An Estimation of Systematic errors in the Pressure Measurement to Realize the Helium Vapor Pressure Scale

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