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8 Pyrometers Classification and Radiation Laws 8 .1  Classification of Pyrometers The simplest and oldest non-contact way of estimating the temperature of a radiating body is by observing its colour . Table 8 .1 summarises the relationship between temperature and colour . Using this method, experienced practitioners can estimate temperatures over about 700 °C, with a precision sufficient for simpler heat-treatment processes . This is shown in a witty way in Figure 8 .1, which is taken from Forsythe's paper (Forsythe, 1941) . It was presented at the historical Symposium on Temperature in November 1939, a symposium that was a milestone in further development of thermometry . Table 8 .1 Temperature correlation with colours of radiating bodies Temperature (°C)  Colour  Temperature (°C)  Colour 550-580  Black/purple  830-880  Dark orange 580-650 Brown/purple 880-1050 Orange 650-750 Purple 1050-1150 Yellow/orange 750-780  Dark carmine  1150-1250  Yellow 780-800 Carmine 1250-1320 White/yellow 800-830 Orange/c a r mine s i Figure 8 .1 First pyrometric temperature measurement Temperature Measurement Second Edition L. Michalski, K. Eckersdorf, J. Kucharski, J. McGhee Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic) 152  PYROMETERS CLASSIFICATION AND RADIATION LAWS Pyrometers, also known as infrared thermometers, or radiation thermometers, are non- contact thermometers, which measure the temperature of a body based upon its emitted thermal radiation, thus extending the ability of the human eye to sense hotness . No disturbance of the existing temperature field occurs in this non-contact method . In pyrometry the most important radiation wavelengths which are situated between from 0 .4 to 20 ltm belong to the visible and infrared (IR) radiation bands . In addition to the methods outlined in Chapter 1 it is also possible to classify pyrometers according to their spectral response and operating method, as shown in Figure 8 .2 and described in more detail later . Manually operated, or hand operated, pyrometers : In manually operated pyrometers the human operator is an indispensable part of the measuring channel . Figure 8 .3 illustrates that the operator's eye acts as a comparator . An eye comparison is made between the one wavelength (0 .65 Eun)  disappearing  M O filament A pyrometers  N E U R 0 .55 pin  A A L T two wavelengths  two-colour  L E pyrometers 0 .65 ,um H E R M A ___ ____ ___-________-__ total radiation total  pyrometers A I  one wavelength A  photoelectric A T I  wavelength band  pyrometers  +  U O  ~E  T M A two wavelength bands  two wavelength  i  T pyrometers 1 c :multi-wavelength . several wavelength bands  pyrometers Figure 8 .2 Classification of pyrometers by wavelength and operating method CLASSIFICATION OF PYROMETERS  153 OPTICAL OPERATOR'S TARGET SYSTEM  EYE MEASURING OPERATOR INSTRUMENT v REFERENCE UNIT Figure 8 .3 Structure of a manually operated pyrometer radiation from the source with a signal from a reference unit whereupon the operator activates the read-out instrument . The following two types belong to the group of manually operated pyrometers : " Disappearing filament pyrometers based upon matching the luminance of the object and of the filament, by adjusting the lamp current . The observer's eye is the detector . Their operating wavelength band is so narrow as to allow them to be regarded as monochromatic pyrometers of A e = 0.65 Vim . "  Two-colourpyrometers or ratio pyrometers deduce the temperature from the ratio of the radiation intensity emitted by the object in two different spectral wavebands, which are most commonly 0 .55 and 0 .65 pm . Automatic pyrometers :  A simplified block diagram of an automatic pyrometer, which is shown in Figure 8 .4, is composed of the following main parts : "  optical system concentrating the radiation on radiation detector, "  radiation detector which may be either a thermal or a photoelectric sensor, "  signal converter, conditioning the detector output signal before being displayed, " measuring instrument, which may have an additional analogue or digital output . The following four types belong to the group of automatic pyrometers : " Total radiation pyrometers using thermal radiation detectors, which are heated by the incident radiation . In reality the wavelength band used is about 0 .2 to 14 Pin resulting from transmissivity of the optical system . " Photoelectric pyrometers operate in chosen wavelength bands in which the signal is generated by photons bombarding a photoelectric detector . "  Two-wavelength pyrometers, also called ratio pyrometers, in which the emitted radiation intensity in two wavelengthbands is compared by photoelectric detectors . OPTICAL TARGET SYSTEM DETECTOR SIGNAL MEASURING CONVERTER INSTRUMENT Figure 8 .4 Block diagram of an automatic pyrometer 154  PYROMETERS CLASSIFICATION AND RADIATION LAWS " Multi-wavelength pyrometers, where the source radiation, which is concentrated in some wavelength bands, is incident upon photoelectric detectors . They are used for measuring the temperature of bodies with low emissivity . Automatic pyrometers are produced for use in stationary or portable applications . However, the technical parameters ofboth types are nearly identical in practice . Stationary pyrometers, which are usually more robust, can withstand higher ambient temperatures . 8 .2  Radiation, Definitions and Laws 8 .2 .1  Absorption, reflection and transmission of radiation Thermal radiation is a part of electromagnetic radiation . Let us assume that a radiant heat flux, (P, defined as a quantity of heat in a unit time, is incident on the surface of a solid . Of this heat flux, the portion, (Da , is absorbed, whilst (D P is reflected and (D T is transmitted . The following definitions are introduced : " absorptivity, a= (Da /(D " reflectivity, p= q) P /(D (8 .l) " transmissivity, r = (D, /(D Applying the principle of energy conservation shows that for every solid : a + p + r = 1  (8 .2) In the case of transparent bodies, as represented in Figure 8 .5, many internal reflections cause additional absorption . For example, Harrison (1960) notes that the total reflected heat flux, (D P , is composed of the primary heat flux (DpI , and a secondary one `f p . L . _ REFLECTED FLUX  TRANSMITTED FLUX OF~~Df1 P2 Owl ~T u m  m s ABSORBED INCIDENT  ` /  FLUX HEAT FLUX  =" Figure 8 .5 Decomposition of the heat flux, (1), in a transparent body RADIATION,DEFINITIONS AND LAWS  155 There are three specific cases : I .  a =1, p= 0, , r = 0 the body is a black body, which totally absorbs all incident radiation . 2 . a = 0, p =1, r = 0 the body is a white body, which totally reflects all incident radiation . 3 . a = 0, p = 0, z =1  the body is a transparent body as all of the incident radiation is completely transmitted . The concept of a black body is very important in pyrometry . Figure 8 .6 presents some configuration properties approaching those of a black body . Heinisch (1972) shows that in the cavities presented in Figure 8 .6, total absorption of the incident radiation is reached by its multiple internal reflection . Similarly to the factors, a, p and z, which are valid for total radiation, the spectral properties, ax , pX and z ? , at the wavelength A, may also be introduced : as = (DA, /) pa =(DAP /('  (8 .3) zX = (DXt /(D Equation (8 .2) then becomes : a k + pa + TX =1  (8 .4) The values of a, p and z depend upon the material, its surface state and temperature while a x , p) and z ) , additionally depend upon the wavelength, A . 8 .2.2 Radiation laws The radiant intensity W or the radiant exitance is the heat flux per unit area expressed as the ratio of the heat flux dD, emitted from the infinitesimal element of the surface dA, to the surface area dA itself : W = ~ W/m 2 (8 .5) (a)  (b)  (c)  (d) r I 1 II, ~ d Figure 8 .6 Models of a black body 156  PYROMETERS CLASSIFICATION AND RADIATION LAWS In the same units as the radiant intensity, the heat flux density, q, of the incident radiation is given by : q = ~ W/m 2  (8 .5a) This also takes account of the conduction and convection heat flux in addition to the radiation heat flux . The spectral radiant intensity, Wk, is defined as : W~ = dW W/m 2 pin  (8 .6) Planck's law gives the radiant flux distribution of a black body as a function of the wavelength and of the body's temperature by the relation : W OA °~ - CC 2 IRT -1  (8 .7) where W °A is the spectral radiant intensity of a black body, W/m 2 pm (the suffix `o' will be used in future to indicate a black body), A is the wavelength, pin, T is the absolute temperature of the thermal radiator, K, c, is the first radiation constant whose value is c i = 3 .7415 x 10 -16 W m 2 and c 2 is the second radiation constant with a value of c 2 = 14 388 pin K . For a given wavelength range, from X i to )L 2 , equation (8 .7) can be evaluated as : Az elf-s where W °, ~ _,~ 2 is the band radiant intensity of a black body . Hackforth (1960) has shown that if AT << c2, Planck's law of equation (8 .7) can be replaced, using the same notation, by a simpler Wien's law : el V eC2 11T The spectral radiant intensity W °A of a black body as a function of wavelength A, at different temperatures, calculated from Planck's law, is shown in Figure 8 .7 At all temperatures of importance in radiation pyrometry, the errors, which result from replacing Planck's law by Wien's law, are negligibly small . The relative errors may be calculated from the relation : RADIATION,DEFINITIONS AND LAWS  157 AW o ; _ W .X,w - W .R,P1 = e __  /XT  8.10 W ay W .,~,w where Wo3,W is the spectral radiant intensity calculated from Wien's law and W O X , p l is calculated as above from Planck's law . The relative errors calculated from equation (8 .10) are presented in Table 8 .2 as a function of the values of the product AT . Table 8 .2 Relative errors resulting from replacing Planck's law in equation (8 .7) by Wien'slaw in equation (8 .9) as a function of the value of the product AT AT (m .K)  1 .25 x 10 -3  1 . 5x10 -3 2x10 -3 3x10 W .),/ W .?, (%)  0 .001  0 .007  0 .08  0 .8 Figure 8 .7 shows that the maxima of the spectral radiant intensity are displaced towards the shorter wavelengths with increasing temperature . At the given temperature, T, where the maximum is reached, the wavelength Amax , may be easily calculated from Wien's displacement law to obtain : Amax T = 2 896 ltm K  (8 .11) Forany given temperature, the area under the corresponding curve is a measure of the total power radiated at all wavelengths by a black body so that : W o = fW a Ad1  (8 .12) ,'- 0 The ratio of the spectral radiant intensity, Wj, at the wavelength, A, of a non-black body to the spectral radiant intensity of a blackbody, W oj, at the same temperature is called the spectral emissivity cA . E~ = W ;L  (8 .13) Wo ; If the spectral emissivity el of a given body is constant for each wavelength (i .e . al =constant) such a body is called a grey body . Similarly to equation (8 .13), if all wavelengths from 0 to oc, are taken into consideration, the term total emissivity, s, is used : W e= W  (8 .14) 0 i 158  PYROMETERS CLASSIFICATION AND RADIATION LAWS where W is the radiant intensity of any given body and W o is the radiant intensity of a black body at the same temperature . Following Kirchhoff's law, the spectral absorptivity, ak, of all opaque bodies equals their emissivity, cX, so that : For a given wavelength band, from A, to ~ 2 , Kirchhoff's law is expressed by : - band ii  i  band V '  - -_ 1 ' 11 10- , ., , -' .  . . ; . , 140 K 0  1  2  3  4 WAVELENGTH 1 . jim .  . .  .  . lack body, W~, versus wavelength at different temperatures equation in accordance with Planck's law in RADIATION, DEFINITIONS AND LAWS  159 When all wavelengths from .11 > 0 to '12 > oo are taken into consideration, the corresponding form for equation (8 .15a), which is also valid, then becomes : (8.15b) where a is the total absorptivity, and s is the total emissivity . The Stefan-Boltzmann law, which represents the dependence of the total radiant intensity, W ., of a black bodyupon the temperature, T, is expressed as : W,, = JA o Wo,d ;, = a O T a (8 .16) where W,, ; is the spectral radiant intensity of a black body as given by Forsythe (1941), The radiation constant of a black body, a,, has a value a, = 5 .6697x10_ 8 W/m 2 K 4 . Equation (8 .16) can be expressed in a more readily usable form as : 4 Wo C°(100)  (8 .16a) where C o is the technical radiation constant of a black body, with the value : C o = 6 o x 10 8 = 5 .6697 W/m 2 K 4 For grey bodies equation (8 .16a) becomes : 4 W = C°£ 100 ( T )  (8 .17) where C o is as before, and 8 is the total emissivity . In technical practice the majority of real bodies may be regarded as grey ones . 8 .2 .3  Total emissivity and spectral emissivity Spectral emissivity e Aand total emissivity, e were defined by equations (8 .13) and (8 .14) . Knowledge of the values of c and e,, , especially at A = 0 .65 Vm, for different materials, is necessary, to be able to calculate the corrections to be introduced when making pyrometric temperature measurements . The emissivity of different materials, which depends heavily upon the surface state, its homogeneity and temperature, may only be determined approximately . Worthing (1941) describes methods for the measurement of emissivity . Comparison of the properties of different materials, independent of their surface state may be made using the specific total emissivity, e', and the specific spectral emissivity, E' . . The values of e' and e ;L are determined for the direction normal to surface for flat 160  PYROMETERS CLASSIFICATION AND RADIATION LAWS samples, which should be polished and sufficiently thick . This last condition allows semi- transparent bodies to be regarded as totally opaque . The values of E and E,~ are also determined for the direction normal to the surface . Approximate values for the emissivity of different materials are given in Tables XIX and XX . It must be stressed that uneven, rough and grooved surfaces may have much higher values of emissivity than are their specific emissivities . Using the Maxwell theory of electromagnetism, Considine (1957), following Drude, have proposed an approximate formula to calculate the specific spectral emissivity, E ;1, of metals as : E ;1 = K  (8 .18) where K = 0 .365 S2-'"z, p is the resistivity in S2cm, and A is the wavelength in cm . Equation (8 .18) which is valid for A > 2 pm, uses the original units of Drude . The emissivity of non-conductors, which is a function of the material refractive index, n,l, is given in BS 1041, p . 5 by the formula : 4nj E,~ =  (8 .19) (nX +1)2 where nA which is the refractive index of the material, has a value in the range of 1 .5 to 4 for most inorganic compounds and in the range 2 .0 to 3 .0 for metallic oxides . For most clean metals the emissivity is low, with a value of about 0 .3 to 0 .4, falling sometimes to 0 .1 for aluminium . Spectral emissivities of metals become lower at lower temperatures where the wavelengths are longer . Non-metallic substances have emissivities of about 0 .6 to 0 .96, which do not vary greatly with temperature . It should be borne in mind, that the appearance of non-metals in visible light cannot be a basis for predicting their emissivities . Most non- metals, such as wood, brick, plastic and textiles at 20 °C have a value of total emissivity nearly equal to unity . 8 .2 .4  Radiant heat exchange Consider two parallel surfaces, having identical areas A and the respective temperatures and emissivities T I , T 2 , E l , 02, emitting thermal radiation towards each other with the intensities given by the Stefan-Boltzmann law in equation (8 .16a) . The heat flux (power) (D12 exchanged between these surfaces, for T 1 > T 2 , is given by : CO  2 012  (1/E l )+(/ E2)-1 (100) 4 -(100)4  (8 .20) where C o is the technical radiation constant, and A is the radiating area .