement is thus
Numerically, this becomes
Figure 2. Simpler measurement system.
It is thus obvious that the greatest error arises from the thermometer’s inaccuracy, not that of the voltmeter.
There are many instances where thermocouples are connected directly to the measuring instrument, and this illustrates how important it is to know the temperature of the connection panel. If you use different values for the accuracy of the thermometer, eTref, you quickly discover that the accuracy of measuring Tx is essentially the accuracy of Tref. Thus, we may write
Tx = 103.55 oC ± 0.93 oC