techniques for approximating the international temperature ... - BIPM

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92 More recently, Seifert [(1980), (1984)] considered a relation similar to Eq. (8.3) relating W68(Ar t.p.) to W68(H20 b.p.): W68(H20 b.p.) = -0.525 29 W68(Ar t.p.) + 1.506 108 (8.4) Using the WCCT-68(T68) ratio of 1.128 402 for W68(O2 b.p.)/W68(Ar t.p.), Seifert's equation can be converted to the form of Eq. (8.3); the result is shown as curve S in Fig. 8.2. Curve S has a more negative slope than the others and rises above V at lower values of W(H20 b.p.). The coefficients a1 and b1 of Eq. (8.3) are given in Table 8.1 for all of the curves in Fig. (8.2). Table 8.1: Coefficients a1, b1 of Eq. (8.3) for the Curves in Fig. (8.1). _________________________________________________________________________ Curve a1 b1 reference _________________________________________________________________________ B 0.977 86 -1.870 0 Brodskii (1963) V 0.982 826 -1.882 572 Berry (1972) L 0.903 485 -1.680 508 Berry (1963) M 0.779 641 -1.365 254 Berry (1963) S 1.087 070 -2.148 156 Seifert (1980), (1984) _________________________________________________________________________ Equation (8.3) allows a secondary realization from 90 K to 273 K with calibration at only the triple point of water and the boiling point of either oxygen or water, the other being estimated from Eq. (8.3). The coefficients a1, b1 for curve L are probably the most representative. Used with the IPTS-68 defining equation for the range 90.188 K to 273.15 K, this secondary realization is probably accurate to within ± 30 mK when W(H20 b.p.) ~ 1.3920 and ± 10 mK when W(H20 b.p.) > 1.3925. In Eq. (8.3), W(O2 b.p.) could be replaced with W(Ar t.p.) and W(H20 b.p.) by W(ln f.p.) (with suitable adjustment of the coefficients a1 and b1), and an equivalent accuracy would result. According to the finding of Bedford (1972b), extrapolation to about 70 K will produce little further degradation in accuracy. Although temperatures between 125 K and 273 K are less sensitive to an error in W(O2 b.p.) than in W(H20 b.p.), it is probably better and usually more convenient to calibrate at
93 the oxygen or argon point and deduce the resistance ratio at the steam point. Moreover, few laboratories now maintain a steam point, and most capsule thermometers cannot safely be heated as high as the tin freezing point, another reason to prefer calibration at the oxygen point and deduction of W(H20 b.p.). As indicated by Seifert, a relation similar to Eq. (8.3) based upon the argon triple point is even better. It obviates the need for any boiling-point measurement, requiring only two simple triple-point determinations. Seifert (1984) has extended this method by using one- or two-point comparisons with a standard PRT (at, e.g., 160 K and 78 K) to replace the argon-triple-point measurement. The accuracy is little degraded thereby. (c) Several possibilities for secondary realization based upon Cragoe Z-functions rather than simple resistance ratios have been proposed. Among early investigations were those of Cragoe (1948), Corruccini (1960), (1962), and Barber (1962). The Z-function is defined by Z( T) R( T) − R( T1) = , (8.5) R( T ) − R( T ) where T1 and T2 are fixed-point calibration temperatures at or near the extremities of the range. The Z-function for a particular choice of calibration temperatures is tabulated and temperatures are calculated by interpolating deviations from the table in some specified way. The Z-function tabulation acts as a reference function equivalent to Wr(T90). Besley and Kemp (1978) incorporate the Z-function into a reference function using T1 = 4.2 K (boiling helium) and T2 = 273.15 K (melting ice) in Eq. (8.5). They define a reference function of the form 16 n ⎡ ln( Z) + 3. 54⎤ T* = ∑ A n ⎢ n 0 3. 54 ⎥ = ⎣ ⎦ 2 1 (8.6) using the mean value of Z of a group of 19 thermometers each with W(4.2 K) < 4 x 10 -4 . Temperature (T = T* - ∆T*) is determined for any particular thermometer in terms of a deviation from Eq. (8.6) of the form 1/ 2 ⎡ ⎛ T * ⎞ ⎤ ∆ T* = a ⎢1− ⎜ ⎟ ⎥ ∆T , (8.7) ⎢⎣ ⎝ 40 K ⎠ ⎥⎦ where ∆T = b + c W(4.2 K) + d W(4.2 K) 2 , T* ≤ 40 K (8.8) and ∆T = 0 . T* > 40 K (8.9)
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BUREAU INTERNATIONAL DES POIDS ET M
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TECHNIQUES FOR APPROXIMATING THE IN
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iv W(100 °C) = 1.385 (exact value
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Centre for Quantum Metrology Nation
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2. Type J viii a) temperature range
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c) temperature range from 1664.5 °
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xii
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xiv Acknowledgments This monograph
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xvi 3.3.2 Melting Points of Gold (1
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xviii 11.3 Thermal Contact 111 11.4
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1 1. Introduction The Comité Consu
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3 thermometers except in special ex
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5 The accuracies with which tempera
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Table 1.1: Summary of Some Properti
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PART 1: TECHNIQUES AND THERMOMETERS
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11 Fig. 2.1: One form of apparatus
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13 Fig. 2.3: Flow cryostat, shown w
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15 Fig. 2.4: Stirred liquid bath fo
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17 contained within a cylindrical c
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19 Fig. 2.5: Schematic drawing of a
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21 device SRM 767 [Schooley et al.
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23 Table 3.1 : Current Best Estimat
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25 The widely-used, but not very re
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28 fraction of sample melted) can g
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30 Fig. 3.2a: Apparatus for the cal
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32 Fig. 3.3: Sealed cell for realiz
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34 Final readings of the thermomete
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36 temperatures differ (usually) sy
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38 Fig. 3.4: Cross sectional drawin
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40 Fig. 3.5: Miniature graphite bla
Page 62 and 63: 42 4. Germanium Resistance Thermome
Page 64 and 65: 44 Fig. 4.3: Example of the Π-type
Page 66 and 67: 46 Fig. 4.4: Differences between dc
Page 68 and 69: 48 - conversely, p-doped thermomete
Page 70 and 71: 50 Fig. 4.6: Effect of a radio-freq
Page 72 and 73: 52 that it will not be subject to m
Page 74 and 75: ln R n = ∑ i= 0 54 ⎛ ln T - P
Page 76 and 77: 56 Fig. 5.1: Resistance (Ω) and s
Page 78 and 79: 58 thermometer wires) caused a more
Page 80 and 81: 60 6. Vapour Pressure Thermometry*
Page 82 and 83: 62 transitions, but it could be app
Page 84 and 85: n ∑ i= 2 64 L x [ Π − k ] P =
Page 86 and 87: 66 Fig. 6.3: Diagram at constant pr
Page 88 and 89: 68 Fig. 6.4: Schematic construction
Page 90 and 91: 70 Fig. 6.6: Use of an evacuated ja
Page 92 and 93: 72 Following this, the connecting t
Page 94 and 95: 74 Fig. 6.9: (c) N2, CO, Ar, O2, CH
Page 96 and 97: 76 the Weber-Schmidt equation [Webe
Page 98 and 99: 78 Table 6.1: Temperature values (K
Page 100 and 101: 80 into the bulb (hydrous ferric ox
Page 102 and 103: 82 Fig. 6.12: Effect on the vapour
Page 104 and 105: 84 the remaining liquid increases.
Page 106 and 107: 86 Curie constant (C⊥ is about 0.
Page 108 and 109: 8.1 General Remarks 88 8. Platinum
Page 110 and 111: 90 For a group of 45 thermometers h
Page 114 and 115: 94 For thermometers with W(4.2 K) <
Page 116 and 117: 96 after 500 h at 1700 °C in air,
Page 118 and 119: 98 normally extends about 50 cm bac
Page 120 and 121: 100 inhomogeneities result from the
Page 122 and 123: 9.5 Approximations to the ITS-90 10
Page 124 and 125: 104 10. Infrared Radiation Thermome
Page 126 and 127: 106 almost negligible. The final ac
Page 128 and 129: 108 11. Carbon Resistance Thermomet
Page 130 and 131: 110 Fig. 11.1: Resistance-temperatu
Page 132 and 133: 112 Table 11.1: Typical Time Consta
Page 134 and 135: 114 calibration after each cool-dow
Page 136 and 137: 116 12. Carbon-Glass Resistance The
Page 138 and 139: 118 Fig. 12.1: Resistance-temperatu
Page 140 and 141: 120 14. Diode Thermometers Diodes c
Page 142 and 143: 122 2 BT V = E0 − − CT ln ( DT)
Page 144 and 145: 124 Fig. 15.1: Principal features o
Page 146 and 147: 126 For a thermometer graduated abo
Page 148 and 149: 128 rise decreases with time but in
Page 150 and 151: 130 Fig. 16.1: (a) Fabrication of I
Page 152 and 153: 132 capillaries of a twin- (or four
Page 154 and 155: 134 advised to choose the thermomet
Page 156 and 157: 136 Fig. 16.6: Distribution of the
Page 158 and 159: 138 and between different thermomet
Page 160 and 161: 140 therefrom) can then be used wit
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142
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144 Fig. 16.8: Tolerances for indus
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146 Stability on thermal cycling is
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18.2.1 Type T Thermocouple 148 With
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150 within ± 0.5 to 0.7 percent. T
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152 insulation even though it be af
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154 Table 18.4: Recommended Sheath
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156 In the case of the Types K and
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158 temperature is measured with th
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160 19. Thermometry in Magnetic Fie
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162 Type of Sensor T(K) Magnetic Fl
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164 be noted that these lower tempe
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166 Fig. 19.2: The change in calibr
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168 Carbon-glass thermometers (Chap
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Ancsin, J. and Phillips, M.J. (1984
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172 Berry, R.J. (1972): The Influen
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174 Brodskii, A.D. (1968): Simplifi
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176 Crovini, L., Perissi, R., Andre
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Hudson, R.P. (1972): Principles and
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180 Lengerer, B. (1974): Semiconduc
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182 OIML (1985): International Reco
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184 Rusby, R.L. (1975): Resistance
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186 Seifert, P. and Fellmuth, B. (1
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188 Ween, S. (1968): Care and Use o
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190 Fig. A.1: Differences between t
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National Institute of Metrology P.O
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194 Appendix C Some Suppliers of Va
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196 Appendix D Calculations Relativ
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198 4. The calculation of the numbe
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200 Appendix F Interpolation Polyno
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- temperature range from 0 °C to 1
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204 where: d0 = 0; d5 = -3.17578007
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