ヘリウム蒸気圧温度目盛実現における圧力測定の系統誤差の評価

抄録

The systematic error in the pressure measurement is estimated quantitatively for establishing the precise helium vapor pressure temperature scale in the temperature range from 0.5K to 5K. From this estimate, a design of the cryostat, in which the temperature scale can be realized with the uncertainty of 0.1mK, is described.
The thermomolecular effect and the hydrostatic pressure head are considered as the sources of the systematic error. The uncertainties in the correction are also estimated for both sources of error.
The Weber-Schmidt equation is used to estimate the thermomolecular effect for both ⁴He and ³He, which gives negative correction to the pressure value measured by the pressure gauge at room temperature. The thermomolecular effect for ⁴He is shown to be negligible, if the temperature range is restricted above lambda point. In the case of ³He, in turn, the uncertainty in the correction for the thermomolecular effect at about 0.5K is shown to be critical unless properly designed cryostat is used. From the analysis of the temperature dependence of thermomolecular effect, an example of a set of tubings for the measurement of ³He vapor pressure is shown to give uncertainty of only 0.05mK in the correction for the thermomolecular effect. In this example, the diameter of the tubing is changed by three steps according to the temperature range to minimize the heat input into the ³He pot.
The hydrostatic pressure head gives, on the contrary, positive correction of about 0.3mK at most on the temperature scale. The correction is made by measuring the gas pressure in the capillary thermally attached to the sensing line used in the vapor pressure measurement. This technique is simpler than the conventional method which is based on the measurement of the temperature at several points along the sensing line and on the deduction of temperature between those points by interpolation. The uncertainty of the correction following the present technique is estimated to be less than 0.04mK for both ⁴He and ³He, assuming the probable errors in the several parameters. As the systematic error resulting from the non-ideality of gaseous helium can't be measured by this technique, this error should be added to the uncertainty of the correction. The total uncertainty is shown to be less than 0.09mK.
In conclusion, we give a design of a pressure sensing line which is expected to limit the uncertainty in realizing the helium vapor pressure scale to 0.05mK between 0.6K and 4.2K and to 0.1mK between 0.5K and 5.2K.