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Type T Thermocouples

Thermoelectricity

Within the chamber of a lyophilizer we most often use thermocouples to measure temperature.   Although other devices would work and from time to time may be used, thermocouples are inexpensive, and accurate.  In this document we are going to explore what thermcouples are, how they work, and what precautions should be observed in their use.   In addition, we will show the methods for how to compute temperature from the voltage measurements, since it is instructive in understanding the inherent inaccuracies associated with this temperature measurement method.

Thermocouples operate on the Seebeck principle. Thomas Seebeck was an Estonian doctor who in 1822 assembled a circle composed of half bismuth and half copper.  He noticed, quite by accident, that when a compass was held near the joined metals that the needle was deflected away from magnetic north, being wholly influenced by the joined metals.   This became known as the Seebeck effect. Although Seebeck didn't recognize it, the effect is totally electrical in nature, and it isn't confined to metals of two different types, and it has little to do with the junction.

If one has a metal wire homogenously composed of one or a mixture of metals [For example constantan is an alloy of 60% Cu and 40% Ni. For the purpose of this discussion it is homogeneous.]  with the two ends at different temperatures, then the electrons (and/or holes) will distribute themselves differently at different temperatures leading directly to a static charge between the two ends of the wire that is proportional to the temperature difference. Most clearly this is not a thermocouple, since there is no "couple".  There is only one wire.  Moreover, one cannot practically measure the voltage difference, since the wires of the voltmeter would also be at different temperatures and would experience the same effect to a greater or lesser state and with wire having probably different composition. This thermoelectricity was not a discovery of Seebeck, but is the current basis for the operation of thermocouples. Within reason, the length and diameter of the wire are of no consequence.

Sinle Wire connected to voltmeter
Thermocouples

Everything in this document except for the numerical values and tables is applicable to all thermocouple types.  We focus on type T only because it is the one most popular for use in a lyophilizer.  Indeed, other types, and in particular type J might work just as well. A thermocouple, as used for the measurement of temperature is an open circuit consisting of two wires joined at one end and not the other.  In order to assure good electrical contact as well as assure that the joined ends are at exactly the same temperature, they are usually welded together.

Thermocouple

Since the junction end largely defines a single point in space, we can assume that it is at a single temperature.  However, the "open" end could conceivably vary by a few degrees.  If it does, and that variation is not planned, then the measured result will be incorrect.  There are "calibration" equations provided by  NIST [srdata.nist.gov]   that use a temperature of zero degrees C as the reference temperature (T2 = the open end).  However, it isn't necessary to actually have the reference end at 0°C.  Instead, it is necessary to accurately know the temperature of the reference end.  When it is accurately known, then the NIST calibration equations can be used to compute the voltage between T2 and 0°C and that voltage can be added to the measured voltage to mathematically compensate for not having the reference (T2) at 0°C.  The derived voltage can then be used in the calibration equation to arive at a correct temperature.  This technique is known as cold junction compensation. In case you are wondering about the Seebeck effect on other non-thermocouple wires in the circuit - good you should worry.  There is a Law of intermediate metals which states that "any two junctions composed of a single wire of any conductor, will not have a measureable thermo-voltage, as long as the two nodes are at the same temperature.   Further, a wire on one side of the circuit (think voltmeter lead wires) is cancelled out by a wire on the other side of the circuit if the matching ends of each wire are at the same temperature.  The two voltmeter leads are usually OK because one end of the set is in the controlled reference junction box and the other ends are at a similar temperature in the voltmeter.  However, some care should be taken to assure that these volmeter leads are not differentially heated inside the voltmeter itself.

It appears that there is a 'catch 22' and indeed there is.  You have to have a reference temperature in order to use thermocouples to measure temperature.  In other words, if we don't go to the trouble of building an ice bath that is carefully (its harder than you think) prepared to be exactly at 0°C, then we have to independently measure the temperature at the reference end.  Again, we have to measure temperature in order to measure temperature.  Moreover, and more bad news still, is that the final measured temperature at T1 can be no more accurate than the measured temperature at T2.  The upshot of this is that we ought to be asking about the method used for measuring temperature at the reference and we ought to be very particular about examining the reference junctions and be satisfied that they are protected from temperture shifts that might cause one or more of the junctions (assuming multiple thermocouples connected at the reference end) to be at a different temperature from the reference measurement.

As an example of cold junction compensation we can look at Allen Bradley's 1746-NT8 thermocouple module for the SLC 500 series PLC.  It has places to attach 8 thermocouples with a cover to buffer local temperature changes.  It also has two thermistor assemblies located on either end of the terminal block and used for measuring the reference junction temperature.  Thermistors are nothing more than temperature sensitive resistors.  That is, their resistance changes with temperature.  Each one must be calibrated and they are subject to drift over time.  In the application of measuring a reference junction, the drift is of no consequence if (and only if) the entire system - thermocouples and thermistors together - are calibrated to known temperature standards regularly.  Since thermocouples are also subject go calibration concerns, regular system calibration is recommended.

Thermocouple Arithmetic

NIST publishes fitted polynomial coefficients for use in converting measured voltages to temperature with various thermocouple metals. The equation for type T wire are shown in the tables below. There is also an NIST data set correlating temperature and milliVolts for each even degree of temperature from -270°C to 400°C.

Calibration Equation from NIST
Calculate Temperature from milliVolt(E) input
j Coefficient CF Coefficient CG Equations
00.00000000000.000000000
125.949192000025.9280000000
2 -.2131696700-0.7602961000
3 0.7901869200 0.0463779100
4 0.4252777700-2.1653940E-3
5 0.1330447300 6.0481000E-5
6 0.0202414460-7.2900000E-7
7 1.2668170E-3 0.0000000000
Calibration Equation from NIST
Calculate milliVolts from Temperature(T) input
j Coefficient CF Coefficient CG Equations
00.00000000000.000000000
13.8748106364E-023.8748106364E-02
24.4194434347E-05 3.3292227880E-05
31.1844323105E-07 2.0618243404E-07
42.0032973554E-08 -2.1882256846E-09
59.0138019559E-10 1.0996880928E-11
62.2651156593E-11 -3.0815758772E-14
73.6071154205E-13 4.5479135290E-17
83.8493939883E-15-2.7512901673E-20
92.8213521925E-17 
101.4251594779E-19 
114.8768662286E-22 
121.0795539270E-24 
131.3945027062E-27 
147.9795153927E-31 

Now consider the figure below.  Let the polynomial in Table 1 and 2 be programed into 2 functions, T1(E)will accept milliVolts and return Temperature while mV2(T) will accept Temperature and return milliVolts.



To obtain the temperature at one of the thermocouple tips (for example node 2 in the figure) do the following.

  1. Measure the voltage at the reference node where the thermistor is located - junctions 1 and 3 in the figure.
  2. Convert the thermistor temperature to a voltage, thus obtaining a milliVolt value between 0°C and the thermistor temperture. Function mV2(T) will do that.
  3. Add together the two milliVolt results from 1 and 2.
  4. Use the milliVolt to Temperature function, T1(E), above to convert the result from 3 into a Temperature.

It is unlikely that you would ever want to do the above steps. They are performed primarily by engineers designing thermocouple modules for electronic equipment.   However, it is instructive to see how it is done because one gains a broad appreciation for the importance of keeping the temperature of the reference junctions tightly controlled.   You may likely be using a module that has only one thermistor in the vicinity of the junctions and it doesn't have to be very different in temperature   from the junction temperatures in order to introduce error.