Applied Electronics and Instrumentation 3(2+1)

LESSON 30. Temperature measurement by mechanical effect and electrical effect

The liquid in glass thermometer is one of the most common types of temperature measurement devices. The construction details of such an instrument are shown in the following figure-. A relatively large bulb at the lower portion of the thermometer holds the major portion of the liquid, which expands when heated and rises in the capillary tube, upon which are etched appropriate scale markings. At the top of the capillary tube another bulb is placed to provide a safety feature in case the temperature range of the thermometer is inadvertently exceeded. Alcohol and mercury are the most commonly used liquids. Alcohol has the advantage that it has a higher coefficient of expansion than mercury, but it is limited to low temperature measurements because it tends to boil away at high temperatures. Mercury cannot be used below its freezing point of –38.78°F (-37.8°C). the size of the capillary depends on the size of the sensing bulb, the liquid, and the desired temperature range for the thermometer.

In operation, the bulb of the liquid-in-glass thermometer is exposed to the environment whose temperature is to be measured. A rise in temperature causes the liquid to expand in the bulb and rise in the capillary, thereby indicating the temperature. It is important to note that the expansion registered by the thermometer is the difference between the expansion of the liquid and the expansion of the glass. The difference is a function not only of the heat transfer to the bulb from the environment, but also of the heat conducted into the bulb from the stem; the more the stem conduction relative to the heat transfer from the environment, the larger the error. To account for such conduction effects the thermometer is usually calibrated for a certain specified depth of immersion. High grade mercury in glass thermometers have the temperature scale markings engraved on the glass along with a mark which designates the proper depth of immersion. Very precise mercury-in-glass thermometers may be obtained from the National Bureau of Standards with calibration information for each thermometer.

Mercury-in-glass thermometers are generally applicable upto about 600°F (315°C), but their range may be extended to 1000°F (538°C) by filling the space above the mercury with a gas like nitrogen. This increases the pressure on the mercury, raises its boiling point, and thereby permits the use of the thermometer at higher temperatures.

 A very widely used method of temperature measurement is the bimetallic strip. Two pieces of metal with different coefficients of thermal expansion are bonded together to form the device shown in Fig. When the strip is subjected to a temperature higher than the bonding temperature, it will bend in one direction; when it is subjected to a temperature lower than the bonding temperature, it will bend in the other direction. Eskin and Fritze have given calculation methods for bimetallic strips. The radius of curvature r may be calculated as

                                     T[3(1+m)² + (1+mn)[m² + (1/mn)]]

                        r =        -------------------------------------------

                                                6(x₂-x₁)(T-T₀)(1+m)²

where t = combined thickness of the bonded strip

            m = ratio of thickness of low- to high-expansion materials

            n = ratio of moduli of elasticity of low- to high- expansion materials

            x₁ = lower coefficient of expansion

            a₂ = higher coefficient of expansion

            T = temperature

            T₀ = initial bonding temperature

Fluid expansion thermometers represent one of the most economical, versatile, and widely used devices for industrial temperature measurement applications. The principle of operation is indicated in Fig. A bulb containing a liquid, gas, or vapor is immersed in the environment. The bulb is connected by means of a capillary tube to some type of pressure measuring device, such as the Bourdon gage shown. An increase in temperature causes the liquid or gas to expand, thereby increasing the pressure on the gage; the pressure is thus taken as an indication of the temperature. The entire system consisting of the bulb, capillary, and gage may be calibrated directly. It is clear that the temperature of the capillary tube may influence the reading of the device because some of the volume of fluid is contained therein. If an equilibrium mixture of liquid and vapor is used in the bulb, however, this problem may be alleviated, provided that the bulb temperature is always higher than the capillary tube temperature. In this circumstance the fluid in the capillary will always be in a subcooled liquid state, while the pressure will be uniquely specified for each temperature in the equilibrium mixture contained in the bulb.

Capillary tubes as long as 200 ft (60 m) may be used with fluid-expansion thermometers. The transient response is primarily dependent on the bulb size and the thermal properties of the enclosed fluid. Highest response may be achieved by using a small bulb connected to some type of electric pressure transducer through a short capillary.

Temperature measurement by electrical effects

Electrical methods of temperature measurement are very convenient because they furnish a signal that is easily detected, amplified, or used for control purposes. In addition, they are usually quite accurate when properly calibrated and compensated.

Electrical resistance thermometer

One quite accurate method of temperature measurement is the electrical resistance thermometer. It consists of some type of resistive element, which is exposed to the temperature to be measured. The temperature is indicated through a measurement of the change in resistance of the element. Several types of materials may be used as resistive elements, and their characteristics are given in Table . The linear temperature coefficient of resistance x is defined by

                                                               R₂ – R₁

                                                     x = -----------------

                                                            R₁T₂ – R₂T₁

Where R₂ and R₁ are the resistances of the material at temperatures T₂ and T₁, respectively. The relationship in Equation is usually applied over a narrow temperature range such that the variation of resistance with temperature approximates a linear relation. For wider temperature ranges the resistance of the material is usually expressed by a quadratic relation

                                    R = R₀ (1+aT + bT²)

Where R = resistance at temperature T

            R₀ = resistance at 0°F

            a,b = experimentally determined constants

            It may be noted that the platinum resistance thermometer is used for the International Temperature Scale between the oxygen point and the antimony point, as described in Chap.

Various methods are employed for construction of resistance thermometers, depending on the application. In all cases care must be taken to ensure that the resistance wire is free of mechanical stresses and so mounted that moisture cannot come in contact with the wire and influence the measurement.

The resistance measurement may be performed with some type of bridge circuit, as described in Chap.4. For steady-state measurements a null condition will suffice, while transient measurements will usually require the use of a deflection bridge. One of the primary sources of error in the electrical resistance thermometer is the effect of the resistance of the leads which connect the element to the bridge circuit. Several arrangements may be used to correct for this effect, as shown in Figure. The Siemen’s three lead arrangement is the simplest type of corrective circuit. At balance conditions the center lead carries no current and the effect of the resistance of the other two leads is canceled out. The Callender four-lead arrangement solves the problem by inserting two additional lead wires in the adjustable leg of the bridge so that the effect of the lead wires on the resistance thermometer is canceled out. The floating-potential arrangement in Fig.--- is the same as the Siemen’s connection, but an extra lead is inserted. This extra lead may be used to check the equality of lead resistance. The thermometer reading may be taken in the position shown, followed by additional readings with the two right and left leads interchanged, respectively. Through this interchange procedure the best average reading may be obtained and the lead error minimized.

Thermoelectric effects

The most common electrical method of temperature measurement uses the thermocouple. When two dissimilar metals are joined together as in fig, an emf will exist between the two points A and B, which is primarily a function of the junction temperature. This phenomenon is called the seebeck effect. If the two materials are connected to an external circuit in such a way that a current is drawn, the emf may be altered slightly owing to a phenomenon called the Peltier effect. Further, if a temperature gradient exists along either or both of the materials, the junction emf may undergo an additional slight alteration. This is called the Thomson effect. There are, then, three emfs present in a thermoelectric circuit; the seebeck emf, caused by the junction of dissimilar metals; the Peltier emf, caused by a current flow in the circuit; and the Thomson emf, which results from a temperature gradient in the materials. The seebeck emf is of prime concern since it is dependent on junction temperature. If the emf generated at the junction of two dissimilar metals is carefully measured as a function of temperature, then such as junction may be utilized for the measurement of temperature. The main problem arises when one attempts to measure the potential. When the two dissimilar materials are connected to a measuring device, there will be another thermal emf generated at the junction of the materials and the connecting wires to the voltage measuring instrument. This emf will be dependent on the temperature of the connection, and provision must be made to take account of this additional potential.

Two rules are available for analysis of thermoelectric circuits :

1. If a third metal is connected in the circuit as shown in fig., the net emf of the circuit is not affected as long as the new connections are at the time temperature. This statement may be proved with the aid of the second law of thermodynamics and is known as the law of intermediate metals.

2. Consider the arrangements shown in fig. The simple thermocouple circuits are constructed of the same materials but operate between different temperature limits. The circuit in Fig. develops an emf of E₁ between temperatures T₁ and T₂; the circuit in Fig. develops an emf of E₂ between temperatures T₂ and T₃. The law of intermediate temperatures states that this same circuit will develop an emf of E₃ = E₁ + E₂ when operating between temperatures T₁ and T₃, as shown in fig.

It may be observed that all thermocouple circuit must involve at least two junctions. If the temperature of one junction is known, then the temperature of the other junction may be easily calculated using the thermoelectric properties of the materials. The known temperature is called the reference temperature. A common arrangement for establishing the reference temperature is the ice bath shown in fig. An equilibrium mixture of ice and air saturated distilled water at standard atmospheric pressure produces a known temperature of 32°F. when the mixture is contained in a Dewar flask, it may be maintained for extended periods of time. Note that the arrangement in Fig maintains both thermocouple wires at a reference temperature of 32°F, whereas the arrangement in Fig. maintains only one at the reference temperature. The system in Fig. would be necessary if the binding posts at the voltage measuring instrument were at different temperatures, while the connection in Fig would be satisfactory if the binding posts were at the same temperature. To be effective the system in Fig. must have copper binding posts; the binding posts and leads must be of the same material.

It is common to express the thermoelectric emf in terms of potential generated with a reference junction at 32°F. Standard thermocouple tables have been prepared on this basis, and a summary of the output characteristics of the most common thermocouple combinations is given in Table . These data are shown graphically in, alongwith the behaviour of some of  the more exotic thermocouple materials. The output voltage E of a simple thermocouple circuit is usually written in the form

                        E = AT + ½ BT² + ½ CT³

Where T is the temperature in degrees Celsius and E is based on a reference junction temperature of 0°C. the constants, A, B and C are dependent on the thermocouple material. Powell gives an extensive discussion of the manufacture of materials for thermocouple use, inhomogeneity ranges and power series relationships for thermoelectric voltages of various standard thermocouples.

The sensitivity, or thermoelectric power, of a thermocouple is given by

                                                 dE

                                    S =       ---- = A + BT + CT²

                                                dT

Reference Junction Considerations

For the most precise work, reference junctions should be kept in a triple-point of water apparatus whose temperature is 0.01±0.0005°C. Such accuracy is rarely needed, and an ice bath is used much more commonly. A carefully made ice bath is reproducible to about 0.001C°, but a poorly made one may have an error of 1C°. Figure  shows one method of constructing an ice-bath reference junction. The main sources of error are insufficient immersion length and an excessive amount of water in the bottom of the flask. Automatic ice baths that use the Peltier cooling effect as the refrigerator, rather than relying on externally supplied ice (which must be continually replenished), are available with an accuracy of 0.05C°. These systems use the expansion of freezing water in a sealed bellows as the temperature sensing element that signals the Peltier refrigerator when to turn on or off by displacing a microswitch.

Since low-power heating is obtained more easily than low-power cooling, some reference junctions are designed to operate at a fixed temperature higher than any expected ambient. A feedback system operates an electric heating element to maintain a constant and known temperature in an enclosure containing the reference junctions. Since the reference junction is not at 32°F, the thermocouple-circuit net voltage must be corrected by adding the reference junction voltage before the measuring junction temperature can be found. This correction is, however, a constant.

Electrical resistance sensors

The electrical resistance of various materials in a reproducible manner with temp, form the basis of the temp. sensing method. Resistance temperature detector (RTD) has come into use. Semiconductor types appeared later and have been given the generic name thermistor. Any of the various established techniques of resistance measurement may be employed to measure the resistance of these devices, with both bridge and ‘ohmmeter’ methods being common.