14 Temperature measurement

 

14.1 Principles of temperature measurement

Temperature measurement is very important in all spheres of life and especially so in the process industries. However, it poses particular problems, since temperature measurement cannot be related to a fundamental standard of temperature in the same way that the measurement of other quantities can be related to the primary standards of mass, length and time. If two bodies of lengths l₁ and l₂ are connected together end to end, the result is a body of length l₁ + l₂. A similar relationship exists between separate masses and separate times. However, if two bodies at the same temperature are connected together, the joined body has the same temperature as each of the original bodies.

This is a root cause of the fundamental difficulties that exist in establishing an absolute standard for temperature in the form of a relationship between it and other measurable quantities for which a primary standard unit exists. In the absence of such a relationship, it is necessary to establish fixed, reproducible reference points for temperature in the form of freezing and boiling points of substances where the transition between solid, liquid and gaseous states is sharply defined. The International Practical Temperature Scale (IPTS)Ł uses this philosophy and defines six primary fixed points for reference temperatures in terms of:

• the triple point of equilibrium hydrogen            -259.34°C

• the boiling point of oxygen                                   -182.962°C

• the boiling point of water                                     100.0°C

• the freezing point of zinc                                      419.58°C

• the freezing point of silver                                  961.93°C

• the freezing point of gold                                   1064.43°C

                      (all at standard atmospheric pressure)

The freezing points of certain other metals are also used as secondary fixed points to provide additional reference points during calibration procedures.

Instruments to measure temperature can be divided into separate classes according to the physical principle on which they operate. The main principles used are:

• The thermoelectric effect

• Resistance change

• Sensitivity of semiconductor device

• Radiative heat emission

• Thermography

• Thermal expansion

• Resonant frequency change

• Sensitivity of fibre optic devices

• Acoustic thermometry

• Colour change

• Change of state of material.

 

14.2 Thermoelectric effect sensors (thermocouples)

Thermoelectric effect sensors rely on the physical principle that, when any two different metals are connected together, an e.m.f., which is a function of the temperature, is generated at the junction between the metals. The general form of this relationship is:

                            e = a₁T + a₂T² + a₃T³ +…+ a_nTⁿ (14.1)

where e is the e.m.f. generated and T is the absolute temperature.

This is clearly non-linear, which is inconvenient for measurement applications. Fortu[1]nately, for certain pairs of materials, the terms involving squared and higher powers of T (a2T2, a3T3 etc.) are approximately zero and the e.m.f.–temperature relationship is approximately linear according to:

                                           e  a₁T                                 (14.2)

Wires of such pairs of materials are connected together at one end, and in this form are known as thermocouples. Thermocouples are a very important class of device as they provide the most commonly used method of measuring temperatures in industry.

Thermocouples are manufactured from various combinations of the base metals copper and iron, the base-metal alloys of alumel (Ni/Mn/Al/Si), chromel (Ni/Cr), constantan (Cu/Ni), nicrosil (Ni/Cr/Si) and nisil (Ni/Si/Mn), the noble metals platinum and tungsten, and the noble-metal alloys of platinum/rhodium and tungsten/rhenium. Only certain combinations of these are used as thermocouples and each standard combination is known by an internationally recognized type letter, for instance type K is chromel-alumel. The e.m.f.–temperature characteristics for some of these standard thermocouples are shown in Figure 14.1: these show reasonable linearity over at least part of their temperature-measuring ranges.

A typical thermocouple, made from one chromel wire and one constantan wire, is shown in Figure 14.2(a). For analysis purposes, it is useful to represent the thermocouple by its equivalent electrical circuit, shown in Figure 14.2(b). The e.m.f. generated at the point where the different wires are connected together is represented by a voltage

source, E₁, and the point is known as the hot junction. The temperature of the hot junction is customarily shown as T_h on the diagram. The e.m.f. generated at the hot junction is measured at the open ends of the thermocouple, which is known as the reference junction.

In order to make a thermocouple conform to some precisely defined e.m.f.–temperature characteristic, it is necessary that all metals used are refined to a high degree of pureness and all alloys are manufactured to an exact specification. This makes the materials used expensive, and consequently thermocouples are typically only a few centimetres long. It is clearly impractical to connect a voltage-measuring instrument at the open end of the thermocouple to measure its output in such close proximity to the environment whose temperature is being measured, and therefore extension leads up to several metres long are normally connected between the thermocouple and the measuring instrument. This modifies the equivalent circuit to that shown in Figure 14.3(a). There are now three junctions in the system and consequently three voltage sources, E₁, E₂ and E₃, with the point of measurement of the e.m.f. (still called the reference junction) being moved to the open ends of the extension leads.

The measuring system is completed by connecting the extension leads to the voltage measuring instrument. As the connection leads will normally be of different materials to those of the thermocouple extension leads, this introduces two further e.m.f.-generating junctions E₄ and E₅ into the system as shown in Figure 14.3(b). The net output e.m.f. measured (Em) is then given by:

                                 E_m = E₁ + E₂ + E₃ + E₄ + E₅                         (14.3)

and this can be re-expressed in terms of E₁ as:

                                  E₁ = E_m - E₂ - E₃ - E₄ - E₅                        (14.4)

In order to apply equation (14.1) to calculate the measured temperature at the hot junction, E₁ has to be calculated from equation (14.4). To do this, it is necessary to calculate the values of E₂, E₃, E₄ and E₅.

It is usual to choose materials for the extension lead wires such that the magnitudes of E₂ and E₃ are approximately zero, irrespective of the junction temperature. This avoids the difficulty that would otherwise arise in measuring the temperature of the junction between the thermocouple wires and the extension leads, and also in determining the e.m.f./temperature relationship for the thermocouple–extension lead combination.

A zero junction e.m.f. is most easily achieved by choosing the extension leads to be of the same basic materials as the thermocouple, but where their cost per unit length is greatly reduced by manufacturing them to a lower specification. However, such a solution is still prohibitively expensive in the case of noble metal thermocouples, and it is necessary in this case to search for base-metal extension leads that have a similar thermoelectric behaviour to the noble-metal thermocouple. In this form, the extension leads are usually known as compensating leads. A typical example of this is the use of nickel/copper–copper extension leads connected to a platinum/rhodium–platinum thermocouple. Copper compensating leads are also sometimes used with some types of base metal thermocouples and, in such cases, the law of intermediate metals can be applied to compensate for the e.m.f. at the junction between the thermocouple and compensating leads.

To analyse the effect of connecting the extension leads to the voltage-measuring instrument, a thermoelectric law known as the law of intermediate metals can be used. This states that the e.m.f. generated at the junction between two metals or alloys A and C is equal to the sum of the e.m.f. generated at the junction between metals or alloys A and B and the e.m.f. generated at the junction between metals or alloys B and C, where all junctions are at the same temperature. This can be expressed more simply as:

                              e_AC = e_AB + e_BC                        (14.5)

Suppose we have an iron–constantan thermocouple connected by copper leads to a meter. We can express E₄ and E₅ in Figure 14.4 as:

                    E₄ = e_iron-copper; E₅ = e_{copper-constantan}

The sum of E₄ and E₅ can be expressed as:

                       E₄ + E₅ + e_iron-copper + e_{copper-constantan}

Applying equation (14.5):

                      e_iron-copper + e_{copper-constantan} = e_{iron-constantan}

Thus, the effect of connecting the thermocouple extension wires to the copper leads to the meter is cancelled out, and the actual e.m.f. at the reference junction is equivalent to that arising from an iron–constantan connection at the reference junction temperature, which can be calculated according to equation (14.1). Hence, the equivalent circuit in Figure 14.3(b) becomes simplified to that shown in Figure 14.4. The e.m.f. Em measured by the voltage-measuring instrument is the sum of only two e.m.f.s, consisting of the e.m.f. generated at the hot junction temperature E₁ and the e.m.f. generated at the reference junction temperature E_ref. The e.m.f. generated at the hot junction can then be calculated as:

                          E₁ = E_m + E_ref

E_ref can be calculated from equation (14.1) if the temperature of the reference junction is known. In practice, this is often achieved by immersing the reference junction in an ice bath to maintain it at a reference temperature of 0°C. However, as discussed in the following section on thermocouple tables, it is very important that the ice bath remains exactly at 0°C if this is to be the reference temperature assumed, otherwise significant measurement errors can arise. For this reason, refrigeration of the reference junction at a temperature of 0°C is often preferred.