techniques for approximating the international temperature ... - BIPM

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ln R n = ∑ i= 0 54 ⎛ ln T - P ⎞ Bi⎜ ⎟ i (4.2) ⎝ S ⎠ where R is the thermometer resistance, T is the temperature, M and P are origin-shifting constants, N and S are scaling constants, and Ai and Bj are coefficients resulting from the curve fitting. (ii) approximation of the characteristic in two subranges which overlap several kelvins (range of overlap about 5 K to 10 K) (iii) value of n is about 12 for a range 1 to 30 K, but may be about 5 for the range 1 to 5 K for the same accuracy (iv) number of calibration points greater than about 3 n, or 2 n if the distribution of points is carefully controlled (v) calibration points at nearly equal intervals in In T except near the ends of any calibration range (and perhaps in the range of overlap), where there should be a distinctly higher density of points. An ideal spacing is such that the m points are distributed according to the formula + x1 xm - x ⎛ i -1 ⎞ + cos⎜ p⎟ 2 2 ⎝ m -1 ⎠ xm 1 , (i = 1 to m) where x1 and xm are the lower and upper limits respectively of the independent variable (In R or In T in equations 4.1 and 4.2 respectively). Using this method, the errors introduced by spurious oscillations are comparable with the uncertainty of the input data. For the selection of the optimum degree several criteria must be applied (Fellmuth (1986), (1987)], which is easy if orthogonal functions are used. It is possible that the number of calibrations points can be greatly reduced if the general behaviour of the characteristic of the individual thermometer is known or if a larger uncertainty is tolerable. Unfortunately, in the literature, only isolated data on this matter are available. It must be emphasized that a direct application of literature techniques is only possible if the same type of thermometer is used; and that special interpolation equations can approximate the characteristics of particular types of thermometers sufficiently closely with a lower degree than would result from application of Eq. (4.1) or (4.2), but their use can cause considerable difficulty if these equations are not matched to the characteristic of the individual thermometer to be calibrated.
55 5. Rhodium-Iron Resistance Thermometers Rhodium-iron resistance thermometers were developed by Rusby (1972) for use below the normal range of the platinum resistance thermometer. It was found that, of various small concentrations of iron in rhodium, the one that would give the most sensitive and yet moderately linear thermometer was 0.5 atomic percent iron [Rusby (1975)]. Rusby (1982), who uses a group of them at the National Physical Laboratory to carry the primary temperature scale below 30 K, has given a review of ten years of performance. Present suppliers of rhodium-iron thermometers are listed in Appendix C. 5.1 Range of Use and Sensitivity The range of use is normally from about 0.5 K to 30 K, although the sensitivity is good up to room temperature and at lower temperatures. For a capsule-type thermometer containing helium gas, the lower limit of about 0.5 K is set by the rapidly-increasing selfheating. The normal upper limit (~ 30 K) is in the region where the superior platinum resistance thermometer has adequate sensitivity. In contrast to pure metals, for which the sensitivity dR/dT decreases steadily with decreasing T at small values of T, the sensitivity of rhodium with about 0.5% iron impurity is relatively constant at about 0.4 Ω/K down to 100 K, decreases to ≤ 0.2 Ω/K near 25 K, then increases rapidly by about a factor of 10 as T decreases to 0.5 K as illustrated in Fig. 5.1 for a thermometer with an ice-point resistance of 100 ohm. The industrial type has a sensitivity about 6% lower than the standard type. It is in this low temperature region of increasing sensitivity that rhodium-iron has its chief application. The rapid change in sensitivity in the low temperature region means that, to obtain a precision of 1 mK at 30 K, the rhodium-iron resistance must be measured to 1 part in 10 5 , compared to 10 in 10 5 for platinum. Because the rhodium-iron resistance is much higher, however, the voltage sensitivity at 30 K is higher than for platinum. The sensitivity of rhodium-iron is much lower than that of germanium. 5.2 Fabrication The standard-type thermometer of H. Tinsley and Co., Ltd. (U.K.) is constructed as follows: the 0.05 mm diameter wire is wound in the form of coils inside four glass tubes which in turn are encapsulated in a 5 mm diameter platinum sheath as shown in Fig. 5.2. The sheath contains helium at about 1/3 atmosphere pressure. The leads are 0.3 mm
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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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Page 25 and 26: 5 The accuracies with which tempera
Page 27 and 28: Table 1.1: Summary of Some Properti
Page 29 and 30: PART 1: TECHNIQUES AND THERMOMETERS
Page 31 and 32: 11 Fig. 2.1: One form of apparatus
Page 33 and 34: 13 Fig. 2.3: Flow cryostat, shown w
Page 35 and 36: 15 Fig. 2.4: Stirred liquid bath fo
Page 37 and 38: 17 contained within a cylindrical c
Page 39 and 40: 19 Fig. 2.5: Schematic drawing of a
Page 41 and 42: 21 device SRM 767 [Schooley et al.
Page 43 and 44: 23 Table 3.1 : Current Best Estimat
Page 45: 25 The widely-used, but not very re
Page 48 and 49: 28 fraction of sample melted) can g
Page 50 and 51: 30 Fig. 3.2a: Apparatus for the cal
Page 52 and 53: 32 Fig. 3.3: Sealed cell for realiz
Page 54 and 55: 34 Final readings of the thermomete
Page 56 and 57: 36 temperatures differ (usually) sy
Page 58 and 59: 38 Fig. 3.4: Cross sectional drawin
Page 60 and 61: 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 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 112 and 113: 92 More recently, Seifert [(1980),
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
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104 10. Infrared Radiation Thermome
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106 almost negligible. The final ac
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108 11. Carbon Resistance Thermomet
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110 Fig. 11.1: Resistance-temperatu
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112 Table 11.1: Typical Time Consta
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114 calibration after each cool-dow
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116 12. Carbon-Glass Resistance The
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118 Fig. 12.1: Resistance-temperatu
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120 14. Diode Thermometers Diodes c
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122 2 BT V = E0 − − CT ln ( DT)
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124 Fig. 15.1: Principal features o
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126 For a thermometer graduated abo
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128 rise decreases with time but in
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130 Fig. 16.1: (a) Fabrication of I
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132 capillaries of a twin- (or four
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134 advised to choose the thermomet
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136 Fig. 16.6: Distribution of the
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138 and between different thermomet
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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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