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196 Appendix D Calculations Relative to the Filling of a Vapour Pressure Thermometer Notations Ta - minimum temperature to be attained. At this temperature the bulb is completely filled with liquid. Tb - maximum temperature to be attained. The bulb is empty of liquid except for a small quantity v which remains for security and which can be neglected. ∏a, ∏b - the corresponding saturated vapour pressures. Tf ∏f T0 - temperature used for condensation when filling. - corresponding saturated vapour pressure. - room temperature. P0 - filling pressure at T0. Tm - average temperature along the capillary, equal to as the case may be. T0 + Tf 2 T0 , + Ta 2 Vb - the bulb volume partially filled with a volume vc of liquid. Vc - volume of the capillary. VT - volume of the reservoir. V0 - totality of volumes of connectors and manometer that remain at room temperature. M - molar mass of the pure filling substance. N - number of moles to be introduced. v L n1 - number of moles of liquid = ⋅ ρ n2 - number of moles of vapour in the bulb = M P( Vb v L ) RT − (p, pressure in the bulb, = pa, pb, pM, or p0). ρa, ρb - density of liquid at temperature Ta, Tb respectively. n3 - number of moles in the capillary = n4 - number of moles in the various volumes at room temperature = n5 PV RT - number of moles in the volume of the reservoir = N - total number of moles. We assume that the vapour phase obeys the perfect gas law. VT being generally much larger than the other volumes, we can make some approximations: c m PV RT T 0 PV RT , or 0 0 T 0 + T 2 b
197 1. At the lowest temperature, Ta, we have vL ~ Vb V n = ρ b 1 M n2 = 0; a VT not connected; n5 = 0 n 2Π V a c 3 = ; R( T0 + Ta ) The total number of moles, N, must be ≤ n1 + n3 + n4 a c 0 b N ⎢ + V0 ⎥ + ⋅ ρa RT0 T0 + Ta M n 4 Π aV = RT ≤ Π ⎡ 2V T ⎤ V (D1) ⎣ ⎦ 2. At the highest temperature, Tb, there is only a small volume v of liquid in the bulb (v - 0). v n ρ n Vb − v = ; 1 = b n2 Π b M RTb ΠbV 0 4 = ; n5 = 0. RT0 The total number of moles, N, must be n 0 2Π b c 3 = ; R( T0 + Tb ) vρb Π b ⎡T0 2VcT0 ⎤ N ≥ + ⎢ ( Vb − v) + V0 + ⎥ (D2) M RT0 ⎣Tb T0 + Tb ⎦ 3. From relations (D1) and (D2), we obtain or v Π b ⎡T0 2Vc T0 ⎤ Π a ⎡ 2VcT0 ⎤ v bρ a ρ b + ⎢ ( Vb − v) + V0 + ⎥ ≤ ⎢ + V0 ⎥ + , M RT0 ⎣Tb T0 + Tb ⎦ RT0 ⎣T0 + Ta ⎦ M ⎡ρ a Π b ⎤ V0 ⎡ρ b Π b ⎤ 2Vc ⎡ Π b Π a ⎤ v b ⎢ − ⎥ ≥ [ Π b − Π a ] + v⎢ − ⎥ + ⎢ − ⎥ . (D3) ⎣ M RTb ⎦ RT0 ⎣ M RTb ⎦ R ⎣T0 + Tb T0 + Ta ⎦ This expression determines the volume Vb of the bulb (to a first approximation, we can neglect the last two terms and overestimate the value). 198 0 V
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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
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42 4. Germanium Resistance Thermome
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44 Fig. 4.3: Example of the Π-type
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46 Fig. 4.4: Differences between dc
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48 - conversely, p-doped thermomete
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50 Fig. 4.6: Effect of a radio-freq
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52 that it will not be subject to m
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ln R n = ∑ i= 0 54 ⎛ ln T - P
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56 Fig. 5.1: Resistance (Ω) and s
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58 thermometer wires) caused a more
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60 6. Vapour Pressure Thermometry*
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62 transitions, but it could be app
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n ∑ i= 2 64 L x [ Π − k ] P =
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66 Fig. 6.3: Diagram at constant pr
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68 Fig. 6.4: Schematic construction
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70 Fig. 6.6: Use of an evacuated ja
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72 Following this, the connecting t
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74 Fig. 6.9: (c) N2, CO, Ar, O2, CH
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76 the Weber-Schmidt equation [Webe
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78 Table 6.1: Temperature values (K
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80 into the bulb (hydrous ferric ox
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82 Fig. 6.12: Effect on the vapour
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84 the remaining liquid increases.
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86 Curie constant (C⊥ is about 0.
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8.1 General Remarks 88 8. Platinum
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90 For a group of 45 thermometers h
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92 More recently, Seifert [(1980),
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94 For thermometers with W(4.2 K) <
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96 after 500 h at 1700 °C in air,
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98 normally extends about 50 cm bac
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100 inhomogeneities result from the
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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
Page 166 and 167: 146 Stability on thermal cycling is
Page 168 and 169: 18.2.1 Type T Thermocouple 148 With
Page 170 and 171: 150 within ± 0.5 to 0.7 percent. T
Page 172 and 173: 152 insulation even though it be af
Page 174 and 175: 154 Table 18.4: Recommended Sheath
Page 176 and 177: 156 In the case of the Types K and
Page 178 and 179: 158 temperature is measured with th
Page 180 and 181: 160 19. Thermometry in Magnetic Fie
Page 182 and 183: 162 Type of Sensor T(K) Magnetic Fl
Page 184 and 185: 164 be noted that these lower tempe
Page 186 and 187: 166 Fig. 19.2: The change in calibr
Page 188 and 189: 168 Carbon-glass thermometers (Chap
Page 190 and 191: Ancsin, J. and Phillips, M.J. (1984
Page 192 and 193: 172 Berry, R.J. (1972): The Influen
Page 194 and 195: 174 Brodskii, A.D. (1968): Simplifi
Page 196 and 197: 176 Crovini, L., Perissi, R., Andre
Page 198 and 199: Hudson, R.P. (1972): Principles and
Page 200 and 201: 180 Lengerer, B. (1974): Semiconduc
Page 202 and 203: 182 OIML (1985): International Reco
Page 204 and 205: 184 Rusby, R.L. (1975): Resistance
Page 206 and 207: 186 Seifert, P. and Fellmuth, B. (1
Page 208 and 209: 188 Ween, S. (1968): Care and Use o
Page 210 and 211: 190 Fig. A.1: Differences between t
Page 212 and 213: National Institute of Metrology P.O
Page 214 and 215: 194 Appendix C Some Suppliers of Va
Page 218 and 219: 198 4. The calculation of the numbe
Page 220 and 221: 200 Appendix F Interpolation Polyno
Page 222 and 223: - temperature range from 0 °C to 1
Page 224 and 225: 204 where: d0 = 0; d5 = -3.17578007
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