Application of rational functions in primary and secondary thermometry
摘要
A method has been developed for determining the acoustic and electromagnetic resonance frequencies in acoustic gas thermometry by approximating the frequency dependencies of the acoustic signal and complex electromagnetic radiation transmission coefficient of the resonator. The method does not require specifying the initial iteration of the approximation parameters. The method is based on utilizing a rational function to represent the function used to approximate the frequency dependences in the acoustic gas thermometry. The process of approximating the experimental frequency dependences by a rational function includes a quickly converging series of linear approximations that can be easily implemented using a PC. Since there is no need to specify the initial iteration of the approximation parameters, the process of approximating the frequency dependences and determining resonant frequencies can be simplified and accelerated quite significantly. A rational function was used to approximate resistance vs. temperature dependencies of the standard rhodium-iron thermometers in the temperature range from 0.5 to 273 K as an alternative for traditional approximation by two different polynomial functions in the temperature subranges from 0.5 to 26 K and from 26 to 273 K. It was shown that in case of approximating the temperature dependence of the resistance of a rhodium-iron thermometer by a single rational function, the resulting deviation from the experimental points does not exceed 0.5 mK in the range from 0.5 to 273 K. The number of approximation parameters of the rational function is smaller compared to the approximation with two different polynomials, while the deviation from the experimental points is comparable. The obtained result significantly simplify the resistance-to-temperature conversion when using rhodium-iron thermometers.