Abstract
At NBS an acoustical thermometer has been used to obtain values of temperature at every degree from 5 to 20 °K as a basis for a temperature scale. This scale has been compared with four other temperature scales in the region from 10 to 20 °K. Since the acoustical thermometer is an entirely new approach to precision thermometry in this range the comparison of its resulting scale with scales based upon gas thermometry from 12 to 20 °K is significant. Indications of inaccuracies in the equilibrium hydrogen vapor pressure scales, and also in the He4 vapor pressure scale, are presented.
For a number of years the National Bureau of Standards has been engaged in a low temperature thermometry program, one objective of which is the establishment of a primary temperature scale which would include the region 4 to 14 °K. After consideration of the relative merits and disadvantages of conventional gas thermometry, it was decided that an investigation of temperature measurements derived from the speed of sound in helium gas should be initiated. In addition to the application in the range 4 to 14, the acoustical thermometer should also provide an independent check above 14 °K and below 4 °K. The “acoustical interferometer” appeared to be the best instrument for the experimentation.
A general discussion of the acoustical interferometer has been presented by J. L. and E. S. Stewart [1];1 more specific application to low temperatures has been reported by Van Itterbeek and his coworkers [2–4]. While it is not the intention of the present paper2 to discuss the acoustical interferometer as an operating instrument, it is necessary to mention that it involves a constant frequency and a variable path as opposed to a resonating column in which the path length is fixed and the frequency variable.3
When an experimental determination of the speed of sound in helium gas as a function of pressure at a constant temperature has been made, the data can be treated to yield values of absolute temperature by means of eq (1).
| (1) |
where W is the speed of sound in helium gas; (Cp/Cv)p=0 = 5/3; RM = 8.314×107 (erg/°K mole); MHe=4.0026; p is the pressure; α = 1/(RT)[2B+ 4/3(T)(dB/dT)+4/15(T2)(d2B/dT2)]; B is the second virial coefficient; and T, the absolute temperature.
In practice, values of the speed, W, are experimentally determined at pressures sufficiently low that the plot of W versus p is linear and can be extrapolated to zero pressure; the intercept is then the value of the speed of sound for an ideal gas, and eq (1) reduces to
where W0 is the speed intercept at p = 0. It is to be noted that the acoustical temperature determination eliminates troublesome corrections that are involved in gas thermometry, i.e., dead space corrections, gas adsorption and precise volume changes and pressure determinations.
One of the most critical parts of the thermometer is the portion of the apparatus which contains the sonically excited helium gas. This is at the temperature to be maintained constant and determined. To aid in accomplishing this, several secondary thermometers of high sensitivity (germanium resistors) were in intimate thermal contact with the region. One resistor served as a sensor for an automatic heater controlling unit while two other resistors indicated how well a constant temperature was being maintained and also served as secondary thermometers which were calibrated by the acoustical thermometer. All of this portion of the apparatus was suitably thermally insulated from the surrounding liquid helium or liquid hydrogen bath so that it could be isothermally floated in the temperature region of interest. While this portion of the acoustical thermometer was maintained constant in temperature the speed of sound in the helium 4 gas was measured as a function of pressure. (This is referred to as an isotherm in our work.)
During the hours that are spent on any given isotherm, germanium resistance values are systematically measured. In general five to sevenpressure-speed points were measured to establish each isotherm. Figures 1 and 2, typical of the determined isotherms, indicate how the isotherm is extrapolated to zero pressure; the intercept affords a simple calculation of the isotherm temperature.
Figure 1. 20.050 °K Isotherm.
The dashed line is the extrapolation of the isotherm to zero pressure.
Figure 2. 6.061 °K Isotherm.
At the lowest pressures the dashed line depicts the extrapolation to zero pressure. At the highest pressure, the dashed line indicates departure of the isotherm from a linear representation (the solid line).
For the pressures employed in the temperature range of interest, all of the isotherms are linear within the limits of experimental reproducibility. At sufficiently large pressures, however, departures from linearity are to be expected. For example, in figure 2 the measurements indicate that the isotherm has noticeably departed from linearity at 0.6 atm and above, whereas in figure 1 a linear representation of the isotherm up to 1.2 atm appears satisfactory. We have generally observed that experimental reproducibility of points on an isotherm is ±0.002 °K. If one conducts measurements at pressures sufficiently low that the isotherm can be represented by a straight line, an important check on the consistency of the isotherms is afforded by the smoothness of the plot of isotherm slopes as a function of the determined temperatures. The slopes naturally are related to the virial coefficients and will permit their determination.
Isotherms have been determined every degree from 5 to 20 °K and accordingly at each temperature several germanium resistors were calibrated. Because it was desirable to compare the acoustical thermometer scale with other existing scales in regions of overlap, several germanium resistors were calibrated by Riddle’s group against the NBS (1955) provisional scale which is based on earlier gas thermometry4 and preserved by a group of platinum resistors.
Every germanium resistor which was used has a history of at least one year in our laboratory and some have demonstrated a reproducible 4.2 °K calibration (against the He4 vapor pressure scale, T58) within 0.001 °K even when subjected to 100 thermal cyclings between room temperature and 4.2 °K. Of the two resistors which were calibrated against the NBS (1955) provisional scale, one was calibrated in May 1963 and the other in June 1964. Both resistors were compared to the acoustical thermometer scale in June 1964 by being mounted in the acoustical thermometer and brought to the acoustically determined temperatures at which the instrument germanium resistors had been calibrated. This has afforded a comparison of acoustically determined temperatures with those associated with the NBS (1955) provisional scale between 10 and 20 °K. And, since the NBS (1955) provisional scale has recently been compared with other scales, the acoustically determined temperatures can be related to these also. This has been done in figure 3.
Figure 3. Values of temperature determined with the acoustical thermometer are compared with temperature scales from Pennsylvania State University, Physical-technical Radio-technical Measurements Institute, The National Physical Laboratory, and the NBS (1955) provisional scale.
△, PSU;□, PRMI; ●, NBS; ○, NPL; ×, +, acoustical thermometer.
Most of figure 3 has originated from the National Physical Laboratory and has been confirmed by PRMI.5 It is to be noted that there is an excellent agreement between the acoustically determined temperature and both the NPL and NBS scale from 12 to 20 °K. Indeed, even the departure of the NPL scale from the NBS scale in the vicinity of 14 °K appears to be strongly supported. Unfortunately it has not been convenient to compare our temperatures with the NBS scale at 10 °K. We are not in a position at present to state the accuracy of our temperature determinations but we have stated the experimental reproducibility of our isotherm measurements previously in this paper.
Our experience thus far, although it is limited, cautions us to doubt the accuracy of published hydrogen vapor-pressure scales. Our preliminary measurements indicate that the “accepted” equilibrium hydrogen boiling point may be 20 mdeg lower than its thermodynamic temperature; this possible inaccuracy may also exist throughout the hydrogen vapor pressure scale to some extent. Quite consonant with this conclusion is the possibility of error in the T58 He4 vapor scale also. Preliminary measurements again indicate that the He4 boiling point may be 0.006 °K too low; and that He4 vapor pressure scale temperatures near 2 °K may be 0.003 °K low also.
It is expected that the values of acoustically determined temperatures described in this paper will result in a provisional scale which will be used by the National Bureau of Standards principally for calibrations of germanium resistance thermometers from 5 to 20 °K.
Footnotes
This paper was presented at the 1964 meeting of the Thermometry Advisory Committee of the International Committee of Weights and Measures.
Figures in brackets indicate the literature references at the end of this paper.
The NBS acoustical interferometer has been cursorily described in the literature [5, 6] the details will appear later.
Measurement of the sound speed in helium gas yielding absolute temperature determinations have also been conducted with the resonating tube. Some results have been reported by De Laet [7] and by Brodsky, Kremlevsky, and Savateev [8].
The NBS (1955) provisional scale was obtained by subtracting 0.010 °K from the NBS (1939) scale [9].
The general plot was included in a paper submitted by C. R. Barber to the Thermometry Advisory Committee of the International Committee of Weights and Measures (Sept. 1964). At the same meeting a paper submitted by M. P. Orlova, D. I. Sharevskaja, and D. N. Astrov confirmed in detail the results of C. R. Barber.
References
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