Refractive index gas thermometry between 13.8 K and 161.4 K

We have measured the refractive index of helium using a quasi-spherical copper microwave resonator at five different temperatures in the interval between the triple point of hydrogen at 13.8 K and the triple point of xenon at 161.4 K for pressures up to 380 kPa. From these results and additional measurements of the refractive index of neon near 54.4 K, 83.8 K and 161.4 K we determine the differences (T - T90) between the thermodynamic temperature T and its approximation T90 by the International Temperature Scale of 1990 (ITS-90). We have estimated the isothermal compressibility of copper and the effective compressibility of our microwave resonator by different methods including resonant ultrasound spectroscopy (RUS) and microwave measurements with helium at 273.16 K. We compare the results of these compressibility estimates and discuss the associated uncertainty. From the refractive index measurements, we estimate the second density virial coefficient of helium and neon which are found in good agreement with the ab initio calculations of the same properties.