Determination of thermodynamic temperature and⁴He virial coefficients between 4,2 K and 27,0 K by dielectric constant gas thermometry

Abstract

Primary dielectric constant gas thermometry (DCGT) has been used to establish a quasi-continuous temperature scale in the range 4,2 K to 27,0 K with a measurement uncertainty which increases with rising temperature from 0,6 mK to 1,2 mK (confidence level 95 %). (It should be noted that previous papers refer to the 68 % level which yields about one half of the uncertainty values.) The large number of experimental data for 4 He (about thirty isotherms, more than 200 triplets of pressure, temperature, and dielectric constant) allowed, furthermore, the determination of the temperature dependencies of the second and third virial coefficients, without any constraints. The virial coefficients thus obtained exhibit good agreement with data based primarily on conventional gas thermometry and potential calculations. The established temperature scale is compared with the isotherm and constant volume gas thermometry scale NPL-75. A flat sinusoidal form for the differences between the two scales may be seen, which is in accordance with other published data. However, the differences are well within the thermodynamic uncertainties estimated for the NPL-75 and the DCGT scale. This result supports the theoretical polarizability value with a relative combined uncertainty of 6 10 -5 , i.e. the bounds for the polarizability value of 4 He have been decreased by one order of magnitude compared with the available rigorous theoretical bounds.

Dielectric-Constant Gas-Thermometry Scale from 2.5 K to 36 K Applying 3He, 4He, and Neon in Different Temperature Ranges

“…For neon, a polynomial of second order was sufficient. The smooth polynomials have been used to deduce weighted means with the weights related to the uncertainties (for DCGT1, see [1]; for DCGT2, see [2], Sects. 3.1 and 3.2).…”

“…The basic idea of DCGT [11], more extensively discussed in [1,2,12], is to replace the density in the equation of state of a gas with the dielectric constant, ε, and to measure it by incorporating a capacitor in the gas bulb. The dielectric constant of an ideal gas is given by the relation ε = ε 0 + α 0 N/V , where ε 0 is the exactly known electric constant, α 0 is the static electric dipole polarizability of the particles, and N/V is the number density, i.e., the equation of state of an ideal gas can be written in the form p = kT (ε − ε 0 )/α 0 .…”

“…The procedure used for the multi-isotherm fitting was extensively discussed in [1,12]. Only a short summary will be given here.…”

“…The two generations of DCGT led to results for the thermodynamic temperature between 2.5 K and 27 K [1][2][3] with a standard uncertainty of a few tenths of a millikelvin in the whole range. Whereas the main goal of the first generation was to check the existing thermodynamic C. Gaiser (B) · B. Fellmuth · N. Haft Physikalisch-Technische Bundesanstalt, Abbestr.…”

Cryogenic properties of optomechanical silica microcavities

“…Below 7 K, the effective refractive index temperature dependence becomes negative. This is a consequence of the presence of the surrounding exchange gas, since additional measurements performed at 50 mbar presented an increased negative shift, of −520 MHz/K at 2 K. From the recorded pressure evolution in the experimental chamber, the change in the Helium refractive index have been estimated [14] at a level of ca.−10 ppm/K at 5 K, which is in agreement with the measured value of (−.15 ppm/K). A quantitative study of the surrounding Helium contribution will allow to measure for the first time silica's optical refractive index at low temperatures (note that the temperature dependence of silica's microwave dielectric constant is known to reverse [15]).…”