Practical Temperature Scales Between 11 K and 273 K

Abstract

The International Practical Temperature Scale has a lower temperature limit of 90.18 K; measurements below this temperature are commonly made in terms of the various "national" scales. All of these scales differ significantly from the thermodynamic scale and exhibit undesirable variations in the size of the degree as a consequence; the national scales, moreover, are comparison scales, which are widely considered to be less satisfactory than scales defined in terms of fixed points and interpolating instruments. Various proposals for replacing this mixture by a single scale have been or are being developed; these are all based, in the 12 K to 90 K range, on the results of a comparison of four national scales recently carried out at Moscow and Teddington.This paper attempts to analyze the reproducibility of some of these proposed scales and their relation to the current best estimate of the thermodynamic scale. The significant lack of reproducibility found for these proposed scales below 50 K may either be tolerated, or alternatively must be reduced by further restrictions on thermometer characteristics. These proposed scales exhibit systematic variations in the size of the degree with temperature. These variations can be substantially reduced by modification of the mathematical treatment of the experimental data on which the scales are based; one such modification is presented here.Further analysis of the behavour of current and proposed scales will be enormously facilitated if the results of additional, highly accurate comparisons over wide temperature ranges and involving many types of thermometers become available.* The CCT64 table ([4] and section I11 below) is an analytical function of resistance ratio against temperature (for a hypothetical platinum resistance thermometer) based on five determinations, from four laboratories, of the thermodynamic scale. The resistance ratio W of a thermometer is its resistance at temperature T divided by its resistance a t the ice point (273.15 I().

Notes on the Application of the International Practical Temperature Scale of 1968

“…9,11, and14 of Ref. [4] are not exactly AW(T,,) for these thermometers, but are closely the same. 90 K, for example, 19 of the 21 terms are required to obtain T,, to within 1 mK.…”

“…It is not immediately obvious how many iterations will be required to obtain T,, to within a given tolerancethis depends upon the magnitudes of A W( T,,), dA W ( T,,)/dT,,, and d W( T,,)/dT,,. However, simple considerations show that the second approximation to T,, will almost always be accurate to within 1 mK and usually to better than 0.1 mK, except perhaps below 20 K. PRESTON-THOMAS and BEDFORD [4] show h W( T,,) for many thermometers** from which it may be seen that AW(Tg8) typically ranges from 0 a t 273.15 K to about +200 x 10-6 at 20K, with occasional extreme values of 400 x 10-6, while dA W ( T,,)/dT,, is seldom greater than 3 x 10-6/K. As an example we can take the maximum commonly encountered values of AW(T,,) = 200 x 10-6 and dAW(T,,)/dT,, = 3 x 10-,/K a t 20 K [where d W( T,,)/dT,, = 727 x 10-6/K].…”

Non-uniqueness of the ITS-90 (uncertainties in temperature measurements)

“…Curve d (equation ( 14) of [6]) is equivalent to Figure 1.7f of [5]. Several features are evident from Tables 4, 5 and 6 and Figure 4: (a) The magnitude of the extrinsic non-uniqueness due to uncertainties of calibration is independent of the quality of the PRT (vertical scans of columns (7, 8), (9, 10), (11,12) and (13, 14) of Table 4, as well as equivalent columns in Tables 5 and 6 An uncertainty in the Zn point, however, in effect changes the length of the temperature interval of the adjacent fixed-point ranges and thus has a more pronounced effect than an uncertainty in the Al point. It seems, then, that even if a deviation function of higher degree than used in the ITS-90 is required to describe the resistance anomaly of certain PRTs, the resulting increased extrinsic non-uniqueness due to uncertainties of calibration may more than offset the reduced intrinsic non-uniqueness resulting from the use of a more appropriate deviation function.…”

“…There are also a number of articles in which the work of various experimenters were later analysed by others; e.g. [11,12]. None of these subsequent analyses revealed the existence of shortrange resistance anomalies.…”

Investigation of the Resistance-Temperature Properties of Platinum for Resistance Thermometry over the Range from 14 K to 90 K

“…The problem of extension and revision of the IPTS-48 below 0 "C is now solved. A great amount of work has been done : the new improved reference table is calculated; the method of calculation of a correction curve based on seven fixed points and four interpolation equations is chosen [ 5 ] . This table and the method of calculating a correction curve are included in the text of the IPTS-68 [6] approved by the International Committee of the BIPM.…”