techniques for approximating the international temperature ... - BIPM
techniques for approximating the international temperature ... - BIPM techniques for approximating the international temperature ... - BIPM
52 that it will not be subject to mechanical constraints, and to fill the remaining gap with a suitable material that allows good heat transfer, such as one of a variety of greases, motor oil, Wood's metal, etc. Anything containing a solvent that can damage the sheath or its seals (which may be an epoxy) should be avoided and, as well, the material should be oxide-free. It is also essential to thermally anchor the leads to the body, or to a shield maintained at the temperature of the body. The leads should be of small diameter ≤ 0.1 mm), electrically insulated, and a considerable length should be attached to the body with, for example, varnish or nail polish [Hust (1970)]. Generally, the largest thermal leak is via the leads. 4.4.2 Time Constant The value of the time constant depends upon the temperature, the environment, the thermal contact with the environment, and the thermal conductivity of the sheath, lead wires, and other components of the thermometer. It can only be measured in situ. Some typical time constants for germanium thermometers of various types under different conditions are given in Table 4.1 [Blakemore (1972), Halverson and Johns (1972)]. Note that the dimensions and masses of the thermometers do not account for all of the time constant variations. On abruptly cooling a thermometer from 300 K to 4.2 K, about 20 s is required for the thermometer to reach equilibrium. The time constant increases with temperature because of the rapid increase of the thermal capacity of the thermometer with respect to the thermal conductivity. To minimize the time constant of a germanium thermometer one must ensure that the lead wires are properly thermally anchored as near as possible to the thermometer itself. 4.5 Calibration and Interpolation Formulae A description of the resistance/temperature characteristics of germanium resistance thermometers is not possible by simple formulae based on theoretical considerations. As the characteristics can be very different from thermometer to thermometer, individual calibrations at a large number of points are necessary. To approximate the characteristic with the minimum possible uncertainty from the experimental data, a suitable fitting method has to be used. Furthermore, the calibration itself should already take into account any peculiarities of the fitting method [Powell et al. (1972)]. The results and conclusions in the literature concerning the efficiency of various fitting methods are obscure and, in some cases, contradictory because
53 Table 4.1: Typical Time Constants in Helium Liquid and Vapour for Various Germanium Thermometers. Time Constant (s) Manufacturer Thermometer Time Constant in helium vapour Characteristics (s) in liquid at 1.27 cm above helium the liquid level ________________________________________________________________________ Scientific Mass 0.081 g Instruments Length 4.75 mm 0.010 0.180 type p- 1000 Ω at 4.2 K Diameter 2.36 mm _________________________________________________________________________ CryoCal type CR1000 Mass 0.290 g type n- 857 Ω at 4.2 K Length 11 mm 0.03 0.200 Diameter 3.1 mm _________________________________________________________________________ Honeywell type II Mass 0.5 g (at 3 cm) (circa 1963) Length 11 mm 0.05 0.38 Diameter 3.5 mm - only in a few cases are different methods compared directly; - the results obtained are valid only for the individual thermometer types investigated; - the uncertainties of the input data are very different in the various papers; - some questions (for example weighting and smoothing with spline functions) are not sufficiently investigated; - the mathematical bases are often incompletely described. Hence it is not possible to give here a recipe which can be applied in all cases. A classification of the various least squares fitting methods with general remarks on their efficiency was made by Fellmuth (1986), (1987). Only one method is recommended here; it allows the characteristics of all germanium resistance thermometers mentioned in Appendix C to be approximated in the temperature range from about 1 K to 30 K with high precision (uncertainty less than 1 mK). The features of this method are: (i) interpolation equations: ln T n = ∑ i= 0 ⎛ ln R - M⎞ Ai⎜ ⎟ i (4.1) ⎝ N ⎠
- Page 21 and 22: 1 1. Introduction The Comité Consu
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- Page 29 and 30: PART 1: TECHNIQUES AND THERMOMETERS
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- Page 35 and 36: 15 Fig. 2.4: Stirred liquid bath fo
- Page 37 and 38: 17 contained within a cylindrical c
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- Page 58 and 59: 38 Fig. 3.4: Cross sectional drawin
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- Page 64 and 65: 44 Fig. 4.3: Example of the Π-type
- Page 66 and 67: 46 Fig. 4.4: Differences between dc
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- Page 70 and 71: 50 Fig. 4.6: Effect of a radio-freq
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- Page 86 and 87: 66 Fig. 6.3: Diagram at constant pr
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- Page 112 and 113: 92 More recently, Seifert [(1980),
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- Page 116 and 117: 96 after 500 h at 1700 °C in air,
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53<br />
Table 4.1: Typical Time Constants in Helium Liquid and Vapour <strong>for</strong> Various Germanium<br />
Thermometers.<br />
Time Constant (s)<br />
Manufacturer Thermometer Time Constant in helium vapour<br />
Characteristics (s) in liquid at 1.27 cm above<br />
helium <strong>the</strong> liquid level<br />
________________________________________________________________________<br />
Scientific Mass 0.081 g<br />
Instruments Length 4.75 mm 0.010 0.180<br />
type p- 1000 Ω at 4.2 K Diameter 2.36 mm<br />
_________________________________________________________________________<br />
CryoCal type CR1000 Mass 0.290 g<br />
type n- 857 Ω at 4.2 K Length 11 mm 0.03 0.200<br />
Diameter 3.1 mm<br />
_________________________________________________________________________<br />
Honeywell type II Mass 0.5 g (at 3 cm)<br />
(circa 1963) Length 11 mm 0.05 0.38<br />
Diameter 3.5 mm<br />
- only in a few cases are different methods compared directly;<br />
- <strong>the</strong> results obtained are valid only <strong>for</strong> <strong>the</strong> individual <strong>the</strong>rmometer types<br />
investigated;<br />
- <strong>the</strong> uncertainties of <strong>the</strong> input data are very different in <strong>the</strong> various papers;<br />
- some questions (<strong>for</strong> example weighting and smoothing with spline functions)<br />
are not sufficiently investigated;<br />
- <strong>the</strong> ma<strong>the</strong>matical bases are often incompletely described.<br />
Hence it is not possible to give here a recipe which can be applied in all cases. A<br />
classification of <strong>the</strong> various least squares fitting methods with general remarks on <strong>the</strong>ir<br />
efficiency was made by Fellmuth (1986), (1987). Only one method is recommended here; it<br />
allows <strong>the</strong> characteristics of all germanium resistance <strong>the</strong>rmometers mentioned in Appendix<br />
C to be approximated in <strong>the</strong> <strong>temperature</strong> range from about 1 K to 30 K with high precision<br />
(uncertainty less than 1 mK). The features of this method are:<br />
(i) interpolation equations:<br />
ln T<br />
n<br />
= ∑<br />
i=<br />
0<br />
⎛ ln R - M⎞<br />
Ai⎜<br />
⎟ i (4.1)<br />
⎝ N ⎠
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