Thermomolecular Pressure Difference Measurements for Precision Helium−3 and Helium−4 Vapor-Pressure Thermometry

Abstract

Thermolecular pressure differences due to thermal transpiration were measured to find the corrections for low‐temperature vapor‐pressure thermometry using helium−3. The experimental apparatus consisted basically of several stainless‐steel, pressure‐sensing tubes, each connected to the same pressure container inside a cryostat. The upper, or warm, ends of the tubes were connected to differential pressure gauges outside the cryostat. The gauges measured the differences in warm end pressures between a 0.29‐cm radius reference tube and tubes of 0.14‐, 0.055‐, and 0.0271‐cm radii for a variety of cold end temperatures and pressures. The results for saturated and unsaturated helium−3 and unsaturated helium−4 are identical but greater at the maxima than the values computed from the semiempirical Weber—Schmidt equation, which was based on measurements with unsaturated helium−4. However, experimental data for saturated helium−4 in the low‐pressure region were much higher than the Weber—Schmidt equation and the other data. This disagreement was attributed to superfluid film flow. An outline of the derivation of the differential equation describing thermal transpiration is given in this report. Theoretical predictions for the high‐pressure region of saturated helium−4 are in agreement with the experimental data. It is concluded that a revision of the Weber—Schmidt equation is needed for precision thermometry.