14 Temperature measurement

 

14.2.1 Thermocouple tables

Although the preceding discussion has suggested that the unknown temperature T can be evaluated from the calculated value of the e.m.f. E₁ at the hot junction using equation (14.1), this is very difficult to do in practice because equation (14.1) is a high order polynomial expression. An approximate translation between the value of E1 and temperature can be achieved by expressing equation (14.1) in graphical form as in Figure 14.1. However, this is not usually of sufficient accuracy, and it is normal practice to use tables of e.m.f. and temperature values known as thermocouple tables. These include compensation for the effect of the e.m.f. generated at the reference junction (E_ref), which is assumed to be at 0°C. Thus, the tables are only valid when the reference junction is exactly at this temperature. Compensation for the case where the reference junction temperature is not at zero is considered later in this section.

Tables for a range of standard thermocouples are given in Appendix 4. In these tables, a range of temperatures is given in the left-hand column and the e.m.f. output for each standard type of thermocouple is given in the columns to the right. In practice, any general e.m.f. output measurement taken at random will not be found exactly in the tables, and interpolation will be necessary between the values shown in the table.

 

Example 14.1

If the e.m.f. output measured from a chromel–constantan thermocouple is 13.419 mV with the reference junction at 0°C, the appropriate column in the tables shows that this corresponds to a hot junction temperature of 200°C.

Example 14.2

If the measured output e.m.f. for a chromel–constantan thermocouple (reference junc[1]tion at 0°C) was 10.65 mV, it is necessary to carry out linear interpolation between the temperature of 160°C corresponding to an e.m.f. of 10.501 mV shown in the tables and the temperature of 170°C corresponding to an e.m.f. of 11.222 mV. This interpolation procedure gives an indicated hot junction temperature of 162°C.

 

14.2.2 Non-zero reference junction temperature

If the reference junction is immersed in an ice bath to maintain it at a temperature of 0°C so that thermocouple tables can be applied directly, the ice in the bath must be in a state of just melting. This is the only state in which ice is exactly at 0°C, and otherwise it will be either colder or hotter than this temperature. Thus, maintaining the reference junction at 0°C is not a straightforward matter, particularly if the environ[1]mental temperature around the measurement system is relatively hot. In consequence, it is common practice in many practical applications of thermocouples to maintain the reference junction at a non-zero temperature by putting it into a controlled environment maintained by an electrical heating element. In order to still be able to apply thermocouple tables, correction then has to be made for this non-zero reference junction temperature using a second thermoelectric law known as the law of intermediate temperatures. This states that:

                              E(T_h,T₀) = E(T_h,T_r) + E(T_r,T₀)                              (14.6)

where: E(T_h,T₀) is the e.m.f. with the junctions at temperatures T_h and T₀, E(T_h,T_r) is the e.m.f. with the junctions at temperatures T_h and T_r, and E(T_r,T₀)is the e.m.f. with the junctions at temperatures T_r and T₀, T_h is the hot junction measured temperature, T₀ is 0°C and T_r is the non-zero reference junction temperature that is somewhere between T₀ and T_h.

Example 14.3

Suppose that the reference junction of a chromel–constantan thermocouple is main[1]tained at a temperature of 80°C and the output e.m.f. measured is 40.102 mV when the hot junction is immersed in a fluid.

The quantities given are Tr = 80°C and E(T_h,T_r) = 40.102 mV

From the tables, E(T_r,T₀) = 4.983 mV

Now applying equation (14.6), E(T_h,T₀) = 40.102 + 4.983 = 45.085 mV

Again referring to the tables, this indicates a fluid temperature of 600°C.

In using thermocouples, it is essential that they are connected correctly. Large errors can result if they are connected incorrectly, for example by interchanging the extension leads or by using incorrect extension leads. Such mistakes are particularly serious because they do not prevent some sort of output being obtained, which may look sensible even though it is incorrect, and so the mistake may go unnoticed for a long period of time. The following examples illustrate the sort of errors that may arise:

Example 14.4

This example is an exercise in the use of thermocouple tables, but it also serves to illustrate the large errors that can arise if thermocouples are used incorrectly. In a particular industrial situation, a chromel–alumel thermocouple with chromel–alumel extension wires is used to measure the temperature of a fluid. In connecting up this measurement system, the instrumentation engineer responsible has inadvertently inter[1]changed the extension wires from the thermocouple. The ends of the extension wires are held at a reference temperature of 0°C and the output e.m.f. measured is 14.1 mV. If the junction between the thermocouple and extension wires is at a temperature of 40°C, what temperature of fluid is indicated and what is the true fluid temperature?

Solution The initial step necessary in solving a problem of this type is to draw a diagrammat[1]ical representation of the system and to mark on this the e.m.f. sources, temperatures etc., as shown in Figure 14.5. The first part of the problem is solved very simply by looking up in thermocouple tables what temperature the e.m.f. output of 12.1 mV indicates for a chromel–alumel thermocouple. This is 297.4°C. Then, summing e.m.f.s around the loop:

                  V = 12.1 = E₁ + E₂ + E₃ or E₁ = 12.1 - E₂ - E₃

            E₂ = E₃ = e.m.f._{(alumel-chromel)40} = -e.m.f._{(chromel-alumel)40} * = - 1.611 mV

Hence:

                   E₁ = 12.1 + 1.611 + 1.611 = 15.322 mV

Interpolating from the thermocouple tables, this indicates that the true fluid temperature is 374.5°C.

Example 14.5

This example also illustrates the large errors that can arise if thermocouples are used incorrectly. An iron–constantan thermocouple measuring the temperature of a fluid is connected by mistake with copper–constantan extension leads (such that the two constantan wires are connected together and the copper extension wire is connected to the iron thermocouple wire). If the fluid temperature was actually 200°C, and the junction between the thermocouple and extension wires was at 50°C, what e.m.f. would be measured at the open ends of the extension wires if the reference junction is main[1]tained at 0°C? What fluid temperature would be deduced from this (assuming that the connection mistake was not known about)?

Solution

Again, the initial step necessary is to draw a diagram showing the junctions, tempera[1]tures and e.m.f.s, as shown in Figure 14.6. The various quantities can then be calculated: