Appendix I: Cryogenic Reference Tables

Transcription

1 Appendix I: Cryogenic Reerence Tables Appendices 217 Appendix I: Cryogenic Reerence Tables Cryogenic heat low calculations The heat low Q conducted across small temperature dierences can be calculated using the ormula: Q = -KA dt ~ = -KA T Eqn. 1 dx L where K is the thermal conductivity, A is the cross-sectional area, T is the temperature dierence, and L is the length o the heat conduction path. Thermal conduction across signiicant temperature dierences should be calculated using thermal conductivity integrals. Note that the thermal conductivity and the thermal conductivity integral o a material can depend strongly on composition and abrication history. Without veriication, the data in the accompanying igures should be used only or qualitative heat low calculations. Calculating the heat conduction through a body with its ends at greatly dierent temperatures is made diicult by the strong temperature dependence o the thermal conductivity between absolute zero and room temperature. The use o thermal conductivity integrals (called thermal boundary potentials by Garwin) allows the heat low to be calculated as Q = -G(Θ 2 Θ 1 ) Eqn. 2 where Θ is the integral o the temperature-dependent thermal conductivity, K, calculated as Θ 1 = T 1 0 KdT Eqn. 3 and G is a geometry actor calculated as 1 Θ 1 = x 2 G x 1 dx A where A(x) is the cross sectional area at position x along the path o heat low. Note that G=A/L in the case o a body o length L and uniorm cross-sectional area A. Equation 1 is only applicable to bodies within which a common thermal conductivity integral unction applies. Reerence: R. L. Garwin, Rev. Sci. Instrum. 27 (1956) 826. Eqn. 4

2 218 Appendices Appendix I: Cryogenic Reerence Tables Figure 1 Thermal conductivity o selected materials

3 Appendix I: Cryogenic Reerence Tables Appendices 219 Figure 2 Thermal conductivity integral o selected materials

4 220 Appendices Appendix I: Cryogenic Reerence Tables Table 1 Thermodynamic properties or various cryogenic liquids Temperature (K) pressure Normal boiling point Critical point (kpa) Critical point (kpa) Latent heat o vaporization Critical density (kg/m 3 ) Helium a Hydrogen Neon Nitrogen Oxygen Argon Krypton Xenon CO Methane Ethane Propane Ammonia a values or helium are those o the lambda point L (J/g) Density (g/ml) Table 2 Gamma radiation-induced calibration osets as a unction o temperature or several types o cryogenic temperature sensors Radiation-induced oset (mk) at temperature Model 4.2 K 20 K 77 K 200 K 300 K Platinum b PT-103 NA d 10 d 10 d Rhodium-iron b RF-100-AA 2 d 15 d 15 d 5 d 5 d Cernox b CX-1050-SD d 5 d 25 d 25 d Carbon-glass b CGR Germanium b GR-1400-AA NA NA Ruthenium oxide b RO d d NA GaAlAs diode b TG-120P Silicon diode b DT-470-SD Silicon diode b DT-500P-GR-M Silicon diode b SI-410-NN Platinum c PT-103 NA 50 5 d Rhodium-iron c RF d 15 d d 15 d Rhodium-iron c RF-100-AA 5 d 5 d 5 d 10 d 5 d Carbon-glass c CGR Germanium c GR-1400-AA 2 d 2 d 5 d NA NA GaAlAs diode c TG-120P Silicon diode c DT-470-SD Silicon diode c DT-500P-GR-M 10 d 10 d 5 d 5 d 100 b c d Sensors were irradiated in situ at 4.2 K with a cobalt-60 gamma source at a dose rate o 3,000 Gy/hr to a total dose o 10,000 Gy ( rad) Sensors were irradiated at room temperature with a cesium-137 gamma source at a dose o 30 Gy/hr to a total dose o 10,000 Gy ( rad) Deviations smaller than calibration uncertainty

5 Appendix I: Cryogenic Reerence Tables Appendices 221 Table 3 Vapor pressure o some gases at selected temperatures in Pascal (Torr) 4 K 20 K 77 K 150 K Triple e point temperature Water (10 7 ) 273 K Carbon dioxide (10 8 ) 1333 (10) 217 K Argon (10 13 ) (160) h 84 K Oxygen (10 13 ) (150) h 54 K Nitrogen (10 11 ) (730) g 63 K Neon 4000 (30) g g 25 K Hydrogen (10 7 ) 101,325 (760) g g 14 K Note: estimates useul or comparison purposes only (1 Torr = Pa) e Solid and vapor only at equilibrium below this temperature; no liquid Less than Torr g Greater than 1 atm h Above the critical temperature, liquid does not exist Table 4 Thermal contraction o selected materials between 293 K and 4 K Contraction (per 10 4 ) Telon 214 Nylon 139 Stycast SP22 Vespel 63.3 Stycast 2850FT 50.8 Stycast 2850GT 45 Al 41.4 Brass (65% Cu/35% Zn) 38.4 Cu 32.6 Stainless steel 30 Quartz a-axis 25 Quartz c-axis 10 Quartz mean, 15 or typical transducer Titanium 15.1 Ge 9.3 Pyrex 5.6 Si 2.2 Table 5 Electrical resistivity o alloys (in µω cm) Resistivity (295 K) (4.2 K) Brass Constantan CuNi (80% Cu/20% Ni) Evanohm Manganin Stainless steel 71 to to 51

6 222 Appendices Appendix I: Cryogenic Reerence Tables Table 6 Deining ixed points o the ITS-90 Temperature (T 90 /K) Substance i State j Deining instrument 0.65 to 3 3He Vapor pressure point He vapor pressure 3 to 5 He Vapor pressure point thermometer e-he 2 ~17 e-he 2 (or He) Vapor pressure point or gas thermometer point ~20.3 e-he 2 (or He) Vapor pressure point or gas thermometer point Ne O Ar Hg H 2 O Ga Melting point In Freezing point Sn Freezing point Zn Freezing point Al Freezing point Ag Freezing point Au Freezing point Cu Freezing point Constant volume gas thermometer Platinum resistance thermometer i All substances except 3He are o natural isotopic composition; e-h 2 is hydrogen at the equilibrium concentration o the ortho- and para-molecular orms j For complete deinitions and advice on the realization o these various states, see Supplementary Inormation or the ITS-90 Radiation Table 7 Saturated vapor pressure o helium T (K) P (Pa) T (K) P (Pa) T (K) P (Pa)